Method and system for calculating a transformed image from a digital image

0001The present invention provides a method and system for computing a transformed image from a digital image and formatted information relating to a geometric transformation.

<i>Solution</i>

Process

0002For example, the document <patcit id="pcit0001" dnum="US4695964A"><text>US 4,695,964</text></patcit> discloses a method of correcting geometric distorted satellite images. The function of correspondence between the raw image and the corrected image is determined according to the orbit of the satellite or the angle of travel of the images. The correction is calculated by applying the inverse of the mapping function to all pixels in the image. This known method entails the problem that calculating a position of a point in the image is highly time consuming.

0003The invention relates to a method for calculating a transformed image from a digital image and formatted information relating to a geometric transformation, in particular formatted information relating to the distortions and / or chromatic aberrations of a device chain. The method includes the step of computing the transformed image from an approximation of the geometric transformation. As a result, the computation is sparing in memory resource, in memory bandwidth, computing power and therefore in electrical consumption. It also results that the transformed image has no visible or annoying defect for its subsequent use.

0004The digital image is composed of pixels hereinafter referred to as digital pixels. The transformed image is composed of pixels hereinafter referred to as transformed pixels. The transformed pixel is characterized by a transformed position and a transformed value. Preferably, according to the invention, the method comprises the step of calculating the values ​​of the transformed pixels by implementing a general algorithm comprising the following processes:<ul id="ul0001" list-style="dash" compact="compact"><li>process (a), selection process in the digital image, from the formatted information, for each transformed position, of a block of digital pixels,</li><li>process (b), computing process, from the formatted information, for each transformed position, of a digital position in said block of digital pixels,</li><li>process (c), computing process for said transformed position of the transformed pixel value as a function of the values ​​of the digital pixels of said block of digital pixels and said digital position.</li></ul>

0005The formatted information includes parameters. The parameters make it possible to choose at least one mathematical function related to said geometrical transformation. The mathematical function or functions make it possible to calculate the block of digital pixels and the digital position from the transformed position.

0006Preferably, according to the invention the general algorithm is implemented by proceeding as follows:<ul id="ul0002" list-style="dash" compact="compact"><li>selected transformed pixels, hereinafter referred to as the initial transformed pixels, are selected</li><li>methods (a), (b) and (c) of the general algorithm for the initial transformed pixels are applied to obtain initial digital pixel blocks and initial digital positions,</li></ul>

0007Each transformed pixel other than the initial transformed pixels is applied to an optimized algorithm comprising the following processes:<ul id="ul0003" list-style="dash" compact="compact"><li>process (d), process of selecting a block of digital pixels in the digital image, from the initial digital blocks and / or from each initial transformed position,</li><li>process (e), process of calculating a digital position in the block of digital pixels, from the initial digital blocks and / or from each initial transformed position,</li><li>process (f), process of calculating the transformed pixel value as a function of the digital pixel values ​​of the digital pixel block and the digital position.</li></ul>

0008It follows from the combination of technical features that it is thus possible to use formatted information requiring complex calculations for the initial numeric points and to reduce the overall computation time by applying a simpler algorithm to the other points, while retaining a good approximation of the geometric transformation.

0009The method is implemented with hardware and / or software processing means. Preferably, according to the invention, the optimized algorithm implements exclusively integer data or fixed point. It follows from the combination of the technical features that it is possible to execute the general algorithm and the optimized algorithm without processor or floating operator, even if the processes (a) and (b) make floating computations, since (a) ) and (b) are executed much less often than (c) and (d) and it is then possible to emulate the few floating operations used, if any. It results from the combination of technical features that it is thus possible to embed the algorithms for example in a camera by consuming as little power as possible and going as fast as possible.

0010Preferably, according to the invention the method further comprises the step of quantizing the digital positions to obtain quantized digital positions. It follows from the combination of the technical features that steps (c) and (f) can be implemented with a limited input number which allows to tabulate coefficients and thus to use a much smaller cache memory and have a lower main memory bandwidth.

0011Preferably, according to the invention, the method further comprises the step of calculating blocks of coefficients. Processes (c) and (f) are performed in:<ul id="ul0004" list-style="dash" compact="compact"><li>using the quantized digital position to select a block of coefficients,</li><li>calculating the transformed pixel value from the coefficient block and the block of digital pixels.</li></ul>

0012It follows from the combination of the technical features that the calculation of the blocks of coefficients can be done before compilation.

0013According to an alternative embodiment of the invention, the calculation processes (c) and (f) of the transformed pixel value can also be applied to a transformation other than the geometrical transformation, in particular the attenuation of the image blur. . As a result, it is possible to realize by consuming less energy and less time, several transformations of the image.

