Tracking a surface in a 3-dimensional scene using natural visual features of the surface

0001The present invention is directed to the fields of computer vision and video processing.

0002One task faced in the field of computer vision is tracking the movement of an object within a video scene. In many cases, tracking the object consists of tracking the location and orientation of the object with respect to a camera-that is, the point in space that is the perspective from which the video scene is captured.

0003One significant subset of the movement tracking task is tracking the movement of a roughly planar, i.e., 2-dimensional, surface within a video scene. Such a surface may be one side of a sheet of paper, either a free-standing sheet of paper or a sheet of paper in a book. It may also a surface presented by virtually any other object. One application of surface tracking is introducing a view of a virtual, 3-dimension object into each frame of the video scene that appears to floal about the surface, termed reality augmentation.

0004Surface tracking has conventionally been addressed through the use of fiducial marker tracking. Fiducial marker tracking involves affixing a special, visually distinct symbol (such as a bold black square having a white interior) to the surface to be tracked; locating the symbol-called a fiducial marker-in each video frame; determining the location of the surface with respect to the camera based on the size of the marker in the video frame and its location in the video frame; and determining the orientation of the surface with respect to the camera based on the orientation of the marker in the video frame.

0005Fiducial marker tracking has significant disadvantages, however. First, fiducial marker tracking fails any time the fiducial marker is not present in the scene. This can happen in a variety of circumstances, even while the surface remains in the scene. For example, the fiducial marker may be occluded by an object that intervenes in space between the camera and the fiducial marker, such as a person's hand or another inanimate object. The fiducial marker may also move outside of the boundaries of the video scene, such as when the camera moves so close to (or zooms in so close to) the surface that the scene can only contain a portion of the surface that excludes the fiducial marker. This disadvantage can only be overcome by adding larger and larger numbers of fiducial markers to the surface, overwhelming the appearance of the surface and obscuring its innate visual features.

0006Second, fiducial marker tracking can fail when the surface is distant from the camera, and the camera's view of the surface is too limited to distinguish the fiducial marker. The only way to address this disadvantage is to use larger and larger fiducial markers, again overwhelming the appearance of the surface and obscuring its innate visual features.

0007In view of these shortcomings, an approach to surface tracking that does not rely on the continuous visibility and distinguishability of fiducial markers affixed to the surface would have significant utility. In "<nplcit id="ncit0001" npl-type="s"><text>Natural Feature Tracking for Augmented Reality", IEEE TRANSACTIONS ON MULTIMEDIA, Vol. 1, No. 1, March 1999, Neumann, U. and You, S. </text></nplcit>discuss natural feature tracking for augmented reality. It is described that natural scene features stabilize and extend the tracking range of augmented reality pose-tracking systems. Robust computer vision methods to detect and track natural features in video images are disclosed. It is suggested to automatically and adaptively select point and region features for properties that lead to robust tracking. A multistage tracking algorithm is disclosed that produces accurate motion estimates, wherein the entire system operates in a closed loop that stabilizes its performance and accuracy. The disclosed multistage strategy includes three basic steps: image warping, motion residual estimation, and motion model refinement. In "<nplcit id="ncit0002" npl-type="s"><text>Markerless Tracking using Planar Structures in the Scene", PROCEEDINGS OF IEEE AND ACM INTERNATIONAL SYMPOSIUM ON AUGMENTED REALITY, October 2000, pages 120-128, Simon G. </text></nplcit>et al. describe a markerless camera tracking system for augmented reality that operates in environments which contain one or more planes. N interest points are detected in a frame i+1. Then, interest points from frame I are matched to interest points from frame i+1 to generate a set of correspondences, from which a 3x3 planar homography is computed. Then, camera position and rotation is computed from the planar homography, which provides motion estimates. It is the object of the present invention to enable an improved determination of the 3-dimensional location and orientation of a subject surface in a distinguished perspective image of the subject surface. The object is solved by the subject matter of the independent claims. Preferred embodiments of the present invention are defined by the dependent claims.

BRIEF DESCRIPTION OF THE DRAWINGS

0008<figref idref="f0001">Figure 1</figref> is an image diagram showing a typical image that, when attached to a surface, can be tracked by the facility.

0009<figref idref="f0002">Figure 2</figref> is a flow diagram showing steps typically performed by the facility in order to track a surface.

0010<figref idref="f0003">Figure 3</figref> is a block diagram showing a typical environment in which the facility operates.

0011<figref idref="f0004">Figure 4</figref> is a pixel diagram showing the relationship between a window used in template matching and a search area within a video frame that contains it.

0012<figref idref="f0004">Figure 5</figref> is a pixel diagram that illustrates the feature point constraints for a candidate pixel.

0013<figref idref="f0005">Figure 6A</figref> shows the output of this first step of the offline feature extraction algorithm for the original image resolution of 200 dpi.

0014<figref idref="f0005">Figure 6B</figref> shows the output at a lower resolution of 100 dpi. Both of these figures reflect a template size of 25 x 25 pixels.

0015<figref idref="f0006">Figure 7</figref> is an image diagram showing sample features extracted from the image shown in <figref idref="f0001">Figure 1</figref>.

0016<figref idref="f0007">Figure 8</figref> is a graph showing the experimental efficacy of different combinations of these prediction methods.

0017<figref idref="f0008">Figures 9A-9C</figref> are tracking diagrams showing tracking results for various resolutions in a scene.

0018<figref idref="f0008">Figures 10A and 10B</figref> are tracking diagrams showing tracking results under an occlusion condition.

0019<figref idref="f0009">Figures 11A-11D</figref> are tracking diagrams showing tracking results for scenes under various degrees of rotation.

0020<figref idref="f0010">Figures 12A and 12B</figref> are image diagrams showing sample images tracked by the facility.

0021<figref idref="f0011">Figure 13</figref> is a coordinate diagram showing the coordinate system used by the facility.

0022<figref idref="f0012">Figures 14A and 14B</figref> are diagrams showing preliminary feature point extraction results.

0023<figref idref="f0013">Figures 15A and 15B</figref> are diagrams showing preliminary feature point extraction results.

0024<figref idref="f0014 f0015">Figures 16A-16H</figref> are tracking diagrams showing the results of sample tracking experiments.

0025<figref idref="f0015">Figures 17A-17D</figref> show template matching results for example images.

DETAILED DESCRIPTION

0026A software facility for tracking a surface in a 3-dimensional scene using natural visual features of the surface ("the facility") is provided. In some embodiments, the facility acquires an image of the surface, and uses it to select visual features of the surface that the facility will use to track the surface. In some embodiments, the facility performs this surface analysis and feature selection on a non-real-time basis. In some embodiments, the facility selects groups of features that are each of a different size, for use when the surface is different distances from the camera. To initially identify the surface in the video frame, in some embodiments, the facility locates a fiducial marker attached to the surface within the video scene, and uses it to determine the surface's distance and orientation relative to the camera. After this point, the facility reiteratively uses earlier tracking results to both (1) select a group of features to search for based upon the distance of the surface from the camera, and (2) delineate search zones in the video scene in which the facility expects to find the natural features based upon their prior positions. The facility then searches these search zones for the natural features in the selected group, and uses their locations in the video scene to determine the surface's location and orientation relative to the camera.

0027The key idea to allow real-time tracking of natural features is to select <i>beforehand</i> the "best" features to track using an offline image processing program, and to choose an appropriate and fast matching method that will allow the detection and matching of these features in real-time during the online tracking phase. Based on these considerations, we chose <i>points</i> as the features to track, and <i>template matching</i> as the matching technique.

0028<figref idref="f0001">Figure 1</figref> is an image diagram showing a typical image that, when attached to a surface, can be tracked by the facility. The image has visual contents 100, including a fiducial marker 110.

0029The offline extraction of the features to track greatly reduces the computation time and makes it possible to track the features in real-time: since the set of specific pixels to track is defined <i>a priori,</i> natural point features do not have to be extracted from each frame, but only to be tracked over time. In other words, the offline feature point extraction generates a set of fixed "natural corners" which perform exactly the same function as the artificial corners introduced by a marker, i.e. to be reference points whose coordinates are known in the object frame. However, as the camera pans in or pans out, the level of detail perceived by the camera changes dramatically. For example, a black letter on a white background is a good feature to track when the camera is close to the planar scene, it might be that this same letter is not visible when the camera is far away from the scene. This problem can be solved by performing the offline feature extraction independently at different resolutions and adapting the set of features online as the camera moves.

