Imaging methods and apparatus.

0001This invention relates to imaging methods and apparatus.

0002More particularly the invention relates to such methods and apparatus for forming three-dimensional images.

0003The invention is applicable to computed tomography imaging methods and apparatus and will be described with particular reference thereto although it will be appreciated that the invention also has application to other imaging methods and apparatus such as magnetic resonance imaging methods and apparatus.

0004Computed tomography (CT) and magnetic resonance imaging (MRI) enables cross-sectional images of the human anatomy to be generated. Data obtained by CT or MRI is assembled and a gray scale is assigned in accordance with data obtained from a particular section of the data.

0005As organs are, however, three-dimensional in reality, a series of slices or scans must be taken, and a mental integration is required to visualize the actual anatomy. A need is presented to place such a series of reconstructed planar images in a more familiar format. This type of image reformation aids physicians in their mental integration. It also aids in filling the communication gap between radiologists, referring physicians, collaborators, and their patients. Better planning in medical treatments or surgical operations is resultant from this type of imaging.

0006In the last decade, there have been many suggested methods to reformat cross-sectional images and present them as a three-dimensional image from any perspective view. Essentially, five different approaches have been tried. These include the cuberille approach, the octree approach, the ray tracing approach, the triangulation approach, and the contour approach. Each of these approaches, however, suffers from its own distinct disadvantages.

0007In order for a three-dimensional imaging processor to become practically useful, a system response must be extremely fast, ideally less than one second per frame if not real time. In the prior art systems, implementation at such speeds could only be achieved with use of special purpose hardware. Such special purpose hardware is extremely expensive, and is generally not cost effective. Such dedicated hardware is not usable for other process operations except for its particular three-dimensional reformatting.

0008Another disadvantage of the prior art lies particularly with the cuberille-type approach. In such systems, preprocessing of original image data is required as the underlying model of this approach assumes that the three-dimensional object is composed of cubes of the same size. Since, in fact, input data from a CT or MRI scanner is typically not cubic as the distance between two consecutive slices is commonly much larger than the slice of pixels or reconstructed images, resolution and accuracy is forfeited.

0009The present invention contemplates new and improved imaging methods and apparatus which overcome all of the above referred problems and others, and provides a system for forming three-dimensional images which is simple, economical, and readily adaptable to general purpose processor means.

0010According to the invention there is provided an imaging apparatus for forming a three-dimensional image of a specimen comprising: acquisition means for acquiring slice data indicative of a physical property of a plurality of substantially planar regions of the specimen, each planar region being divided into a plurality of subregions represented by subregion data representative of that portion of the slice data unique thereto; means for assigning a viewing value to substantially all subregions of at least one of the plurality of generally planar slices, the viewing value being assigned in accordance with subregion data thereof; means for apportioning of at least a first one of the planar regions to form a region of interest; means for defining a boundary of interest within the region of interest; means for assembling image data representative of substantially all subregions of the boundary of interest as a function of subregion data unique thereto; scaling means for assigning a scaled value representative of at least a portion of the image data, whereby data representative of a first, second, and third dimensions of the object is assigned; and means for projecting the image data onto a viewing surface.

0011The invention also provides a method of forming a three-dimensional image of a specimen comprising the steps of: acquiring slice data indicative of a physical property of a plurality of substantially planar regions of the specimen, each planar region being divided into a plurality of subregions represented by subregion data representative of that portion of the slice data unique thereto; assigning a viewing value to substantially all subregions of at least one of the plurality of planar slices, the viewing value being assigned in accordance with subregion data thereof; apportioning of at least a first one of the planar regions to form a region of interest; extrapolating the region of interest to at least a second planar region to form at least one extrapolated region of interest; defining a boundary of interest within the region of interest; assembling image data representative of substantially all subregions of the boundary of interest as a function of subregion data unique thereto; assigning a scaled value representative of at least a portion of the image data, whereby image data representative of a first, second, and third dimensions of the object is assigned; and projecting the image data onto a viewing surface.