0014The digital image can come from a sensor with multiple channels. Channels can be combined to produce color planes. Preferably in this case, according to the invention, the calculation processes (c) and (f) of the transformed pixel value also make it possible to combine the channels in order to obtain the color planes. It follows from the combination of technical features that, in the case of 3 RGB color planes, the calculation time and power consumption to implement the general algorithm and / or the optimized algorithm are divided up to three. It also results from the combination of technical features that accuracy is better. It also results from the combination of technical features that, in the case of a device that integrates a channel combination function, including a digital camera, it is possible at low additional cost to add the processing of geometric transformations.

0015The digital image can be composed of color planes. Preferably in this case, according to the invention, the method is such that, to correct the chromatic aberrations, a different geometrical transformation is applied to each color plane.

0016Preferably, according to the invention, the method further comprises the step of combining the geometric transformation with another variable geometric transformation according to the digital image, in particular a zoom. It results from the combination of technical features that it is possible with a small overcost in time and energy, to apply to the digital image another geometrical transformation including a zoom, at the same time as the geometric transformation. It also results from the combination of technical features that it is possible to apply the geometric transformation to a digital image that has undergone another geometric transformation.

0017The formatted information may depend on variable features depending on the digital image, including the size of the digital image. Preferably in this case, according to the invention, the method further comprises the step of determining the value of the variable characteristics for the digital image. The processes (a) and (b) use the formatted information depending on the value, thus determined, of the variable characteristics. It follows from the combination of the technical features that the implementation of the method for formatted information dependent on a variable characteristic is reduced to the implementation of the method for formatted information that does not depend on any variable characteristic.

0018Preferably, according to the invention, the formatted information is related to distortion defects and / or chromatic aberrations of the appliance chain. The parameters are related to a measured field.

0019The transformed image may differ from the image obtained by applying the geometric transformation to the digital image. Preferably in this case, according to the invention, the method further comprises the following steps:<ul id="ul0005" list-style="dash" compact="compact"><li>the stage of choosing a threshold,</li><li>the step of choosing the general algorithm and / or the optimized algorithm and / or the initial transformed points, so that the difference is less than the threshold.</li></ul>

0020It follows from the combination of technical features that the computation time is minimal to achieve a certain level of image quality.

0021The transformed image may differ from the image obtained by applying the geometric transformation to the digital image. Preferably in this case, according to the invention, the method further comprises the following steps:<ul id="ul0006" list-style="dash" compact="compact"><li>the stage of choosing a threshold,</li><li>the step of choosing the general algorithm and / or the optimized algorithm and / or the initial transformed points and / or the quantization of the quantized digital positions, so that the difference is less than the threshold.</li></ul>

0022It follows from the combination of technical features that the computation time is minimal to achieve a certain level of image quality.

0023Preferably, according to the invention, the method further comprises the step of sorting the transformed positions so that the blocks of digital pixels selected by the processes (a) and / or (d) have an average number of digital pixels common determined. It results from the combination of technical features that a small cache memory or a small number of registers is sufficient to contain a large part of the pixel values ​​necessary for successive iterations of the processes (a) and / or (d). It also results from the combination of technical features that the memory bandwidth is greatly reduced. It also results from the combination of technical features that it is not necessary to keep the complete digital image in a memory. It also results from the combination of technical features that it is not necessary to keep the complete transformed image in a memory. It also results from the combination of technical features that the cost and power consumption are reduced.

System

0024A system for calculating a transformed image from a digital image and formatted information relating to a geometric transformation, including formatted information relating to distortion and / or chromatic aberrations of a device chain. The system includes calculating means for calculating the transformed image from an approximation of the geometric transformation.

0025The digital image is composed of pixels hereinafter referred to as digital pixels. The transformed image is composed of pixels hereinafter referred to as transformed pixels. The transformed pixel is characterized by a transformed position and a transformed value. Preferably, according to the invention, the system comprises calculation means for calculating the values ​​of the transformed pixels by implementing computer processing means comprising a general algorithm comprising the following processes:<ul id="ul0007" list-style="dash" compact="compact"><li>process (a), selection process in the digital image, from the formatted information, for each transformed position, of a block of digital pixels,</li><li>process (b), calculation process, from the formatted information, for each transformed position, of a digital position in the block of digital pixels,</li><li>process (c), computing process for the transformed position of the transformed pixel value as a function of the digital pixel values ​​of the digital pixel block and the digital position.</li></ul>

0026The formatted information includes parameters. The parameters allow to choose at least one mathematical function related to the geometric transformation. The mathematical function or functions make it possible to calculate the block of digital pixels and the digital position from the transformed position.