0030In all other respects, the general principle of natural-feature based tracking is the same as the marker-based tracking. Four coplanar feature points whose coordinates are known in the page and their projections in the image plane provide correspondences that allow calculating the planar homography and the extrinsic parameters. The main difference is that there are usually a lot more than four feature points available, thus providing a natural mechanism to cope with occlusions: if the tracked planar scene has a reasonable size, it is very unlikely that the user's hand will occlude all the available features in the image.

0031One drawback of the natural feature tracking however is that the tracker's initialization appears to be a delicate task: detecting four natural feature points in the first video frame requires template matching on the whole image for every single possible feature point. This search is computationally expensive and ineffective if the video frame does not provide a perpendicular view of the scene to track. To overcome this drawback, a marker is placed on the page to provide the initial homography as described further below. This homography is used to un-warp the image so that the tracker has a perpendicular view of the scene. From there the tracker knows where to look for the predefined natural point features and no longer needs the marker to be in view. A search size is fixed and template matching is carried out in windows around the predicted feature points' positions. The four "best" natural point features detected are selected as input for updating the homography. The updated homography is also used to generate new templates around the feature points, since the region around a pixel changes as the camera moves. The previous feature points' locations and displacement are used to predict their location in the next frame. Then the tracker estimates the current resolution of the planar scene as seen by the camera and changes the set of predefined features to track if appropriate. Finally, the camera pose is estimated and the virtual model can be rendered on the top of the book page.

0032<figref idref="f0002">Figure 2</figref> is a flow diagram showing steps typically performed by the facility in order to track a surface. The facility begins in market based initialization mode 210. In step 211, the facility converts an image of the surface into binary form. In step 212, the facility extracts connected components from the binary version of the image of the surface. In step 213, the facility extracts the contours from the image of the surface. In step 214, the facility rejects any false contours among the extracted contours, and performs sub-pixel recovery of the coordinates of the corners of the marker. In step 215, the facility computes the homography of the surface (that is, its location and orientation relative to the camera), and un-warps the image of the surface by normalizing it with respect to the surface's determined location and orientation with respect to the camera. In step 216, the facility selects the best visual features of the surface, such as the best four features. These selected features are sometimes referred to as "point features."

0033After the steps of the marker-based initialization mode 210 are completed, the facility enters a natural feature tracking mode 220. In step 221, the facility updates the templates established during the marker-based initialization phase. In step 222, the facility uses earlier tracking results to predict the locations in the video image at which the surface's point features will occur in the next video frame. In step 223, the facility attempts to detect the point features near the predicted locations in the video frame using a template-matching process. In step 224, the facility updates the surface's homography using the results of step 223. In step 225, the facility evaluates the resolution in feature point selection for the next iteration of the natural feature tracking mode. In some embodiments, step 225 precedes step 221 in the natural feature tracking mode (not shown).

0034After completing the steps of natural feature tracking mode 220, the facility performs a test 230 to determine whether the most recent iteration of the natural feature tracking mode failed to track the surface in the video scene. If so, the facility continues in the marker-based initialization mode to re-locate the surface in the video scene, else the facility continues in the natural feature tracking mode to continue tracking the surface.

0035<figref idref="f0003">Figure 3</figref> is a block diagram showing a typical environment in which the facility operates. The environment contains a computer system 300, which includes one or more processors 310 for executing programs, such as the facility; a video interface 320 that is connected to a camera 360 for acquiring individual images and/or video sequences comprised of images; a persistent storage device 330; a memory 340, containing at least the facility 341; and a computer-readable medium drive 350 for reading information or installing programs such as the facility from computer-readable media, such as a floppy disk, a CD-ROM, or a DVD. Those skilled in the art will appreciate that data and/or programs may be transferred between memory and the persistent storage device for purposes of memory management and data integrity. While various embodiments are described in terms of the environment described above, those skilled in the art will appreciate that the facility may be implemented in a variety of other environments including combinations of one or more computer systems or similar devices connected in various ways.

1.

Offline Feature Extraction

0036This subsection illustrates the design of the feature extraction scheme that detects the best candidate points for template matching at different resolutions.

1.1

Template Matching

0037The offline feature extraction method detects points for which template matching will work well. Therefore, the design of the feature extraction scheme is contingent on the design of the template matching technique. Assuming that the disparity between two successive video frames I_k and I_k+1 is small, then the criterion that can be used to match a point feature is similarity. For points, the universal measure of intensity similarity is correlation. Let p_i be a feature point in I_k, and W be a window of size w+1 and <i>h</i>+1 (with w and h odd numbers) centered on <i>p</i>_i. W defines the template to look for in I_k+1.

0038<figref idref="f0004">Figure 4</figref> is a pixel diagram showing the relationship between a window used in template matching and a search area within a video frame that contains it. Rectangle 400 is the video frame I_k+1. Rectangle 410 is the search area. Rectangle 420 is the search window W, centered on pixel 430 at (y₀, x₀). Window W spans columns x₀ - w/2 through x₀ + w/2, and spans rows y₀ - w/2 through y₀ + w/2.