0012The invention also provides an imaging apparatus for forming a three-dimensional image of a specimen comprising: acquiring means for acquiring image data representative of a three-dimensional image of a specimen; monitor means having a viewing area; means for projecting the image data to the viewing area; means for defining a cutting surface; means for projecting the cutting surface on the viewing area; means for dividing the image data to at least a first portion and a second portion in accordance with the cutting surface; means for generating modified image data representative of divided image data; and means for projecting the modified image data to a viewing surface.

0013The invention also provides a method of imaging comprising the steps of acquiring image data representative of a three-dimensional image of a specimen; projecting the image data to an associated viewing area; defining a cutting surface; projecting the cutting surface on the associated viewing area; dividing the image data to at least a first portion and a second portion in accordance with the cutting surface; generating modified image data representative of divided image data; and projecting the modified image data to an associated viewing surface.

0014An advantage of the present invention is that a method and apparatus is provided wherein a three-dimensional image is generated from a series of slice scans obtained from conventional imagers.

0015Another advantage of the present invention is the provision of a method and apparatus for generating three-dimensional images with increased fidelity and resolution.

0016Another advantage of the present invention is the provision of a method and apparatus for generating three-dimensional images which does not require specialized hardware.

0017Another advantage of the present invention is the provision of a method and apparatus with which surface density of three-dimensional image may be visualized.

0018Still another advantage of the present invention is the provision of a method and apparatus with which cross-sectional cuttings of a three-dimensional image may be selected and viewed.

0019One method and apparatus in accordance with the invention will now be described, by way of example, with reference to the accompanying drawings in which: <ul id="ul0001" list-style="none"><li>Figure 1 is a block diagram of the apparatus;</li><li>Figure 2 is a diagram illustrating a three-dimensional image generated by the apparatus;</li><li>Figure 3 illustrates a segmented object and a projection thereof onto a viewing surface;</li><li>Figure 4 illustrates a scheme for three-dimensional image data projection onto a viewing area;</li><li>Figure 5 is a flow chart for facilitating generation of the three-dimensional image;</li><li>Figure 6 is a flow chart of the viewing operations of the apparatus;</li><li>Figure 7 is a flow chart illustrating an enhancement of the method and apparatus for allowing surface density information to be displayed on the generated three-dimensional image;</li><li>Figure 8 is a continuation flow chart of Figure 7;</li><li>Figure 9 illustrates a specimen image for cutting and viewing using the apparatus;</li><li>Figure 10 illustrates a procedure for cutting an image using the apparatus;</li><li>Figure 11 is a flow chart of the cutting operation using apparatus; and</li><li>Figure 12 illustrates an alternate cutting operation to that described in Figure 11.</li></ul>

0020Referring to the drawings Figure 1 illustrates a block diagram of a diagnostic imaging apparatus providing a three-dimensional representation of a specimen. An acquisition means for acquiring slice data A is interfaced with a data processor/control circuit B. As illustrated, the acquisition means A is comprised of a CT scanner and will be described with particular reference thereto. It will be appreciated, however, that similar sliced data may readily be acquired by any other suitable slice image apparatus such as an MRI device.

0021The CT scanner is comprised of an x-ray source 10 which projects a fan beam of x-rays through an image circle 12 to a detector array 14. The x-ray source 10 is variable in relation to the image circle 12 to provide relative motion therebetween under the control of motor means 16. A plurality of generally parallel slices is obtainable by incrementing a subject through the image circle 12 between subsequent scans by such means as the gearing 18. A processor 22 interfaces an x-ray tube control circuit 24 which facilitates acceleration/deceleration control of a rotating anode of x-ray tube 10, as well as controlling generation the x-ray fan beam. An array procesor 26 works under control of a program stored in memory means 28. The array processor functions in conjunction with the processor 22, and under programming noted below. Use of an array processor is advantageous for rapid processing of the three-dimensional image data of the present system.

0022Slice data is acquired from the acquisition means A via data acquire circuitry 30. Images generated from the array processor 22 are reconstructed by the image reconstruction circuitry 32. A control panel 20 allows for human interaction with the processor 22. Finally, a display means 34 allows for viewing of a resultant image.