0027Preferably, according to the invention, the calculation means implement the general algorithm as follows:<ul id="ul0008" list-style="dash" compact="compact"><li>by selecting transformed pixels, hereinafter referred to as the initial transformed pixels,</li><li>applying the general algorithm (a), (b) and (c) processes for the initial transformed pixels to obtain initial digital pixel blocks and initial digital positions.</li></ul>

0028The computing means apply to each transformed pixel other than the initial transformed pixels an optimized algorithm comprising the following processes:<ul id="ul0009" list-style="dash" compact="compact"><li>process (d), process of selecting a block of digital pixels in the digital image, from the initial digital blocks and / or from each initial transformed position,</li><li>process (e), process of calculating a digital position in the block of digital pixels, from the initial digital blocks and / or from each initial transformed position,</li><li>process (f), process of calculating the transformed pixel value as a function of the digital pixel values ​​of the digital pixel block and the digital position.</li></ul>

0029The general algorithm or the optimized algorithm is executed by hardware and / or software processing means. According to an advantageous variant embodiment, the optimized algorithm implements only integer data or fixed point data.

0030Preferably, according to the invention, the system further comprises computer processing means for quantifying the digital positions so as to obtain quantized digital positions.

0031Preferably, according to the invention the system further comprises calculation means for calculating blocks of coefficients. The processes (c) and (f) are executed by the calculation means in:<ul id="ul0010" list-style="dash" compact="compact"><li>using the quantized digital position to select a block of coefficients,</li><li>calculating the transformed pixel value from the coefficient block and the block of digital pixels.</li></ul>

0032The calculation processes (c) and (f) of the transformed pixel value are also applicable to other transformations than the geometrical transformation, in particular the attenuation of the image blur.

0033The digital image from a sensor can have multiple channels. Channels can be combined to produce color planes. Preferably, according to the invention, the calculation processes (c) and (f) of the transformed pixel value are such that they also make it possible to combine the channels in order to obtain the color planes.

0034Preferably, according to the invention, the digital image is composed of color planes. The system is such that, in order to correct the chromatic aberrations, the computer processing means make it possible to apply to each color plane a different geometrical transformation.

0035Preferably, according to the invention, the system is such that the computer processing means make it possible to combine the geometric transformation with another variable geometric transformation according to the digital image, in particular a zoom.

0036The formatted information may depend on variable features depending on the digital image, including the size of the digital image. Preferably in this case, according to the invention the system further comprises computer processing means for determining the value of the variable characteristics for the digital image concerned. The computing means executing the processes (a) and (b) use the formatted information depending on the value, thus determined, of the variable characteristics.

0037Preferably, according to the invention, the formatted information is related to distortion defects and / or chromatic aberrations of the appliance chain. The parameters are related to a measured field.

0038The transformed image may differ from the image obtained by applying the geometric transformation to the digital image. Preferably in this case, according to the invention, the system further comprises computer processing means making it possible to implement a general algorithm and / or an optimized algorithm and / or initial transformed points so that the difference is smaller. at a chosen threshold.

0039The transformed image may differ from the image obtained by applying the geometric transformation to the digital image. Preferably in this case, according to the invention, the system further comprises computer processing means making it possible to implement a general algorithm and / or an optimized algorithm and / or initial transformed points and / or the quantization of the digital positions. quantized so that the difference is less than a chosen threshold.

0040Preferably, according to the invention, the system further comprises computer processing means for sorting the transformed positions so that the blocks of digital pixels selected by the processes (a) and / or (d) have an average number of common digital pixels determined.

detailed description

0041Other features and advantages of the invention will become apparent on reading the description of the embodiments of the invention given by way of indicative and nonlimiting example, and of:<ul id="ul0011" list-style="dash" compact="compact"><li>the <figref idref="f0001">figure 1</figref>an illustration of a simplified embodiment of the invention;</li><li>the <figref idref="f0001">figure 2a to 2d</figref>an improved exemplary embodiment of a method for calculating a transformed image according to the invention;</li><li>the <figref idref="f0002">figure 3</figref>, an operating flow chart of the process of <figref idref="f0001">figure 2a</figref> ;</li><li>the <figref idref="f0002">figure 4</figref>, an illustration of a step of calculating the value of a transformed pixel;</li><li>the <figref idref="f0003">figure 5a</figref>a flowchart of a variant of a method for calculating a transformed image according to the invention;</li><li>the <figref idref="f0004">Figures 5b and 5c</figref>, explanatory illustrations of the process of <figref idref="f0003">figure 5a</figref> ;</li><li>the <figref idref="f0005">figure 6</figref>, an illustration of the step of calculating a value of a transformed pixel making it possible to implement several types of corrections;</li><li>the <figref idref="f0006">figure 7</figref>an illustration of the invention applied to a color image;</li><li>the <figref idref="f0007">figure 8</figref>, an improvement of the invention for calculating neighboring pixels,</li><li>the <figref idref="f0007">Figures 9a</figref> and <figref idref="f0008">9b</figref>, the application of the invention to VRVB type color images,</li><li><figref idref="f0009">figure 10</figref> : Formatted IF information related to geometric distortion defects P5 of a P25 device of a P3 device chain,</li><li><figref idref="f0009">figure 11</figref>an example of a system according to the invention.</li></ul>