0039Finding the pixel in I_k+i that is most likely to correspond to <i>p</i>_i is equivalent to finding the region of size w+1 and <i>h</i>+1 in I_k+1 that has the highest correlation score with W within the search area. <i>Normalized cross-correlation</i> (NCC)-discussed in <nplcit id="ncit0003" npl-type="s"><text>F. Vial, "State of the Art Report on Natural Feature Tracking for Vision - Based Real-Time Augmented Reality", Technical Report, Human Interface Technology Laboratory New Zealand (HITLab NZ), University of Canterbury, Christchurch, New Zealand, 2003</text></nplcit>, has shown to be an effective point correlation method. To calculate the NCC between a template Wand a region of the same size around a pixel (x₀, y₀) in I_k+1, the intensity values for the considered pixels have to be centered. Let <i>i</i> and <i>j</i> be indexes spanning a square region of the same size as <i>W</i>. Then <maths id="math0001"><math display="block"><msubsup><mi>I</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow><mo>%</mo></msubsup><mfenced><msub><mi>x</mi><mn>0</mn></msub><msub><mi>y</mi><mn>0</mn></msub><mi>i</mi><mi>j</mi></mfenced><mo>=</mo><msub><mi>I</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>⁢</mo><mfenced><msub><mi>x</mi><mn>0</mn></msub><mo>+</mo><mi>i</mi><mo>,</mo><msub><mi>y</mi><mn>0</mn></msub><mo>+</mo><mi>j</mi></mfenced><mo>-</mo><msub><mover><mi>I</mi><mo>‾</mo></mover><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mfenced><msub><mi>x</mi><mn>0</mn></msub><msub><mi>y</mi><mn>0</mn></msub></mfenced><mspace width="1em" /><mi>and</mi><mspace width="1em" /><msup><mi>W</mi><mo>%</mo></msup><mfenced><mi>i</mi><mi>j</mi></mfenced><mo>=</mo><mi>W</mi><mfenced><mi>i</mi><mi>j</mi></mfenced><mo>-</mo><mover><mi>W</mi><mo>‾</mo></mover></math><img file="EP1556805B1_D0001.tif" /></maths> are the centered values of the pixel (<i>i</i>,<i>j</i>) within the considered region in <i>I</i>_k+1, and <i>W</i> respectively, with <maths id="math0002"><math display="block"><msub><mover><mi>I</mi><mo>‾</mo></mover><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mfenced><msub><mi>x</mi><mn>0</mn></msub><msub><mi>y</mi><mn>0</mn></msub></mfenced><mo>=</mo><mfrac><mn>1</mn><mrow><mfenced><mi>w</mi><mo>+</mo><mn>1</mn></mfenced><mo>⁢</mo><mfenced><mi>h</mi><mo>+</mo><mn>1</mn></mfenced></mrow></mfrac><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mo>-</mo><mi>w</mi><mo>/</mo><mn>2</mn></mrow><mrow><mi>w</mi><mo>/</mo><mn>2</mn></mrow></munderover></mstyle><mspace width="1em" /><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mo>-</mo><mi>h</mi><mo>/</mo><mn>2</mn></mrow><mrow><mi>h</mi><mo>/</mo><mn>2</mn></mrow></munderover></mstyle><msub><mi>I</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>⁢</mo><mfenced><msub><mi>x</mi><mn>0</mn></msub><mo>+</mo><mi>i</mi><mo>,</mo><msub><mi>y</mi><mn>0</mn></msub><mo>+</mo><mi>j</mi></mfenced></math><img file="EP1556805B1_D0002.tif" /></maths> and <maths id="math0003"><math display="block"><mover><mi>W</mi><mo>‾</mo></mover><mo>=</mo><mfrac><mn>1</mn><mrow><mfenced><mi>w</mi><mo>+</mo><mn>1</mn></mfenced><mo>⁢</mo><mfenced><mi>h</mi><mo>+</mo><mn>1</mn></mfenced></mrow></mfrac><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mo>-</mo><mi>w</mi><mo>/</mo><mn>2</mn></mrow><mrow><mi>w</mi><mo>/</mo><mn>2</mn></mrow></munderover></mstyle><mspace width="1em" /><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mo>-</mo><mi>h</mi><mo>/</mo><mn>2</mn></mrow><mrow><mi>h</mi><mo>/</mo><mn>2</mn></mrow></munderover></mstyle><mi>W</mi><mfenced><mi>i</mi><mi>j</mi></mfenced></math><img file="EP1556805B1_D0003.tif" /></maths> Then, the normalized cross correlation score between W and the region around (<i>x</i>₀,<i>y</i>₀) yields: <maths id="math0004" num="(1.1.1)"><math display="block"><mi mathvariant="italic">NCC</mi><mo>⁢</mo><mfenced><msub><mi>I</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mfenced><msub><mi>x</mi><mn>0</mn></msub><msub><mi>y</mi><mn>0</mn></msub></mfenced><mo>,</mo><mi>W</mi></mfenced><mo>=</mo><mfrac><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mo>-</mo><mi>w</mi><mo>/</mo><mn>2</mn></mrow><mrow><mi>w</mi><mo>/</mo><mn>2</mn></mrow></munderover></mstyle><mspace width="1em" /><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mo>-</mo><mi>h</mi><mo>/</mo><mn>2</mn></mrow><mrow><mi>h</mi><mo>/</mo><mn>2</mn></mrow></munderover></mstyle><msubsup><mi>I</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow><mo>%</mo></msubsup><mfenced><msub><mi>x</mi><mn>0</mn></msub><msub><mi>y</mi><mn>0</mn></msub><mi>i</mi><mi>j</mi></mfenced><mo>⁢</mo><msup><mi>W</mi><mo>%</mo></msup><mfenced><mi>i</mi><mi>j</mi></mfenced></mrow><mrow><msqrt><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mo>-</mo><mi>w</mi><mo>/</mo><mn>2</mn></mrow><mrow><mi>w</mi><mo>/</mo><mn>2</mn></mrow></munderover></mstyle><mspace width="1em" /><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mo>-</mo><mi>h</mi><mo>/</mo><mn>2</mn></mrow><mrow><mi>h</mi><mo>/</mo><mn>2</mn></mrow></munderover></mstyle><msubsup><mi>I</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow><mo>%</mo></msubsup><mo>⁢</mo><msup><mfenced><msub><mi>x</mi><mn>0</mn></msub><msub><mi>y</mi><mn>0</mn></msub><mi>i</mi><mi>j</mi></mfenced><mn>2</mn></msup></msqrt><mo>⁢</mo><msqrt><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mo>-</mo><mi>w</mi><mo>/</mo><mn>2</mn></mrow><mrow><mi>w</mi><mo>/</mo><mn>2</mn></mrow></munderover></mstyle><mspace width="1em" /><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mo>-</mo><mi>h</mi><mo>/</mo><mn>2</mn></mrow><mrow><mi>h</mi><mo>/</mo><mn>2</mn></mrow></munderover></mstyle><msup><mi>W</mi><mo>%</mo></msup><mo>⁢</mo><msup><mfenced><mi>i</mi><mi>j</mi></mfenced><mn>2</mn></msup></msqrt></mrow></mfrac></math><img file="EP1556805B1_D0004.tif" /></maths>

0040An advantage is that the NCC scores between -1 and 1, providing an intuitive range to perform similarity thresholding: a value of -1 indicates no similarity at all whereas a value of 1 shows perfect similarity. Another benefit of using the NCC comes from its insensitivity to illumination changes. If we model an illumination change by the addition of a constant value to all the pixels of the regions, then the score of the NCC will be the same as without that offset. However, correlation is not insensitive to any affine or perspective transformation. Therefore, templates will be generated for each frame grabbed by the system as mentioned above.

0041Moreover, NCC is computationally expensive and can become inefficient when the values of w, h and the size of the search area become large. To compensate for this, a coarse to fine technique will be used: firstly, template matching within the search window is carried out every n pixels to reduce the search complexity by a factor n. The three positions for which the NCC score was the highest are stored. Then the fine search is carried out: template matching is performed for every pixel in the regions around the three stored positions. The highest NCC score provides the final detected position.

1.2

Point Feature Extraction Scheme

0042A front-facing representation of the planar scene to track containing a marker has to be supplied to the tracker. Usually, a JPEG or a GIF file is used as the input image file. Firstly, the marker is detected in the input image using well known techniques, such as those described in <patcit id="pcit0001" dnum="US513725P" dnum-type="L"><text>U.S. Provisional Patent Application No. 60/513,725</text></patcit> (patent counsel's docket no. 37181-8002US00). The position and size of the scene in the input image are calculated and stored in a file.

0043Subsequently, the extraction of the natural features of the scene is performed. The choice of a specific template matching technique to match natural feature points from frame to frame requires that we define a set of constraints for the feature points to be extract from the original image: <ul id="ul0001" list-style="bullet" compact="compact"><li>Constraint 1: the similarity between pixels inside the w x h region around the candidate feature point (and outside the circular area defined in constraint 2.) should be small so that uniform or low contrast regions are rejected. This is equivalent to saying that the template should have a minimum variance.</li><li>Constraint 2: the similarity between pixels inside the w x h region within a circular region of radius n around a candidate feature point should be high so that the best three results in the coarse step of template matching include the region around the correct position of the feature. In other words, this constraint ensures that the correct feature position is not missed by the coarse step of the template matching.</li><li>Constraint 3: there should be no similar region within the search area around a candidate feature point for which template matching is carried out. In other words, we want to make sure that there can be no more than one match for a template of size w and h in the search area of size w_search and h_search around the candidate pixel so that the tracker does not get confused.</li></ul>

0044<figref idref="f0004">Figure 5</figref> is a pixel diagram that illustrates the feature point constraints for a candidate pixel. The candidate pixel 501 is likely to be a good feature within template 503 if: (1) the similarity within a small circular region 502 about the candidate pixel is high; (2) the similarity inside the template 503 and outside the circular region 502 is low, i.e., there is a high variance; and (3) no similar template regions exist within search area 504.

0045The offline feature extraction program proceeds thus: the user gives in the different resolutions for which he or she would like the features to be automatically extracted. The more resolutions are specified, the more accurate the tracker will be but the more processing time will be required. The parameters that have to be fixed for the natural feature extraction are: <ul id="ul0002" list-style="bullet" compact="compact"><li>the template dimensions w and h</li><li>the threshold t_var defining the minimum value of the variance described in constraint 1 above.</li><li>the search size for template matching w_search and h_search</li><li>the threshold t_MaxSim defining the maximum tolerated similarity described in constraint 3.</li><li>the radius <i>r</i> of the small circular region and the threshold t_MinSim defining the minimum tolerated similarity described in constraint 2.</li></ul>

0046Experimental results have been carried out (see Section 3 below) that provide default values for these parameters. In a first step, the feature extraction process only tests for the constraints 1 and 3. The procedure is outlined in the pseudocode shown in Code Block 1 below.

For every resolution chosen by the user

For every pixel pix in the input image

0047<ul id="ul0003" list-style="bullet" compact="compact"><li><i>Generate the template tp of size w and h around pix.</i></li><li><i>Calculate the variance over the region tp excluding the central circular area of radius n.</i><i>If (variance < t_var) reject pix and go to next pixel.</i></li><li><i>For every w x h region reg included in the w_search x h_search window around pix</i><ul id="ul0004" list-style="none" compact="compact"><li><i>→ Calculate the similarity sim between reg and tp with the normalized cross correlation.</i></li><li>→ <i>Update the maximum value of similarity within the search area.</i></li><li>→ <i>If (similarity > t_MaxSim) reject pix and go to next pixel.</i></li></ul><i>End For</i></li><li><i>Pix = sim</i><i>End For</i><i>End For</i></li></ul>

0048Code Block 1

0049The result of this algorithm performed for the image in <figref idref="f0001">Figure 1</figref> at two different resolutions is shown in <figref idref="f0005">Figures 6A and 6B. Figure 6A</figref> shows the output of this first step of the offline feature extraction algorithm for the original image resolution of 200 dpi. <figref idref="f0005">Figure 6B</figref> shows the output at a lower resolution of 100 dpi. Both of these figures reflect a template size of 25 x 25 pixels. In the output images, dark regions indicate highly correlated regions (uniform regions) from which feature points should not be chosen. On the contrary bright regions are image regions for which template matching is likely to work well. As expected, fewer details are visible in the image with lower resolution.