0023In the preferred embodiment, the array processor 26 is comprised of three processor elements for facilitating rapid computation. It will be appreciated, however, that other processing units will function adequately when images are processed in accordance with the teachings of the present system.

0024The processor takes a set of images of consecutive slices of a three-dimensional object generated by the acquisition means A and produces spatially encoded slice data indicative of a physical property thereof. Means is provided for assigning a viewing value to generally all subregions of at least one of the generally planar slices. This viewing value is suitably a gray scale level. These images of consecutive slices are given in a format similar to that of a conventional CT or MRI scanner.

0025The subject procedure for generating the three-­dimensional images renders such a generation to be particularly adaptable to conventional processors such as the subject array processor. Three-dimensional objects under investigation, such as bones or organs, usually extend through many consecutive cross-sectional image slices. For instance, a set of cross-sectional CT images would be required for investigation of a lumbar spine since the spine extends beyond one slice's thickness. To efficiently extract the three-dimensional object from the slice, a three-dimensional box which is large enough to enca psulate the three-dimensional object under investigation is initially selected. This three-­dimensional box, called the box of interest ("BOI") which is smaller than a toll volume represented by a slice set, reduces total information necessary to process and, therefore, reduces the processing time. The BOI functions to apportion each image slice into a two-dimensional region thereof. Each region, referred to as a region of interest ("ROI") is in turn comprised of a plurality of subregions which are represented by data obtained from the data acquisition means. The ROI is preferably selected from a single slice image, and projected or extrapolated onto subsequent slices for practicality. It will be appreciated, however, that in certain situations it may be desirable to select an ROI from two or more regions to encompass a certain volume. For example, a first ROI might be selected having a first set of dimensions, and a second ROI selected having a second set of dimensions which are greater or less than the first, with intermediate slices therebetween being functionally related to the dimensions of the two dimension sets. For most purposes, however, a single ROI with a given set of dimensions extrapolated or projected onto subsequent slices is adequate.

0026After a region of interest has been defined, an object or boundary of interest of a subject is selected from therewithin. Again, such object is suitably selected from a single ROI from a single slice and projected onto subsequent ROI's of the box of interest. In certain situations, however, it is appreciated that the boundary of interest may desirably be selected from two or more of the regions of interest.

0027Selection of the boundary of interest may be made by manual selection from a display, such as by placing a cursor on that boundary, or by isolating a particular boundary with a given gray scale level. In the preferred embodiment, a combination of both is implemented. The region of interest is initially generated as a planar image. A selected range of gray scales is assigned to this region of interest and only those areas falling within this range are then illuminated. An operator or technician then selects, through the control panel 20 (FIGURE 1) which of the surfaces or boundaries within this range are to be taken. This is in turn projected onto subsequent regions of the box of interest.

0028Turning to FIGURE 2, a sample object is illustrated in a box of interest 37 which has in turn been assembled from consecutive slices. The object or specimen 34 is sectioned in its entirety by two slices. Regions of interest 36, 38 are selected from each slice. Each region of interest 36, 38 is itself comprised of subregion data 40 which may be referred to as a picture element or pixel. The pixel is so named due to its use to generate a subsequent image by assignment a unique viewing value or gray scale level thereto which is a function of the physical property of that particular element as gleaned from the slice imaging apparatus.

0029When the pixels 40 of each region of interest 36, 38 are so placed, a volume element ("VOXEL") which is indicative of a volume property of the subject specimen is definable.