Apparatus

0042Referring in particular to the <figref idref="f0009">figure 10</figref>we will describe the concept of P25 device. Within the meaning of the invention, a device P25 can be in particular:<ul id="ul0012" list-style="dash" compact="compact"><li>an image capture apparatus or an image capture apparatus, such as a disposable camera, a digital camera, a reflex camera, a scanner, a fax machine, an endoscope, a camcorder, a surveillance camera, an integrated camera or connected to a telephone, a personal assistant or a computer, a thermal camera, an ultrasound machine,</li><li>an image rendering apparatus, such as a screen, a projector, a television set, virtual reality glasses or a printer,</li><li>a human being with vision defects, for example astigmatism,</li><li>a device that we want to look like, to produce images having for example an appearance similar to those produced by a Leica branded device,</li><li>an image processing device, for example a zooming software which has the edge effect of adding blur,</li><li>a virtual device equivalent to several P25 devices,</li></ul>

0043A more complex P25 device such as a scanner / fax / printer, a photo printing Minilab, a video conferencing device can be considered a P25 device or more than one P25 device.

Device chain

0044Referring in particular to the <figref idref="f0009">figure 10</figref>we will now describe the notion of P3 appliance chain. A P3 appliance chain is a set of P25 appliances. The notion of P3 apparatus string may further include a notion of order.

0045The following examples are P3 device strings:<ul id="ul0013" list-style="dash" compact="compact"><li>a single device P25,</li><li>an image capture apparatus and an image rendering apparatus,</li><li>a camera, a scanner, a printer for example in a Minilab photo printing,</li><li>a digital camera, a printer for example in a Minilab photo printing,</li><li>a scanner, a screen or a printer, for example in a computer,</li><li>a screen or projector and the eye of a human being,</li><li>a device and another device that you want to look like,</li><li>a camera and a scanner,</li><li>an image capture apparatus, an image processing software,</li><li>an image processing software, an image rendering apparatus,</li><li>a combination of the previous examples,</li><li>another set of P25 devices.</li></ul>

fault

0046Referring in particular to the <figref idref="f0009">figure 10</figref>, we will now describe the concept of default P5. The defect P5 of the apparatus P25, a defect related to the characteristics of the optics and / or the sensor and / or the electronics and / or the software integrated in a device P25; examples of defects P5 are for example geometric distortion, blur, vignetting, chromatic aberration, color rendering, flash uniformity, sensor noise, grain, astigmatism, spherical aberration.

Digital image

0047Referring in particular to the <figref idref="f0001">figure 1</figref>, we will now describe the concept of digital image INUM. INUM digital image is an image captured or modified or restored by a P25 device. The INUM digital image can come from a P25 device in the P3 appliance chain. The digital image INUM can be intended for a device P25 of the P3 appliance chain. In the case of animated images, for example video, consisting of a sequence in the time of still images, the term digital image INUM: a fixed image of the image sequence.

Formatted information

0048Referring in particular to the <figref idref="f0009">figure 10</figref>we will now describe the concept of IF formatted information. Formatted information IF is called data related to a geometrical transformation, for example data related to the defects P5 of one or more apparatuses P25 of the appliance chain P3 and making it possible to calculate a transformed image ITR taking into account the defects P5 of the P25 device. The defects P5 may be in particular defects of geometric distortion and / or chromatic aberration. To produce the IF formatted information, various methods based on measurements, and / or captures or restitution of references, and / or simulations can be used.

0049For producing the IF formatted information, it is possible, for example, to use the method described in the international patent application filed on the same day as the present application on behalf of the company Vision IQ and under the title: "Method and system for producing formatted information related to geometric distortions. " In this application, there is described a method for producing formatted IF information related to the P25 apparatus of a P3 appliance chain. The device chain P3 comprises in particular at least one image capture device and / or at least one image recovery device. The method includes the step of producing IF formatted information related to geometric distortions of at least one device in the chain.

0050The apparatus P25 for capturing or restoring an image on a medium. The apparatus P25 comprises at least one fixed characteristic and / or a variable characteristic according to the image. The fixed characteristic and / or variable characteristic is likely to be associated with one or more characteristic values, in particular focal length and / or focus and their associated characteristic values. The method includes the step of producing measured formatted information related to geometric distortions of the apparatus from a measured field. The IF formatted information may include the measured formatted information.