0050The obtained maps of candidate features at different resolutions are used as input for a second algorithm that selects the best point features to track. This operation is performed by enforcing constraint 2 and by thresholding the results obtained. Additional restrictions are that the selected template regions must be as evenly distributed as possible and must not overlap. The t_var parameter directly influences the number of features extracted: the higher t_var is the fewer feature points will fulfil constraint 1. <figref idref="f0006">Figure 7</figref> is an image diagram showing sample features extracted from the image shown in <figref idref="f0001">Figure 1</figref>. <figref idref="f0006">Figure 7</figref> shows the extracted features in the original image for t_var = 10. Each red square identifies a feature extracted for the original resolution (200 dpi) with t_var = 10, t_MaxSim = 0.65 and t_MinSim = 0.85. Having a large number of extracted features allows the tracker to cope better with occlusions but slows down the tracking process and may confuse the tracker under some occlusive conditions.

0051On the other hand, few features speeds up the tracking process but leads the system to be much more sensitive to occlusions. As a consequence, a trade-off has to be made to find the optimal balance between a good occlusion handling and a fast tracking. The locations of the extracted feature points relatively to the marker are stored in a file that will be used during the online tracking mode.

2.

Online Tracking

0052This subsection describes an efficient tracking algorithm of predefined features which allows continued pattern tracking in the presence of significant occlusion. The fundamental idea is to track the known point feature from frame to frame, and to update the homography for the planar scene based on these natural features, instead of simply relying on the four artificial corners provided by the marker.

2.1

Initialization

0053As mentioned earlier, the initialization of the tracker is made using the fiducial marker as described in Section 1.2.

2.2

Feature Selection and Template Updating

0054Now that the initial homography has been computed, the tracker has to decide which natural features are the "best" ones to choose in the current frame. Keeping in mind the fact that our application must run in real-time, we want to choose as few features as possible whose locations are optimal. Therefore, the following heuristic selection method is chosen: <ol id="ol0001" compact="compact"><li>1. Using the homography of the previous frame, obtain the image coordinates of the features from their known coordinates in the object frame. Using the estimate of the current resolution, reject all features that are not visible in the current video frame.</li><li>2. Selection of the first feature point: select the one whose position is the furthest from the video frame center.</li><li>3. Selection of the second feature point: select the one that is the furthest from the first feature point.</li><li>4. Selection of the third feature point: select the one that maximizes the area of the triangle formed with the two first selected feature points.</li><li>5. Selection of the fourth feature point: select the point that maximizes the area of the rectangle formed with the three first selected feature points.</li></ol>

0055The motivation behind this selection scheme is that the homography computed from point features distant from each other is less prone to errors. Once these four points have been selected, the homography from previous frame is also used to generate new templates around the features. This template updating ensures that the rotated view of the template does not prevent the template matching technique from working.

2.3

Coarse Feature Prediction

0056The first stage of the tracking mode consists of predicting the location of the features in the current frame using the homography computed in the previous frame. Assuming temporal coherency, three simple prediction methods can be derived.

0057Firstly, it can be supposed that the feature in the current frame I_k will be located at the same position as in the previous frame I_k-1 using the small interframe motion hypothesis: <maths id="math0005" num="(2.3.1)"><math display="block"><msubsup><mover><mi>p</mi><mo>^</mo></mover><mi>i</mi><mi>k</mi></msubsup><mo>=</mo><msubsup><mi>p</mi><mi>i</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msubsup></math><img file="EP1556805B1_D0005.tif" /></maths> with the superscript "^" designated an estimation.

0058As the camera image is almost always moving, this assumption is almost always violated, and we may therefore rather assume a constant velocity of the feature. So for any frame I_k with k > 2 , the value of the velocity vector ν yields: <maths id="math0006"><math display="block"><mi>v</mi><mfenced><mi>k</mi></mfenced><mo>=</mo><mi>v</mi><mo>=</mo><mfrac><mrow><msup><msub><mi>p</mi><mi>i</mi></msub><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>-</mo><msup><msub><mi>p</mi><mi>i</mi></msub><mrow><mi>k</mi><mo>-</mo><mn>2</mn></mrow></msup></mrow><mrow><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>t</mi></mrow></mfrac></math><img file="EP1556805B1_D0006.tif" /></maths> with Δ<i>t</i> the time elapsed between the frame <i>I</i>_<i>k</i>-1 and <i>I</i>_<i>k</i>-2. We will suppose that the time elapsed between two frames is constant and has a unit value. We can subsequently write <maths id="math0007"><math display="block"><mi>v</mi><mo>≃</mo><msup><msub><mi>p</mi><mi>i</mi></msub><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>-</mo><msup><msub><mi>p</mi><mi>i</mi></msub><mrow><mi>k</mi><mo>-</mo><mn>2</mn></mrow></msup></math><img file="EP1556805B1_D0007.tif" /></maths><maths id="math0008"><math display="inline"><msubsup><mover><mi>p</mi><mo>^</mo></mover><mi>i</mi><mi>k</mi></msubsup></math><img file="EP1556805B1_D0008.tif" /></maths> can then be estimated as: <maths id="math0009"><math display="block"><msubsup><mover><mi>p</mi><mo>^</mo></mover><mi>i</mi><mi>k</mi></msubsup><mo>≃</mo><msubsup><mover><mi>p</mi><mo>^</mo></mover><mi>i</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mo>+</mo><mi>v</mi></math><img file="EP1556805B1_D0009.tif" /></maths><maths id="math0010" num="(2.3.2)"><math display="block"><msubsup><mover><mi>p</mi><mo>^</mo></mover><mi>i</mi><mi>k</mi></msubsup><mo>≃</mo><mn>2</mn><mo>⁢</mo><msubsup><mi>p</mi><mi>i</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mo>-</mo><msubsup><mi>p</mi><mi>i</mi><mrow><mi>k</mi><mo>-</mo><mn>2</mn></mrow></msubsup></math><img file="EP1556805B1_D0010.tif" /></maths> In a similar manner, if we consider that the acceleration of the feature is constant, then its position in frame <i>I</i>_k can be estimated by : <maths id="math0011" num="(2.3.3)"><math display="block"><msubsup><mover><mi>p</mi><mo>^</mo></mover><mi>i</mi><mi>k</mi></msubsup><mo>=</mo><mn>3</mn><mo>⁢</mo><msubsup><mi>p</mi><mi>i</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mo>-</mo><mn>3</mn><mo>⁢</mo><msubsup><mi>p</mi><mi>i</mi><mrow><mi>k</mi><mo>-</mo><mn>2</mn></mrow></msubsup><mo>+</mo><msubsup><mi>p</mi><mi>i</mi><mrow><mi>k</mi><mo>-</mo><mn>3</mn></mrow></msubsup></math><img file="EP1556805B1_D0011.tif" /></maths> Those position estimates are coarse and could not compete in accuracy with the widely used Kalman filtering discussed in <nplcit id="ncit0004" npl-type="s"><text>G. lannizzotto, L. Vita, "On-line Object Tracking for Colour Video Analysis," Real-Time Imaging, 8:2, pp. 145-155, April 2002</text></nplcit>, and <nplcit id="ncit0005" npl-type="s"><text>D. Koller, G. Klinker, E. Rose, D. Breen, R. Whitaker, M. Tuceryan, "Real-time Vision-Based Camera Tracking for Augmented Reality Applications," in Proc. of the ACM Symposium on Virtual Reality Software and Technology, pp. 87-94, Lausanne, Switzerland, September 1997</text></nplcit>, but they have the great advantage of being computationally cheap. Following one, two or all three of these estimations, one can predict the position of <i>p_i</i> in the current frame.