0030In general, an object under investigation must undergo further processing from the three-dimensional box which encapsulates it. In the present system, this processing is referenced to as segmentation. Segmentation consists of multiple computer graphics and image processing techniques used in unison. These techniques include thresholding, contouring, and region growing. The segmentation process allows for the image processing to be completed on a standard processor. In segmentation, once the object of interest is extracted from the three-­dimensional box in the fashion illustrated above, the object is represented in a concise fashion. In the present system, the scan line representation technique is implemented. In this technique, an ob]ect is represented by a set of segments which fill the object volume completely. Each segment is, in turn, represented by its two end points, the slice number in which the segment belongs, and the row number of the segment within the slice. Turning particularly to FIGURE 2(b), it will be seen that creation of two such segments has been illustrated. The segment 46 is created from the endpoints (pixels) 48, 50, while the segment 56 is created from the endpoints 58, 60.

0031With reference to FIGURE 3, the presently described three-dimensional reformatting process is capable of generating perspective three-dimensional images of an object 66 in any given viewing direction. Each viewing direction is associated with a rectangle or a square viewing surface such as 68 on which corresponding perspective three-dimensional images are formed. This rectangle or viewing area is referred to as a screen for the reason that the generated three-dimensional image is viewed by displacing it on a two-dimensional viewing area. Such as that continued in display console 34 (FIGURE 1).

0032A perspective three-dimensional view of a three-­dimensional object may be viewed as being comprised of orthogonal projections to the screen of points on the surface of the object onto that screen. To provide a depth cue effect in the viewing of the generated image, the projected points on the screen are assigned, via a scaling means, with a viewing value such as a number representing a shade of gray, called a gray level. This assigned gray level is inversely proportional to a shortest distance from a corresponding point on the surface of the object along a normal to the screen. The viewing directions is assumed to be normal to the screen. In this framework, if two points on a surface of the object project onto the same point of the screen, only a point closest to the screen is visible. Moreover, points on the surface of the object which are closer to the screen are seen painted whiter, and points on the surface which are further away from the screen are darkened to facilitate a pseudo three-dimensional picture.

0033To render the curvature of the surface of the object at a visible point, the scaling means may alternatively or additionally include means to assign a corresponding gray level multiplied with a weight which is a function of a cosine of an angle of the normal to the screen and the normal to the surface of the object that a particular point in consideration. For an efficient implementation in terms of computational time and computer memory, this angle is estimated from the distance of the surrounding points in the screen to corresponding visible points on the surface of the object. More precisely, the formula used to assign a gray level appears below:<img file="EP0318176A2_D0001.tif" />

0034Turning again to FIGURE 3, as a surface rendering is carried out by the processors, rectangular screen 68 is divided into small squares, called screen pixels. For a good resolution of three-dimensional views of the object, it is advantageous to consider a screen just large enough to contain a projection of the object. To achieve this goal, the diagonal of the box of interest is advantageously chosen to be the side dimension of the screen.

0035The magnification factor of the three-dimensional image is suitably achieved by choosing a screen of smaller size as a number of pixels subdividing the screen remains constant. For example, 256 x 256 pixels or 512 x 512 pixels is suitably chosen. The number of pixels of a screen will be referred to as the screen resolution. A change of three-dimensional views of the object is suitably realized by changing a position of the screen, rather than by rotation of an object itself. With continuing to FIGURE 3, such a positioning of the viewing surface 68 is depicted in relation to the object 66. As noted above, the three-­dimensional object is represented by a set of segments. In such a representation, a line segment belonging to the object represents a part thereof. In a case where all slices are parallel to one another, and when division of a slice into pixels is facilitated by rectangular grids as illustrated in FIGURE 2(c), each segment represents a parallelepiped containing it. Dimensions of the parallelepiped 90 are as follows: -the length of the line segment 46 <u style="single">l</u>; -the common side of pixels in an axial plane of the slice <u style="single">w</u>; and -a distance between the slice containing the line segment and the following slice <u style="single">h</u>. For practical purposes, it is assumed that the union of all the parallelepipedes associated with the segments in the object representation is the three-dimensional object to be displayed. This assumption becomes more and more accurate as the distance between two consecutive slices is smaller and the number of pixels making up each slice gets larger.