0051For producing the IF formatted information, it is possible, for example, to use the method described in the international patent application filed on the same day as the present application on behalf of the company Vision IQ and under the title: "Method and system for reducing the frequency of updates of image processing means. " In this application, there is described a method for reducing the frequency of updates of image processing means, including software and / or a component. Image processing means for modifying the quality of digital images from or intended for a device chain. The device chain comprises at least one image capture apparatus and / or at least one image rendering apparatus. The image processing means implement formatted information related to the defects of at least one apparatus P25 of the appliance chain P3. The IF formatted information depends on at least one variable. Formatted information to match some of the variables and identifiers. The identifiers make it possible to determine the value of the variable corresponding to the identifier taking into account the identifier and the image. It follows from the combination of technical features that it is possible to determine the value of a variable, especially in the case where the physical meaning and / or the content of the variable are known only after the diffusion of the processing means. image. It also results from the combination of technical features that the time between two updates of the correction software can be spaced. It also results from the combination of technical features that the various economic actors that produce devices and / or image processing means can update their products independently of other economic actors, even if they radically change the characteristics of their products. product or can not force their client to update their products. It also results from the combination of technical features that a new functionality can be rolled out gradually starting with a limited number of economic actors and pioneering users.

0052To produce the IF formatted information, it is possible, for example, to use the method described in the international patent application filed on the same day as the present on behalf of the company Vision IQ and under the title: "Method and system for providing formatted information to image processing means. ", publication no. <patcit id="pcit0002" dnum="WO03007239A1"><text>WO 03/007239 A1</text></patcit>. In this application, there is described a method for providing, in a standard format, IF formatted information to image processing means, including software and / or components. IF formatted information is related to defects in a P3 device chain. The device chain P3 comprises in particular at least one image capture apparatus and / or an image restoration apparatus. The image processing means use the IF formatted information to modify the quality of at least one image from or intended for the P3 appliance chain. The IF formatted information includes data characterizing P5 defects of the image capture apparatus, including distortion characteristics, and / or data characterizing defects in the image rendering apparatus, including distortion characteristics.

0053The method includes the step of providing at least one field of the standard format with the IF formatted information. The field is designated by a field name. The field containing at least one field value.

0054For searching and preparing the IF formatted information, one can for example use the method described in the international patent application filed on the same day as the present application on behalf of the company Vision IQ and under the title: "Method and system for modifying the quality of at least one image from or intended for a chain of apparatus." In this application, there is described a method for modifying the quality of at least one image from or intended for a given appliance chain. The determined device chain comprises at least one image capture apparatus and / or at least one image rendering apparatus. The image capture apparatus and / or the image restoration apparatus, gradually put on the market by different economic actors, belong to an indeterminate set of devices. The P25 devices of the set of devices have P5 defects which can be characterized by formatted information. The method comprises, for the image concerned, the following steps:<ul id="ul0014" list-style="dash" compact="compact"><li>the step of listing formatted information sources relating to the devices of the set of devices,</li><li>the step of searching automatically, among the formatted information thus listed, specific formatted information relating to the determined device chain,</li><li>the step of automatically modifying the digital image INUM by means of image processing software and / or image processing components taking into account the specific formatted information thus obtained.</li></ul>

Variable feature

0055We will now describe the notion of variable characteristic. According to the invention, a variable characteristic is called a variable measurable factor from one digital image INUM to the other captured, modified or restored by the same apparatus P25, and having an influence on the defect P5 of the captured image, modified or returned by the P25, including:<ul id="ul0015" list-style="dash" compact="compact"><li>a global variable, fixed for a given digital image INUM, for example a characteristic of the apparatus P25 at the moment of capturing or restoring the image related to a user setting or linked to an automatism of the apparatus P25</li><li>a local variable, variable in a given digital image INUM, for example x, y or ro, theta coordinates in the image, making it possible, if necessary, to apply a different local processing according to the zone of the digital image INUM.</li></ul>

0056Generally not considered as a variable characteristic: a measurable and variable factor from one P25 device to another but fixed from one INUM digital image to another captured, modified or restored by the same P25 device, by for example the focal length for a P25 camera with fixed focal length.

0057The IF formatted information may depend on at least one variable characteristic.

0058By variable characteristic, one can hear in particular:<ul id="ul0016" list-style="dash" compact="compact"><li>the focal point of optics,</li><li>the resizing applied to the image (digital zoom factor: magnification of a part of the image, and / or the sub-sampling: reduction of the number of pixels of the image),</li><li>the non-linear correction of luminance, for example the gamma correction,</li><li>the contour enhancement, for example the deflashing level applied by the P25 apparatus,</li><li>the sound of the sensor and the electronics,</li><li>the opening of the optics,</li><li>the focus distance,</li><li>the number of the view on a movie,</li><li>the over or under exposure,</li><li>the sensitivity of the film or the sensor,</li><li>the type of paper used in a printer,</li><li>the position of the center of the sensor in the image,</li><li>the rotation of the image with respect to the sensor,</li><li>the position of a projector in relation to the screen,</li><li>the white balance used,</li><li>flash activation and / or power,</li><li>the exposure time,</li><li>the gain of the sensor,</li><li>the compression,</li><li>the contrast,</li><li>another setting applied by the user of the apparatus P25, for example a mode of operation,</li><li>another automatic adjustment of the P25 device,</li><li>another measurement done by the P25.</li></ul>

Variable characteristic value

0059The concept of variable characteristic value VCV will now be described. The variable characteristic value VCV is called the value of the variable characteristic at the moment of capturing, modifying or restoring a given digital image INUM.