2.4

Feature Detection

0059The estimated positions of the features are subject to errors due to small errors in the homography as well as due to the approximations introduced in Section 4.4.2. A search window around that position has to be defined to proceed with template matching. The tricky task is to fix the size of this search area. A simple approach is to declare its size constant, and to set it to a value determined empirically by tests in real conditions. This approach is very simple and may not be well adapted to dynamic motions, yet it is the basis of our system since we extracted features assuming a fixed search window size. A large search window allows for more movement, but slows down the matching process since normalized cross correlation has to be carried out for a large number of pixels. Conversely, a small search window size increases the speed of the matching process, but increases the chance of tracker failure due to rapid motion. Please refer to Section 3 for the empirical determination of the window size. The position of the selected features is determined by the template matching process described in 1.1 (typically, a match is found if the NCC score is greater than 0.7) and the radial distortion is corrected.

2.5

Homography Updating and Resolution Estimation

0060Using the four feature point correspondences <maths id="math0012"><math display="inline"><msubsup><mi>p</mi><mi>i</mi><mi>I</mi></msubsup><mo>↔</mo><msubsup><mi>P</mi><mi>i</mi><mi>w</mi></msubsup><mo>,</mo></math><img file="EP1556805B1_D0012.tif" /></maths> a new homography H is determined. A reprojection error measure is defined as: <maths id="math0013"><math display="block"><mi>ε</mi><mo>=</mo><mfrac><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mn>4</mn></munderover></mstyle><msup><mfenced><msubsup><mi>p</mi><mi>i</mi><mi>I</mi></msubsup><mo>-</mo><msubsup><mi mathvariant="italic">HP</mi><mi>i</mi><mi>W</mi></msubsup></mfenced><mn>2</mn></msup></mrow><mn>4</mn></mfrac></math><img file="EP1556805B1_D0013.tif" /></maths>

0061If ε is smaller than a predefined threshold (a value of 5.0 has proven to be a useful threshold value), the homography is accepted and another tracking cycle can begin with the next video frame. If ε is greater than the threshold, it may indicate that the set of point correspondences contains a spurious value due to noise or occlusion. To handle this, the search for a fifth feature point is carried out. If one additional feature point is detected, the planar homography is computed for every subset of four points among five and the one that minimizes ε is chosen as the result. If a fifth feature point cannot be detected, tracking fails and the tracker reverts to the initialization mode. The fiducial marker has to be in view for the tracker to be re-initialized.

0062If the tracking succeeds, an estimate of the viewed resolution of the planar scene is computed as follows: two feature points whose coordinates are known in the world frame and in the image frame are chosen. We know the distance in millimeters separating the two features in the world frame and the distance in pixels separating them in the image frame. Consequently, it is easy to know how many pixels represent a centimeter in world coordinates and to deduce the resolution of the scene that the camera is currently viewing. If necessary, a different set of features corresponding to that resolution is chosen.

3.

Implementation Details

3.1

Determining the Parameters

0063Our feature extraction technique necessitates that we set the dimensions w and h of the template as well as dimensions w_search and h_search of the search size once and for all for the whole process. For simplicity reasons, we declare that both windows are square, that is, w = h and w_search = h_search.

3.1.1

Template Size

0064For normalized cross correlation to be reliable, w has to be large, but this also means that template matching will be computationally expensive. The computation time needed by normalized crossed correlation has been calculated for a range of values of w. A value of 25 pixels has shown to be a good trade-off between reliability and speed for images of dimensions 3800 pixels x 1920 pixels.

3.1.2

Search Area Size

0065Concerning the online tracking phase, the feature prediction method has a direct influence on the size of the search area. A small search area would make faster the matching process but would cause tracking to fail due to the coarse nature of the prediction method. This means that a too small value of w_search will give a higher chance of the tracked feature not being in the search area and causing the tracker to fail. To determine search empirically, tracking in real conditions was carried out for four thousand features with different combinations of prediction methods (2.3.1), (2.3.2), and (2.3.3). The error rate representing the percentage of feature points that were not detected in the search area was calculated as a function of the search area size. The results are shown in <figref idref="f0007">Figure 8</figref>.

0066<figref idref="f0007">Figure 8</figref> is a graph showing the experimental efficacy of different combinations of these prediction methods. The graph 800 is encoded using a key 810, in which the numeral 1 refers to prediction method (2.3.1), the numeral 2 refers to prediction method (2.3.2), and the numeral 3 refers to prediction method (2.3.3).

0067It can be seen that prediction method (2.3.1) gives poor results unless the search window size is large. Furthermore, we observe that any combination of two prediction methods or of the three together gives similar results. To choose a search area size, we look more in details in the range between 41 and 61 pixels to see what value provides an acceptable error rate for every prediction method. The results are shown in Table 1 below.

0068The combination of prediction methods (2.3.1) and (2.3.2) is chosen to reduce the time needed by the prediction stage of the tracker. Consequently, a search area size of 49 is selected since it is the minimum size guaranteeing that the feature points will be found in the search area.

0069Finally, during the online tracking, the coarse step of template matching is performed every n=3 pixels. This value allows enough speed improvement for the tracker to work in real time.

3.2

Performance Evaluation

0070One of the major design goals of our augmented reality system was real-time performance on a standard personal computer. The software runs under the Windows XP operating system and the camera used is an off-the-shelf USB web camera delivering 640 pixel x 480 pixel video frames. The tracking system is currently implemented in C with OpenGL and VRML used to render the augmented graphics on top of the video. All tests have been run on an Intel Pentium IV 2.4 GHz processor, with a GeForce4 Ti 4600 video card.

3.2.1

Offline Feature Extraction

0071The offline feature extraction is the bottleneck of the whole application because of its algorithmic complexity. For small images (640 pixels x 480 pixels) the processing time can be a few minutes. However, when the size of the input becomes large, as it is the case for our application (3800 pixels x 1920 pixels), the time needed to generate the feature map at different resolutions is more than five hours. This remains the main drawback of the application.

3.2.2

Online Tracking

0072The online tracking shows promising results with a frame rate of 25 to 30 frames per second. This proves that the method is suitable for real-time purposes.

0073The scale invariance is tested by starting tracking with the camera far away from the scene and gradually taking it closer to the scene. The multi-resolution template scheme works well as shown in <figref idref="f0008">Figures 9A-9C</figref>.

0074<figref idref="f0008">Figures 9A-9C</figref> are tracking diagrams showing tracking results for various resolutions in a scene. <figref idref="f0008">Figure 9A</figref> shows tracking results for a low resolution, <figref idref="f0008">Figure 9B</figref> for a medium resolution, and <figref idref="f0008">Figure 9C</figref> for a high resolution. The numbered green squares in these figures represents the current point features tracked. A zoomed view of the templates can be seen on the left side of each figure.

0075Occlusion handling is then tested with a typical user's reaction: putting a hand over the scene to track. Here again, the tracker succeeds in choosing alternative feature points, thus providing continuous tracking. The results for occlusion are shown in <figref idref="f0008">Figures 10A and 10B</figref>.

0076<figref idref="f0008">Figures 10A and 10B</figref> are tracking diagrams showing tracking results under an occlusion condition. <figref idref="f0008">Figure 10A</figref> shows tracking results for a scene that is not occluded, while <figref idref="f0008">Figure 10B</figref> shows tracking results for a similar scene that is occluded by a human hand. Because the occlusion of feature 2 shown in <figref idref="f0008">Figure 10A</figref> is prevented in the scene shown in <figref idref="f0008">Figure 10B</figref> by the occlusion, the facility proceeds to register a new feature in the scene of <figref idref="f0008">Figure 10B</figref>, shown there as feature number 4.

0077Note that only the natural feature tracking mode provides any robustness to occlusion. The marker-based initialization mode of the tracker requires the marker to be completely visible. The robustness of the tracker relative to different orientations was also tested. The scene was alternatively viewed from different angles and the tracker succeeded in finding four features, even under severe rotation. An example is shown in <figref idref="f0009">Figures 11A-11D</figref>.

0078<figref idref="f0009">Figures 11A-11D</figref> are tracking diagrams showing tracking results for scenes under various degrees of rotation. <figref idref="f0009">Figure 11A</figref> shows tracking results under no rotation, <figref idref="f0009">Figure 11B</figref> under rotation of 45°, <figref idref="f0009">Figure 11C</figref> under rotation of 60°, and <figref idref="f0009">Figure 11D</figref> under rotation of 80°.