0036It is further assumed that the sampling of the object in study is uniform, that is, the Whole three-­dimensional box of interest is subdivided into non-­overlapping small parallelepipedes or voxels 74 (FIGURE 3) of common size and shape. This assumption is satisfied in a case where all the slices are subdivided by small pixels of equal size, and a distance between two consecutive slices is constant throughout the entire three-dimensional box. The six faces of a voxel consist of two faces in the two slices sandwiching the voxel, and four other faces connecting the two pixels. With the proper choice of the coordinate system, it is suitably assumed that the faces of all of the voxels are perpendicular to an axis of the coordinate system.

0037With reference to FIGURE 4, an elementary face of a voxel is defined as that in a subdivision of the three-­dimensional box. In the Figure, segments from four slices 80, 82 84, and 86 are illustrated. Each elementary face is advantageously defined as a rectangle perpendicular to one of the axis of the coordinate system.

0038From an assumption that the object to be displayed is approximated by a union of the all the parallelepipedes associated with the line segment representing the object, it sufficient to consider only the elementary faces covering the parallelepipedes to construct a three-­ dimensional surface rendering of the object. In the Figure, concepts related to potentially visible elementary faces, non-visible elementary faces, and classification of potentially visible faces are illustrated. Two types of elementary faces are perpendicular to an axis of reference. One type consists of faces facing toward a positive direction of the axis and the other consists of faces oriented toward the negative. For example, a visible elementary face 92 is perpendicular to the y-axis. All together there are six types of elementary faces.

0039An elementary face is defined to be visible if it contains a visible point. For a given view, some elementary faces are visible, and some are not. An elementary face may be visible for one view, but may not be visible for another view.

0040To increase the speed in the formation of the three-­dimensional perspective image of the object in the given direction to render the system adaptable for use in conjunction with a standard processor, most of the non-­visible elementary faces are excluded from the list of faces to be processed. Criteria are seized upon to recognize non-visible faces for the exclusion process.

0041An elementary face is not visible if it is a common elementary face of two parallelepipedes belonging to the object. For a given view, there exists only three types of faces which may be visible. Elementary faces which are not excluded by these criteria are called potentially visible faces.

0042As elementary faces are classified into six different classes, at first those faces which are non-­visible which satisfy at the first criteria at the same time are suitably eliminated.

0043In the example of FIGURE 4, a second elimination criteria, will be noted. Only two elementary faces of a parallelepiped perpendicular to the x-axis are potentially visible. Both of them correspond to end points of a corresponding segment of the object representation, and both are listed in two different lists. It is assumed that within an image slice, line segments representing a three-­dimensional object are parallel to the y-axis.

0044An elementary face perpendicular to the y-axis facing toward the positive direction is a potentially visible face if it is not an elementary face of a parallelepiped right in front of it. An elementary face perpendicular to the y-axis facing toward the negative direction is a potentially visible face if it is not an elementary face of a parallelepiped immediately behind it.

0045An elementary face perpendicular to the x-axis facing toward the positive direction is a potentially visible face if it is not an elementary face of a parallelepiped immediately on top of it. An elementary face perpendicular to the z-axis facing toward the negative direction is a potentially visible face if it is not an elementary face of a parallelepiped immediately below it.

0046If elementary faces oriented toward the positive direction are potential visible, then elementary faces of the opposite direction are not, and vice versa.

0047Potentially visible elementary faces which are perpendicular to an axis are grouped into two different lists. One list consists of faces which are facing toward the positive direction of the axis, and the other consists of faces facing toward the negative direction. Consequently, the potentially elementary faces of the three-dimensional objects are classified and grouped in different lists.

0048For a given view, each elementary face is projected on a viewing area or screen as a parallelogram. Since the size of the elementary face is the same for all elementary faces of the same type, the size of their projections on the screen remains invariant. Each point of the parallelogram is assigned with its distance to the point of the element face along the viewing direction.

0049If more than two points from different elementary faces are projected to the same point on the screen, the projected point is assigned with the shortest distance.

0050On all potentially visible faces are processed in the above manner, the shading of the image of the object on the screen can be done by assigning to each point on the screen as the following: -the point is a background point if there is no point of an elementary face projected on to it, the assigned gray level is a negative number, for instance minus one thousand; -otherwise, the point corresponds to a visible point of the surface of the object.