Parameterizable model

0060For the purposes of the invention, a parameterized model is a mathematical model that can depend on the variable characteristics and relates to one or more defects P5 of one or more apparatuses P25. The IF formatted information relating to a P5 defect of a P25 device may be in the form of the parameters of a parameterizable model depending on the variable characteristics.

Calculation of the transformed image

0061Referring to the <figref idref="f0001">figure 1</figref>a general embodiment of the method and system of the invention will be described.

0062A digital image INUM comprises a set of image elements called pixels PXnum.1 to PXnum.n regularly distributed on the surface of the INUM image. On the<figref idref="f0001">figure 1</figref>these pixels have the shape of squares but they could have a completely different form, circular for example; this depends on the design of the surfaces intended to carry the image in the image capture and rendering apparatus. Moreover, on the<figref idref="f0001">figure 1</figref>, the pixels have been represented in a joined way but in reality, generally there is a spacing between the pixels.

0063The transformed image ITR also comprises a set of pixels called transformed pixels PXTR.1 to PXTR. Each transformed pixel is characterized by a transformed position pxtr and a transformed value vxtr.

0064A transformed image is a corrected or modified image that is obtained by applying a transformation to an image. This transformation, which can be a geometrical transformation, is achieved by integrating formatted information into the calculation that takes into account, for example, defects in the devices used or characteristics that are to be introduced into the image.

0065It will be noted that the formatted information may relate to a limited number of transformed pixels and / or integrate values ​​of variable characteristic VCV according to the image (for example the focal length, the focus, the aperture, etc.), in this case there may be an additional step performed for example by interpolation so as to be reduced to simple formatted information such as that of an apparatus having no variable characteristics, so that the case of the devices with variable focal length is reduced to the case of a device with fixed focal length.

0066In the example of a function x ', y' = f (x, y, t) where t is a variable characteristic, the formatted information may consist of a limited number of values ​​(xi, yi, ti, f (xi, yi, ti)), it is then necessary to calculate an approximation for the other values ​​of x, y, t. According to the same formalism t could be a vector and simultaneously include several variable characteristics. In the case of distortion, the formatted information could possibly consist of vectors making it possible to indicate the displacement that each point follows, or of a set of discrete elements representing the measurement points used during a prior calibration step. or else all functions corresponding to an approximation on this discrete set so as to reduce the size of the formatted information.

0067The formatted information may include data relating to the devices used and studied in a previous phase, but also any information in the format Exif format or otherwise that would provide information on the settings of the camera at the time of shooting (focal, focus , aperture, speed, flash ...).

0068The digital image INUM represents for example the capture of the image of a rectangle. On the<figref idref="f0001">figure 1</figref>, the pixels corresponding to the drawing of the rectangle have been blackened. Due to the distortions of the capture apparatus the rectangle has been deformed as on the INUM image represented in<figref idref="f0001">figure 1</figref>. The invention makes it possible, using a CAPP calculation incorporating approximations according to, among other things, a desired final precision, to obtain the values ​​vxtr of transformed pixels of position pxtr and to obtain on the transformed image ITR a rectangle whose position and pixel value are corrected to the nearest approximations.

0069Note that the application of the CAPP algorithm can, in the case of a distortion, bring the distorted image back to a perfect or almost perfect image. The same algorithm can also bring the deformed image to another possibly distorted image differently so as to produce an image similar to a known type of image (fish-eye effect, retro distortion ...). The same algorithm also makes it possible to reduce the distorted image towards a non-perfect image (in the sense of a square right as on the <figref idref="f0001">figure 1</figref>) but optimal in the eyes of the observer so that it is possible to possibly compensate for geometric defects of perception of the human eye.

0070The <figref idref="f0001">figure 2a</figref> represents an example of the method and improved system according to the invention. On the digital image and on the transformed image, only the pixels that are useful for the description of this method and system have been represented. On the transformed image is represented a pixel PXTR.i whose value we want to know. At the position of a transformed pixel pxtr.i in the transformed image corresponds, in the digital image, a position pxnum.i which is obtained from formatted information (IF) including for example in the case of distortion , the displacement vector needed to add to pxnum.i to fall back to pxtr.i.

0071The invention comprises various stages thus described and represented in <figref idref="f0002">figure 3</figref>.