0079One limitation of some embodiments of the tracker is its sensitivity to rapid motion. If the camera is rotated or translated quickly, the tracker usually fails. This is due to the poor image quality delivered by a simple USB web camera. When the camera moves quickly, the frame provided by the camera is too blurred for template matching to succeed. The use of a higher quality camera with higher shutter-speed should increase considerably the robustness of the tracker to rapid image motion.

6.

Additional Details

0080This section contains additional details about the facility and its implementation.

6.1

Tracked Images

0081<figref idref="f0010">Figures 12A and 12B</figref> are image diagrams showing sample images tracked by the facility. The image of <figref idref="f0010">Figure 12A</figref> consists of letters and photos and has a size of about 20 cm by 28 cm. The image of <figref idref="f0010">Figure 12B</figref> is an example of a color map, and is of size of about 80 cm by 104 cm.

6.2 -

Registration by Template Matching

6.2.1

Coordinates System

0082<figref idref="f0011">Figure 13</figref> is a coordinate diagram showing the coordinate system used by the facility. There is an object coordinate frame centered on the tracked object. The origin of the object coordinates, X_o and Y_o axes lie on the surface, while the Z_o axis is perpendicular to the surface. The camera has a camera coordinate frame and there is a perspective relationship between the camera coordinates and the screen coordinates. Straight lines in the 3D environment should ideally remain straight when transformed into screen coordinates. However in practice this does not happen because of lens distortion. To compensate for this we introduce two screen coordinates; ideal screen coordinates which keep the perspective transformation with camera coordinates, and observed screen coordinates which represent the distorted image from the camera. The transformation from object coordinates to ideal screen coordinates is represented by <maths id="math0014" num="(eq 6.1)"><math display="block"><mtable columnalign="left"><mtr><mtd><mi>h</mi><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi>x</mi><mi>c</mi></msub></mtd></mtr><mtr><mtd><msub><mi>y</mi><mi>c</mi></msub></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></mtd><mtd><mo>=</mo><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi>C</mi><mn>11</mn></msub></mtd><mtd><msub><mi>C</mi><mn>12</mn></msub></mtd><mtd><msub><mi>C</mi><mn>13</mn></msub></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><msub><mi>C</mi><mn>22</mn></msub></mtd><mtd><msub><mi>C</mi><mn>23</mn></msub></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>⁢</mo><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi>R</mi><mn>11</mn></msub></mtd><mtd><msub><mi>R</mi><mn>12</mn></msub></mtd><mtd><msub><mi>R</mi><mn>13</mn></msub></mtd><mtd><msub><mi>T</mi><mn>1</mn></msub></mtd></mtr><mtr><mtd><msub><mi>R</mi><mn>21</mn></msub></mtd><mtd><msub><mi>R</mi><mn>22</mn></msub></mtd><mtd><msub><mi>R</mi><mn>23</mn></msub></mtd><mtd><msub><mi>T</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><msub><mi>R</mi><mn>31</mn></msub></mtd><mtd><msub><mi>R</mi><mn>32</mn></msub></mtd><mtd><msub><mi>R</mi><mn>33</mn></msub></mtd><mtd><msub><mi>T</mi><mn>3</mn></msub></mtd></mtr></mtable></mfenced><mo>⁢</mo><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi>X</mi><mi>o</mi></msub></mtd></mtr><mtr><mtd><msub><mi>Y</mi><mi>o</mi></msub></mtd></mtr><mtr><mtd><msub><mi>Z</mi><mi>o</mi></msub></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mspace width="1em" /></mtd><mtd><mo>=</mo><mi mathvariant="bold">C</mi><mo>⋅</mo><msub><mi mathvariant="bold">T</mi><mi mathvariant="italic">co</mi></msub><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi>X</mi><mi>o</mi></msub></mtd></mtr><mtr><mtd><msub><mi>Y</mi><mi>o</mi></msub></mtd></mtr><mtr><mtd><msub><mi>Z</mi><mi>o</mi></msub></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></math><img file="EP1556805B1_D0014.tif" /></maths> where matrix C contains the intrinsic camera parameters of focal length, scale factor, optical center, aspect ratio and skew factor based on perspective projection model. Matrix T_co represents the transformation between object coordinates to camera coordinates and consists of a translation component and a rotation component.

0083The point (x_c, y_c) in ideal screen coordinates is transformed to the point (x_d, y_d) in observed screen coordinates by the distortion function <maths id="math0015" num="(eq 6.2)"><math display="block"><mtable><mtr><mtd columnalign="right"><mi>x</mi></mtd><mtd columnalign="left"><mo>=</mo><mi>s</mi><mo>⁢</mo><mfenced><msub><mi>x</mi><mi>c</mi></msub><mo>-</mo><msub><mi>x</mi><mrow><mi>d</mi><mo>⁢</mo><mn>0</mn></mrow></msub></mfenced><mo>,</mo><mspace width="2em" /><mi>y</mi><mo>=</mo><mi>s</mi><mo>⁢</mo><mfenced><msub><mi>y</mi><mi>c</mi></msub><mo>-</mo><msub><mi>y</mi><mrow><mi>d</mi><mo>⁢</mo><mn>0</mn></mrow></msub></mfenced></mtd></mtr><mtr><mtd columnalign="right"><msup><mi>d</mi><mn>2</mn></msup></mtd><mtd columnalign="left"><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd columnalign="right"><mi>p</mi></mtd><mtd columnalign="left"><mo>=</mo><mfenced open="{" close="}"><mn>1</mn><mo>-</mo><msup><mi mathvariant="italic">fd</mi><mn>2</mn></msup></mfenced></mtd></mtr><mtr><mtd columnalign="right"><msub><mi>x</mi><mi>d</mi></msub></mtd><mtd columnalign="left"><mo>=</mo><mi mathvariant="italic">px</mi><mo>+</mo><msub><mi>x</mi><mrow><mi>d</mi><mo>⁢</mo><mn>0</mn></mrow></msub><mo>,</mo><mspace width="1em" /><msub><mi>y</mi><mi>d</mi></msub><mo>=</mo><mi mathvariant="italic">py</mi><mo>+</mo><msub><mi>y</mi><mrow><mi>d</mi><mo>⁢</mo><mn>0</mn></mrow></msub></mtd></mtr></mtable></math><img file="EP1556805B1_D0015.tif" /></maths> where (x_d0, y_d0) is the center of distortion, s is the scale parameter and f is the distortion factor. This transformation is a non-linear function but we represent it as follows: <maths id="math0016" num="(eq 6.3)"><math display="block"><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi>x</mi><mi>d</mi></msub></mtd></mtr><mtr><mtd><msub><mi>y</mi><mi>d</mi></msub></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>=</mo><mi mathvariant="bold">F</mi><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi>x</mi><mi>c</mi></msub></mtd></mtr><mtr><mtd><msub><mi>y</mi><mi>c</mi></msub></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>⁢</mo><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi>x</mi><mi>c</mi></msub></mtd></mtr><mtr><mtd><msub><mi>y</mi><mi>c</mi></msub></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>=</mo><msup><mi mathvariant="bold">F</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi>x</mi><mi>d</mi></msub></mtd></mtr><mtr><mtd><msub><mi>y</mi><mi>d</mi></msub></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math><img file="EP1556805B1_D0016.tif" /></maths> So the registration problem reduces to calculation of the transformation matrix T_co. We describe how to do this in the next section.