0051With regard to formula (1), above, the gray level assigned to the point is inversely proportional to the distance of the corresponding visible point on the screen, and it proportional to a power of the cosine of the maximum of two numbers CUTOFF in AVERD. The number CUTOFF is fixed and is chosen once for all. The number AVERD is the sum of four other numbers, each number being obtained by taking the minimum between a number MAXA and the absolute value of the difference between the distances assigned to one of the four opposite pairs of pixels surrounding the pixel in consideration. In the subsequent implementation, the assigned gray level g is computed as a function of the assigned distance d by FORMULA (1) one above.

0052Turning to FIGURES 5 and 6, a diagram of the three-­dimensional image generation process disclosed has been summarized in flow chart form.

0053The foregoing teaches a system for generating a three-dimensional image of a subject specimen. Although it gives a good representation of the specimen's dimensions, often times surface density properties would be advantageous in an analysis of the specimen. It will be recalled that the originally obtained slice data is obtained by such means as a CT scanner or an MRI scanner. If, for example, data were to have been obtained by a CT scanner, slice data is functionally related to an x-ray density of the specimen. Turning to FIGURES 7 and 8, a system is summarized for implementing this available data to obtain surface density representation on a three-­dimensional image will be described in particularity below.

0054The following routine is adapted for generation of a three-dimensional image with surface density information encoded therein. It is, in the preferred embodiment, comprised of a software routine stored in memory 24.

0055The term "density" as used herein refers to, in the example of a CT scanner, the CT number or to T₁, T₂, IR, ... (weighted or non-weighted), in the case of MRI.

0056To create a three-dimensional image with density information from a series of axial slices, a series of tasks which are necessary for a formation of a three-­dimensional image (with surface information only) must be executed. Moreover, coordinates of points on the surface of the object which are visible at the view in consideration must be recorded during the execution of those tasks. Coordinates of potential visible points in the above-described conditional assignment is recorded using 3 two-dimensional arrays of size equal to the size of the screen. For example, if, relative to a viewing screen, (n,n) is a location of a pixel in the projection of an elementary face, the coordinates of the potentially visible point are recorded in the appropriate array at the location (m,n). If the pixel (m,n) is reassigned with a new distance, the previously recorded coordinates are substituted by the coordinates of the corresponding new potentially visible point.

0057After a shaded three-dimensional image pertaining to the surface of a three-dimensional object is created, a new set of tasks must be performed in order to: <ul id="ul0002" list-style="none"><li>(1) extract density information from the slice data obtained from the object at the visible points, using coordinates which were recorded earlier during the three-dimensional view formation;</li><li>(2) perform necessary density interpolation of the density of appropriate pixels or subregions or interest from two different regions of interest;</li><li>(3) combined this computed density value with the gray level representing the surface of the object at the visible point;</li><li>(4) store the above product at the orthogonal projection of the visible point onto the screen on which the three-­dimensional image is formed.</li></ul>

0058In a first step, in the 3 two-dimensional rays of coordinates or visible points the coordinate representation is converted to a column number, a row number, and a region of interest ("ROI") number so that the density number can be retrieved from the original slice data of an appropriate ROI. An array containing the column number, row number, and ROI number of visible pixels is referred to as the X-array, the Y-array and the Z-array respectively. As the resolution of the third dimension of the original slice images is poor, in general, an interpolation across slices is needed. To economize computer storage, an interpolation code is stored in the Z-­array. During such a conversion and storage, a total number, P of pixels within an ROI which are found in the X, Y, and Z-arrays is also stored for each ROI.

0059In a second step, another two-dimensional array is created with a size equal to that of the screen area. This array, which is used to create a final three-dimensional picture with density information, is called the three-­dimensional image density screen. The image density screen containing the three-dimensional image formed without the presence of density information, as described earlier, is called the three-dimensional image surface screen.

0060In a third step, the three-dimensional image density screen is initialized to zero.