0072First, the position pxtr.i of a transformed pixel PXTR.i is identified in the transformed image (step ET1). During a next step (ET2) knowing the position in the ITR image, it can be deduced, using IF formatted information that reflects the characteristics of the capture and / or image reproduction apparatus, the position a block of pixels BPNUM.i of the digital image INUM, which block includes the position pxnum.i of a point corresponding to the transformed pixel PXTR.i. Salt on the example of the<figref idref="f0001">figure 2a</figref>a block of pixels has 5 x 5 pixels.

0073Then, (step ET3), using the formatted information, calculates, for the transformed position pxtr.i of the pixel PXTR.i, the numerical position pxnum.i of the point of the block of digital pixels corresponding to the pixel PXTR.i. As can be seen on the<figref idref="f0001">figure 2a</figref>, this point does not necessarily correspond to the position of the center of a pixel of the block of pixels BPNUM.i. It is therefore understood that the transformed value of the pixel PXTR.i does not correspond to the value of a digital pixel.

0074During the next step (ET4), knowing the position of a point pxnum.i in the BPNUM.i block, the value of a fictitious pixel in the BPNUM block is calculated. i whose point pxnum.i is the center. This imaginary pixel PXFIC has a value that must take into account the value of the pixels surrounding the pxnum.i point in the block and therefore also takes into account the position of this point in the block. According to a simple method, the values ​​of the pixels surrounding the point can be averaged.

0075It is also possible to average the value of the pixels of the block by assigning to the value of each pixel a coefficient which is a function of the distance of this pixel from the position pxnum.i of the point. This amounts to making the following sum for the entire block of pixels.<maths id="math0001"><math display="block"><mi mathvariant="normal">Σvxnum</mi><mn>.</mn><mi mathvariant="normal">j</mi><mo>×</mo><mi>cj</mi><mfenced><mi>pxnum position</mi><mn>.</mn><mi mathvariant="normal">i digital</mi></mfenced></math><img file="EP1523730B1_D0001.tif" /></maths>with vxnum.j = value of a pixel in the block.

0076Cj = coefficient of the pixel as a function of the position pxnum.i of the point.

0077The coefficient of each pixel of a block, depending on the position pxnum.i of the point, can be calculated in different ways. A first way is to use an analytical expression for the calculation of the coefficients of each pixel of the block, as a function, for example, of the order of the approximation surface, the accuracy of the calculator and the position pxnum.i in the block.

0078A simpler way is to limit the number of possible positions of a point in the block by a technique of quantifying the position pxnum.i. In this case, it is expected to make a coefficient table for each possible position of a point in the block. For the different quantized values ​​of positions in a block, several series of coefficients will be calculated with in each series a coefficient value per pixel of the block.

0079Subsequently, during step ET4 previously described, the position pxnum.i of the point in the block will be quantized, which will make it possible to access a series of coefficients with a coefficient per pixel of the useful block. It will suffice to multiply this series of coefficients by the series of values ​​of the same pixels.

0080The <figref idref="f0002">figure 4</figref> schematizes such a process. The position pxnum.i of a point is quantized to a described value that can take a limited number of values ​​from a to n.

0081For each described value of position of a point, one has a table of coefficients Ca to Cn. For a value, "a" for example, the table QU1 gives access to a table of coefficients a1 to year. The value "a", for example, provides access to the table Ca. The table Ca has as many coefficients a1 to year that the pixel block BPNUM.i comprises pixels. These coefficients were each computed as a function of the position pxnum.i of the point in the block so as to give a weight to the value of each pixel. It will be readily understood that the pixels furthest from the position point pxnum.i in the block will have a low weight, while the nearest pixels will have a higher weight.

0082Using the coefficient table Ca and the set of pixel values ​​of the BPNUM.i block, the operation is carried out <maths id="math0002"><math display="block"><mi mathvariant="normal">Σ</mi><mfenced><mi>vxnum</mi><mn mathvariant="normal">.</mn><mi mathvariant="normal">j</mi><mo mathvariant="normal">×</mo><mi>cj</mi></mfenced></math><img file="EP1523730B1_D0002.tif" /></maths>so as to obtain the value of a fictional pixel PXFIC and it is this value that will be assigned to the transformed pixel pxtr.i of the transformed image ITR.

0083In an exemplary embodiment, it can be considered that the position of a point pxnum.i obtained, using formatted information, from the position of a transformed pixel can be expressed by an integer part (or a first number of addressing) and a decimal part (or a second number of addressing). The quantification of the address pxnum.i which has been previously described may relate for example only to the decimal part.

0084The integer part may be the address of a pixel block BPNUM.i in the INUM image or more precisely the address of a defined pixel of this block, for example the pixel PXnum.1 of the block.