6.2.2

Pose and Position Calculation

0084Given that there are n feature points (<i>X_oi</i>, <i>Y_oi, Z_oi</i>) (<i>i</i>=0,1 ,,<i>n</i>-1) in object coordinates and they are projected into <i>(x_di, y_di)</i> (<i>i</i>=0,1 ,,<i>n</i>-1) in observed screen coordinates, an error function is represented in ideal screen coordinates (eq.6.4). <maths id="math0017"><math display="block"><msup><mi mathvariant="italic">err</mi><mn>2</mn></msup><mo>=</mo><mfrac><mn>1</mn><mi>n</mi></mfrac><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></munderover></mstyle><mfenced open="{" close="}"><msup><mfenced><msub><mi>x</mi><mi mathvariant="italic">ci</mi></msub><mo>-</mo><msub><mover><mi>x</mi><mo>‾</mo></mover><mi mathvariant="italic">ci</mi></msub></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><msub><mi>y</mi><mi mathvariant="italic">ci</mi></msub><mo>-</mo><msub><mover><mi>y</mi><mo>‾</mo></mover><mi mathvariant="italic">ci</mi></msub></mfenced><mn>2</mn></msup></mfenced></math><img file="EP1556805B1_D0017.tif" /></maths><maths id="math0018" num="(eq 6.4)"><math display="block"><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi>x</mi><mi mathvariant="italic">ci</mi></msub></mtd></mtr><mtr><mtd><msub><mi>y</mi><mi mathvariant="italic">ci</mi></msub></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>=</mo><msup><mi mathvariant="bold">F</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi>x</mi><mi mathvariant="italic">di</mi></msub></mtd></mtr><mtr><mtd><msub><mi>y</mi><mi mathvariant="italic">di</mi></msub></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mmultiscripts><mi>h</mi><mprescripts /><mspace width="3em" /><none /></mmultiscripts><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mover><mi>x</mi><mo>˜</mo></mover><mi mathvariant="italic">ci</mi></msub></mtd></mtr><mtr><mtd><msub><mover><mi>y</mi><mo>˜</mo></mover><mi mathvariant="italic">ci</mi></msub></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>=</mo><mi mathvariant="bold">C</mi><mo>⋅</mo><msub><mi mathvariant="bold">T</mi><mi>co</mi></msub><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi mathvariant="italic">X</mi><mi mathvariant="italic">oi</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="italic">Y</mi><mi mathvariant="italic">oi</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="italic">Z</mi><mi mathvariant="italic">oi</mi></msub></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math><img file="EP1556805B1_D0018.tif" /></maths>

0085The matrix T_co minimizes this error function. If n is more than 3 and suitable initial values are given for T_co, this calculation is possible. We employ the functions provided by ARToolKit for this calculation. In order to set suitable initial values into T_co, the result for previous frame is used in iterative tracking phase. A black square fiducial and ARToolKit functions are used to set the initial values in initial detection phase.

0086To calculate subsequent values for T_co we need to detect positions in observed screen coordinates which correspond to n feature points in object coordinates. We employ template matching for this process.

6.2.3

Feature Detection by Template Matching

0087Template matching can detect similar regions to the template from images. In general templates have to be prepared beforehand. However this is impossible with this kind of 3D tracking, because the image of a feature point varies by its 6 DOF movement. Therefore the templates have to be generated for each image frame. We assume that the movement of the tracked object is small between each continuous image frame. Then templates are generated from the texture image of the tracked object that is captured beforehand based on the pose and position information in previous frame. Detection of feature positions consists of the following three steps:

1) Calculation of observed screen coordinates (

x_di

,

y_di

) of feature points

0088The tracked object exists in X_o-Y_o surface of the object coordinates. So the feature points can be represented as (<i>X_oi</i>, <i>Y_oi,</i> 0) (<i>i</i>=0,1,,<i>n</i>-1). Given transformation matrix from the object coordinates to camera coordinates in previous frame is T_co, observed screen coordinates (<i>x_di</i>, <i>y_di</i>) corresponding to (<i>X_oi, Y_oi</i>, 0) can be calculate by (eq.1) and (eq.2).

2) Generation of the template in which

(x_di, y_di)

is centered

0089In order to generate the template in which <i>(x_di, y_di)</i> is centered, the transformation from observed screen coordinates to X_o-Y_o surface in the object coordinates is needed. Given <i>Z_o</i>=0, the following equation is obtained. <maths id="math0019" num="(eq 6.5)"><math display="block"><mi>h</mi><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi>x</mi><mi>c</mi></msub></mtd></mtr><mtr><mtd><msub><mi>y</mi><mi>c</mi></msub></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>=</mo><mi mathvariant="bold">C</mi><mo>⋅</mo><msub><mi mathvariant="bold">T</mi><mi>co</mi></msub><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi>X</mi><mi>o</mi></msub></mtd></mtr><mtr><mtd><msub><mi>Y</mi><mi>o</mi></msub></mtd></mtr><mtr><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>=</mo><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi>p</mi><mn>11</mn></msub></mtd><mtd><msub><mi>p</mi><mn>12</mn></msub></mtd><mtd><msub><mi>p</mi><mn>13</mn></msub></mtd></mtr><mtr><mtd><msub><mi>p</mi><mn>21</mn></msub></mtd><mtd><msub><mi>p</mi><mn>22</mn></msub></mtd><mtd><msub><mi>p</mi><mn>23</mn></msub></mtd></mtr><mtr><mtd><msub><mi>p</mi><mn>31</mn></msub></mtd><mtd><msub><mi>p</mi><mn>32</mn></msub></mtd><mtd><msub><mi>p</mi><mn>33</mn></msub></mtd></mtr></mtable></mfenced><mo>⁢</mo><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi>X</mi><mi>o</mi></msub></mtd></mtr><mtr><mtd><msub><mi>Y</mi><mi>o</mi></msub></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>=</mo><mi mathvariant="bold">P</mi><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi>X</mi><mi>o</mi></msub></mtd></mtr><mtr><mtd><msub><mi>Y</mi><mi>o</mi></msub></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math><img file="EP1556805B1_D0019.tif" /></maths> Therefore, <maths id="math0020" num="(eq 6.6)"><math display="block"><mfrac><mn>1</mn><mi>h</mi></mfrac><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi>X</mi><mi>o</mi></msub></mtd></mtr><mtr><mtd><msub><mi>Y</mi><mi>o</mi></msub></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>=</mo><msup><mi mathvariant="bold">P</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi>x</mi><mi>c</mi></msub></mtd></mtr><mtr><mtd><msub><mi>y</mi><mi>c</mi></msub></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>=</mo><msup><mi mathvariant="bold">P</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>⋅</mo><msup><mi mathvariant="bold">F</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi>x</mi><mi>d</mi></msub></mtd></mtr><mtr><mtd><msub><mi>y</mi><mi>d</mi></msub></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math><img file="EP1556805B1_D0020.tif" /></maths> By using this equation, object coordinates for every template pixels are calculated and color values can be substituted in the template from the texture image of the tracked object. Template matching

0090We employ normalized correlation for the template matching. <maths id="math0021" num="(eq 6.7)"><math display="block"><mi>s</mi><mo>=</mo><mfrac><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover></mstyle><mfenced><msub><mi>x</mi><mi>i</mi></msub><mo>-</mo><mover><mi>x</mi><mo>˜</mo></mover></mfenced><mo>⋅</mo><mfenced><msub><mi>y</mi><mi>i</mi></msub><mo>-</mo><mover><mi>y</mi><mo>˜</mo></mover></mfenced></mrow><mrow><msqrt><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover></mstyle><msup><mfenced><msub><mi>x</mi><mi>i</mi></msub><mo>-</mo><mover><mi>x</mi><mo>˜</mo></mover></mfenced><mn>2</mn></msup></msqrt><mo>⁢</mo><msqrt><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover></mstyle><msup><mfenced><msub><mi>y</mi><mi>j</mi></msub><mo>-</mo><mover><mi>y</mi><mo>˜</mo></mover></mfenced><mn>2</mn></msup></msqrt></mrow></mfrac></math><img file="EP1556805B1_D0021.tif" /></maths> where <i>x_i</i> is a pixel value, <i><o ostyle="single">x</o>_i</i> is the mean of pixel values, <i>y_i</i> is a template value and <i><o ostyle="single">y</o>_i</i> is the mean of template values. The calculated value is between -1.0 and 1.0. The position where the biggest value is found matches the corresponding position <i>(x_di, y_di)</i> in observed screen coordinates to feature position (<i>X_oi, Y_oi,</i> 0) in object coordinates.

0091If at least three corresponding positions can be obtained, T_co can be found for the current image frame using the calculation in previous section.

6.3

Improvements for Performance and Accuracy

6.3.1 Multi Scale Templates and Defocusing

0092Templates can be generated by using (eq.6.6), however if the resolution of the texture image is quite different from the resolution of generated templates, the expected templates cannot be found because of the resampling problem. If an interpolation technique is used in resampling, it could be avoided. But it requires much calculation cost. To overcome this some textured images with several resolutions need to be prepared beforehand.

0093We also assume that the camera does not have automatic focus control and that input images are captured with blur in certain distance between the camera and tracked objects. To compensate for this we defocus some texture images by adopting an averaging filter of 3x3 mask.

6.3.2

Feature Selection

0094Feature points in texture images are registered with our software beforehand so they can be used for template matching. However suitable feature points for template matching depend on the resolution. For example, when the camera is near to the tracked object, the resolution of observed image is high and small letters in the image can be used as feature points. On the other hand, when the camera is far from the tracked object, the resolution of observed image is low and small letters cannot be resolved. To compensate for this suitable feature points are independently registered for different resolutions of the texture image.