0061In a fourth step, and ROI with a non-zero total number P is read, and the following operations are performed thereon: <ul id="ul0003" list-style="none"><li>(a) a scan through the Z-array is made to ascertain pixels containing ROI numbers matching ROI numbers in consideration. For example, (m,n) may be assumed to be the location of such a pixel.</li><li>(b) a column number and row number from the X, and Y-arrays is retrieved at the location (m,n). (x,y) is assumed to be the column and row number respectively.</li><li>(c) density information d is read from slice data of the ROI at the location (x,y). Using d as the address, a number D is read through a look-up table which was established, once for all, at an early stage right after the listing of all potentially visible elementary faces. The same look-up table may function as the identity look-up table. In this case, if the value D and d are the same; a non-modified density value is obtained.</li></ul>

0062In some instances, however, non-modified density values do not afford good image quality, especially when the dynamic range of d is large and the three-dimensional object has a complex surface boundary. In such a situation, surface structure is lost in some portions of the image due to low dynamic range capability (0 to 255) out of the display monitor device.

0063To circumvent this problem, a non-linear look-up table may be used. An example of such a look-up table is found in a case where it is subdivided into two parts. The lower part, which corresponds to soft tissue areas, serves as an identity look-up table. An upper part, which corresponds to bony areas, is a look-up table of slope, near zero, starting from the tail of the lower part look-up table. <ul id="ul0004" list-style="none"><li>(d) The number D is multiplied with a weight, w, between 0 and 1. This weight number is found through a look-up table using codes embedded in the Z-array at the location (m,n).</li><li>(e) The product w*D is added to the three-­dimensional image density array at the location (m,n).</li><li>(f) The total number P is decremented by 1.</li><li>(g) Steps (a) through (g) are repeated until the number P becomes zero.</li></ul>

0064In step five, the operations of step four are repeated for all ROI's with a non-zero P.

0065In step 6, for all pixels which correspond to a visible point on the three-dimensional object, the three-­dimensional density content is multiplied with their three-­dimensional surface content, and the product is divided by the maximum value of the three-dimensional image surface array. Contents of remaining pixels is set to a negative number, such as minus 1000. This division is necessarily only when a surface array is not normalized, i.e. the shaded value is not in floating point format (a number between 0 and 1). These six steps form the INCLUSION OF DENSITY INFORMATION of FIGURE 8.

0066The aforenoted procedures are summarized in flow chart form for implementation on the processor in FIGURES 7 and 8.

0067With the foregoing, a system is provided for generating a three-dimensional image from a series of slice scans on a conventional processor means. The system further includes enablement for selective addition of surface density information on a generated three-­dimensional object. Often times, it is also desirable to selectively view a selected portion of a three-dimensional object which has been created. For example, if a spinal image column were illustrated, a physician may desire to "split" the spine along one or more planes to facilitate viewing of an interior surface thereof. For example, turning to FIGURE 9, a three-dimensional image of an object or specimen 100 represents a three-dimensional image. It may be desirous to cut the image 100 into one or more sections. Two sections are illustrated as cut along a surface such as that formed by planes 102, 104.

0068In the subject system, three means exist to define a cut surface for a three-dimensional image. In a first, two curves have a common vertex. The first curve is referred to as a primary curve and the second curve as a directional curve. In the second situation, one curve serves to cut the surface. In the third situation, two curves are used to define a cut surface, the curves in this instance, however, have no common vertex.

0069A curve for the foregoing is defined by a finite number of control points. Each point identified on the screen provides a point on the three-dimensional space of the three-dimensional object image. A curve is obtained by connecting two points of the three-dimensional space associated with two consecutive control points.

0070The first case, noted above, is the most difficult to visualize, and will be described in conjunction with FIGURE 10. In this case, a primary curve and a secondary curve share a common vertex. The cut surface is obtained as illustrated in the FIGURE 10.

0071In block I, the primary curve is illustrated at 110 and the directional curve at 112. These curves meet at a common vertex point v.

0072In block II, both ends of the primary curve are extended until they exceed the three-dimensional BOI. The vector 114 joining the common vertex v and the endpoint of a backward extension of the primary curve is called its backward extension vector.

0073In block III, both ends of the directional curve are extended until they exceed the three-dimensional box. The 118 starting from the common vertex is called a backward extension. The vector 118 joining the common vertex and the endpoint of the backward extension of the directional curve is called its backward extension vector. Extensions 116 and 120 are extensions necessary to exceed the BOI.

0074In block IV, the primary curve is translated with a vector of translation equal to backward extension vector of the directional curve.

0075In block V, the directional curve is translated with the vector of translation equal to the backward extension vector of the primary curve. (It will be noted that after completion of the foregoing two steps, the translated curves are caused to again have one common end point called the new common vertex v′.)

0076In block VI, a cut surface is generated by a method of parallelogram completion, starting from the new common vertex v′ of the extended primary and directional curves. Starting from three non-linear points such as the common vertex v′, a point P, (on the translated primary curve) next to v′ and a point D, (on the translated directional curve) create another point C, which is the fourth vertex of the parallelogram P₁, v′, D₁, C. The next parallelogram completion, starting from the three points P₂, P₁, C₁, create a point C₂. And subsequent parallelograms are completed in a like manner. The parallelogram completion is done along the primary curve till the last parallelogram is out of the three-dimensional box.

0077In the second situation, case two above, that being wherein only one curve is used to bisect the three-­dimensional object, the same general steps are followed except that the directional curve is assumed to be in a line perpendicular to the screen.

0078Turning to FIGURE 12, the third situation, case three above is illustrated. In this case, two curves are implemented having no common vertex. The cut surface is generated as follows.

0079First, a curve 200 is isolated which corresponds to a curve drawn on the three-dimensional image 202.

0080Secondly, as there is at most one intersection point between any region of interest with the three-dimensional curve, there are at most two points of intersection between any region of interest with the two curves. See, e.g. points 204 and 206.

0081Thirdly, on a region of interest with two points of intersection, points are connected with a line 208. This line is considered to be a line of intersection of a cut surface with a region of interest.

0082Fourthly, on a region of interest with one point of intersection, the line of intersection of the cut surface is assumed to be the line passing through the point and parallel to the line of intersection of the cut surface with the above slice. If there is no above slice, direction is assumed to be normal to the screen.

0083Fifthly, on a region of interest with no point of intersection, the line of intersection of the cut surface with a region of interest is assumed to be the orthogonal projection onto the region of interest of a line of intersection of the cut surface with the previous region of interest. If this region of interest is the first region of interest, the line of intersection is assumed to be outside the of the region of interest.

0084Lastly, the lines of intersection of the cut surface with all the regions of interest of the three-dimensional box are used to do the cutting of the actual three-­dimensional object. Cutting can be performed from the lines of intersection since the object is defined only with the slices.

0085The three cases allow for cutting of a three-­dimensional object image easily and efficiently along any plane or planes of interest. This provides an aid to physicians and technicians in an examination procedure.

0086The flow of the aforenoted cutting is as follows: <ul id="ul0005" list-style="none"><li>1. Select a three-dimensional image;</li><li>2. Draw 1 or 2 curves on the three-dimensional image to define a cut surface;</li><li>3. Select the portion to do three-dimensional image by selecting a point on the three-­dimensional image;</li><li>4. Perform the patching of the cut surface based on the curves previously drawn on the screen;</li><li>5. The patch surface divides the box of interest (or three-dimensional box) two parts. Identify the part containing the point selected in step 3;</li><li>6. Perform the actual cutting of the three-­dimensional object and collect the part containing the point selected in step 3; and</li><li>7. Do the three-dimensional image reformatting of the collected part.</li></ul>

0087The invention has been described with reference to the preferred embodiment. Obviously modifications and alterations will occur to others upon the reading and understanding of this specification. It is intended that all such modifications and alterations be included insofar as they come within the scope of the appended claims or the equivalents thereof.