0095As many feature points as possible are registered, and the best of these are dynamically selected in the tracking phase. Because we don't use special hardware for the template matching, the selection of the least number and optimal locations of feature points is desired in order to reduce the calculation cost as much as possible. In addition, the order of selection of feature points is important and is done iteratively with the tracking of each feature point.

0096We employ a heuristic feature selection method as follows. First of all, the most important feature selection policy is that four feature points are detected from images. If this is impossible, detection of three feature points is needed. If fewer than three feature points are detected, then tracking fails. When a feature point is selected, template matching is done for the selected feature. If the template matching succeeds, in other words the maximal value of normalized correlation is greater than 0.7, the feature point are stored and selection of next feature point is continued. If the template matching fails, the feature point is rejected and selection of an alternative feature point is continued. The conditions used by this selection policy are as follows: <ol id="ol0002" compact="compact"><li>1) Common condition that is not relative to selection order <ul id="ul0005" list-style="none" compact="compact"><li>1.1 - The position of the feature point has to be within the image window when its 3D position is projected into the observed screen coordinates by using the T_co matrix obtained from the previous frame.</li><li>1.2 - The resolution of the feature point is satisfied with the condition predefined for each feature when it is projected into the observed screen coordinates.</li></ul></li><li>2) Selection of the first feature point The feature position is the farthest from image center.</li><li>3) Selection of the second feature point The feature position is the farthest from the first feature point.</li><li>4) Selection of the third feature point The area of the triangle that is made with the first and second feature points is maximum.</li><li>5) Selection of the fourth feature point The area of the rectangle that is made with the first, second and third feature points is maximum.</li><li>6) Selection of the fifth feature point</li></ol> The feature is selected in registered order.

0097When template matching succeeds for four feature points, the transformation matrix T_co is calculated from them based on (eq.6.4). If the error is less than a certain value (5.0 in experiments), the object tracking succeeds. If not, missed detections might be included and the detection of a fifth feature point is carried out. If one is found, the transformation matrices T_co are calculated for all combinations of four feature points in the set of five points. Then the transformation matrix with minimum error is picked up as a result. If the detection of a fifth feature point fails, transformation matrices T_co are calculated for all combinations of three feature points in the set of four points. Then the transformation matrix with minimum error is picked up as a result. If the minimum error value is greater than a threshold, the object tracking fails.

6.3.3

Improvement of Performance on Template Matching

0098Normalized correlation has a high calculation cost while it detects matching point well. Our template size is 24x12 pixels for a 640x240 image. Images of 640x480 are input but field sequential images are used for template matching. To further improve performance, template matching is done for gray-scale pixel values that are calculated by averaging color pixels. At the moment, the dimension of matching data is 24x12x1=288 and its calculation cost is still high.

0099To reduce the calculation cost, we employ two steps template matching. First of all, a coarse search is carried out. In scanning on the search area, template matching is done once for every 3 pixels in the x direction and the positions of best three results are stored. Also (eq.6.9) is used for this template matching. <maths id="math0022" num="(eq 6.9)"><math display="block"><mi>e</mi><mo>=</mo><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>0</mn></mrow><mn>11</mn></munderover></mstyle><mspace width="1em" /><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>11</mn></munderover></mstyle><mfenced open="|" close="|"><mfenced><mi>I</mi><mfenced><mn>2</mn><mo>⁢</mo><mi>i</mi><mo>,</mo><mi>j</mi></mfenced><mo>-</mo><mover><mi>I</mi><mo>‾</mo></mover></mfenced><mo>-</mo><mfenced><mi>T</mi><mfenced><mn>2</mn><mo>⁢</mo><mi>i</mi><mo>,</mo><mi>j</mi></mfenced><mo>-</mo><mover><mi>T</mi><mo>‾</mo></mover></mfenced></mfenced></math><img file="EP1556805B1_D0022.tif" /></maths> where <i>I</i>(<i>i,j</i>) is a pixel value at position (<i>i, j</i>) in the region on which template overlaps, <i><o ostyle="single">I</o></i> is an average pixel values in the region in which the template overlaps, <i>T</i>(<i>i</i>,<i>j</i>) is a pixel value at position (<i>i</i>,<i>j</i>) in the template and <i><o ostyle="single">T</o></i> is an average pixel value in the template. As mentioned before, the template size is 24x12 pixels. However this calculation uses one pixel in every two pixels so the calculation cost is reduced.

0100Next, a fine search is carried out. A normalized correlation with a 24x12 template size is used based on (eq.6.7) in regions around the previously obtained three positions. Then the position with highest correlation value is found as the result.

0101In order for this template matching to work well, matching results in the region around the correct position have to keep a high similarity so that they are included in the best three results in the coarse search. Defocusing the texture images aids this 2 step matching process as well.

6.4

Offline Automatic Feature Detection

0102Many suitable feature points have to be registered in images of all resolutions so that the template matching described in section 3 works well. There are two conditions for suitable feature points. <ol id="ol0003" compact="compact"><li>1) There are no similar regions within the search size of template matching.</li><li>2) Similarity within three pixels from the feature point is high.</li></ol>

0103We have developed a method for automatic detection of the best feature points. Suitability as a feature point is examined at every position for texture images of all resolutions. For each point in the texture image, the region of which the point is center is extracted as a template and the maximum value of the normalized correlation is calculated from a search area of 49x49 pixels, excluding the center 5x5 pixel region. This value is calculated at every position in a texture image.

0104<figref idref="f0012">Figures 14A and 14B</figref> are diagrams showing preliminary feature point extraction results. <figref idref="f0012">Figure 14A</figref> shows preliminary feature point extraction results for the image of <figref idref="f0010">Figure 12A</figref> while <figref idref="f0012">Figure 14B</figref> shows preliminary feature point extraction results for the image of <figref idref="f0010">Figure 12B</figref>. Bright pixels in these images means little correlation value, that is, bright position are suitable for condition 1 as a feature point. The square marker regions in the images are also omitted from this calculation.

0105Next, normalized correlation is carried out for the 5x5 region, excluding the center position. If the minimum value is greater than 0.6 and the maximum value less than 1.0, then the position is registered as a feature point. However if its template region has overlaps with the template regions of pre-registered feature points, it is cancelled. <figref idref="f0013">Figures 15A and 15B</figref> are diagrams showing preliminary feature point extraction results. <figref idref="f0013">Figure 15A</figref> shows preliminary feature point extraction results for the image of <figref idref="f0010">Figure 12A</figref> while <figref idref="f0013">Figure 15B</figref> shows preliminary feature point extraction results for the image of <figref idref="f0010">Figure 12B</figref>. Each figure shows feature points extracted at three different levels of resolutions: feature points identified by red boxes at a high level of resolution, feature points identified by green boxes at a medium level of resolution, and feature points identified by blue boxes at a low level of resolution.

6.5

Experiments

0106Experiments were done for texture images in <figref idref="f0001">Fig.1</figref>. We used a PC with an Intel Pentium4 2.0GHz, Linux OS, an analog video capture card and a GeForce3 graphics card. A camera was attached on a HMD and its shutter speed was 1/250sec. 640x480 images were captured and the tracking program was able to work accurately at about 30 frames per seconds. While tracking succeeds, 16 wire-frame cubes are overlaid on the tracked objects.

0107<figref idref="f0014 f0015">Figures 16A-16H</figref> are tracking diagrams showing the results of sample tracking experiments. We can see virtual objects are suitably overlaid on the tracked objects in some conditions.

0108<figref idref="f0015">Figures 17A-17D</figref> show template matching results for example images. The rectangles arrayed along the left edge of each figure show the feature templates generated by the facility for the matched features. Green rectangle regions in images are accepted matching regions and yellow rectangle regions are rejected regions. We can see template matching is attempted until 4 matching regions are found. So registration works well even when textures are occluded by a hand.

0109Tracking sometimes failed when a tracked object rotates quickly because template matching is robust for translation but not robust for rotation of the tracked regions. Another problem was pose and position calculation from 3 feature points. When 3 feature points are almost in a straight line, the registration was bad and it caused tracking to fail in next frame. So the condition to select 3 feature points in the set of 4 points has to be considered.

0110It will be appreciated by those skilled in the art that the above-described facility may be straightforwardly adapted or extended in various ways. While the foregoing description makes reference to preferred embodiments, the scope of the invention is defined solely by the claims that follow and the elements recited therein.