0085The decimal part will indicate the address of the point in the block. For this address it will be possible to quantify the number of possibilities and decide that it can only be expressed on a limited number of bits which will limit the number of tables of coefficients Ca to Cn. For example with an address in the block expressed on 3 bits we will have to predict 8 tables of coefficients Ca to Cn.

0086It is thus possible to execute the method of the invention without processor or floating operator, even if the steps ET2 and ET3 make floating calculations, since these steps will be likely to be executed much less often than the step ET4 and that it is then possible to emulate the few floating operations used, if it exists so that it is possible to embed such algorithms for example in a camera by consuming as little power as possible and going as fast as possible. In this case, the system according to the invention comprises hardware and / or software processing means without processor or floating operator.

0087However, it is possible to use so-called floating processors or operators (example: Intel Pentium processor) as opposed to so-called integer processors or operators (example: Texas Instruments TMS320C54xx signal processing processor).

0088The foregoing method can be applied to all the pixels of the transformed image to know their value from the values ​​of the digital pixels.

0089For this example of a method, for example, a block of digital pixels of square shape has been taken. However as shown in<figref idref="f0001">Figures 2b, 2c and 2d</figref>, this block could have any other form (circular, hexagonal, etc.).

0090We will now describe an improvement of the method and system of the invention to achieve a faster processing. It can be seen that for each transformed pixel, calculating a position of a point in the digital image using the formatted information takes time that can be saved.

0091The <figref idref="f0003">figure 5a</figref> represents a flowchart of an exemplary variant of a method for calculating a transformed image.

0092First, (step ET0), in the transformed image, a number of pixels are selected that will be called initial transformed pixels. For example, four pixels PXINIT.1 to 4 are chosen.

0093For each transformed pixel, the previously described method is carried out. That's why, on the<figref idref="f0003">figure 5a</figref> we find the steps ET1 to ET4 which are the same as those of the <figref idref="f0002">figure 3</figref>. When the steps ET1 to ET4 have been applied to an initial transformed pixel PXINIT.1 to 4, the system questions (step ET5) whether any initial transformed pixels have been processed; if this is not the case, the process of steps ET1 to ET4 recommences for another initial transformed pixel. When all the initial transformed pixels have been processed, the system is ready to proceed to the next step ET6 of the method. At the end of step ET5, we find ourselves in the situation represented in <figref idref="f0004">figure 5b</figref>, with:<ul id="ul0017" list-style="dash" compact="compact"><li>in the transformed ITR image, four transformed pixels PXINIT.1 to 4;</li><li>in the digital image INUM, four initial digital pixel blocks BPINIT.1 to 4 in which there are pninit points 1 to 4. The positions of blocks BPINIT.1 to 4 in the INUM image are known (see step ET2 of the process). The positions of the pninit points 1 to 4 in their respective blocks are also known (see step ET3 of the method).</li></ul>

0094It is now a question of calculating the value of a transformed pixel PXTR.i of the transformed image. On the<figref idref="f0004">figure 5c</figref>, this pixel PXTR.i is located between the initial transformed pixels, but this is not mandatory.

0095During the step ET6, a pixel PXTR.i is thus selected and its position pxtr is acquired in the transformed image.

0096During the step ET7 the relative position of the pixel PXTR.i relative to the initial transformed pixels PXINIT.1 to 4 is calculated. For example, knowing the positions (px.1, px.2, etc.) of all these pixels, the distances 11 to 14 between initial transformed pixels are calculated as well as the distances d1.1, d1. 2, d2.1, ... d4.2 of the pixel PXTR.i to the initial transformed pixels PXINIT.1 to 4. Next, the position of the pixel PXTR.i is expressed in relative position with respect to the initial transformed pixels and / or with respect to the distances separating the initial transformed pixels. This relative position can thus be expressed in percentages of distances. This position can also be expressed in the form of a bilinear relation of the type:<maths id="math0003"><math display="block"><mfenced><mi mathvariant="normal">d</mi><mo>⁢</mo><mn mathvariant="normal">1.1</mn></mfenced><mo>⁢</mo><mfenced><mi mathvariant="normal">d</mi><mo>⁢</mo><mn mathvariant="normal">2.1</mn></mfenced><mo>⁢</mo><mfenced><mi>px</mi><mn mathvariant="normal">.4</mn></mfenced><mo mathvariant="normal">+</mo><mfenced><mn mathvariant="normal">1</mn><mo mathvariant="normal">-</mo><mi mathvariant="normal">d</mi><mo>⁢</mo><mn mathvariant="normal">1.1</mn></mfenced><mo>⁢</mo><mfenced><mi mathvariant="normal">d</mi><mo>⁢</mo><mn mathvariant="normal">2.1</mn></mfenced><mo>⁢</mo><mfenced><mi>px</mi><mn mathvariant="normal">.3</mn></mfenced><mo mathvariant="normal">+</mo><mfenced><mi mathvariant="normal">d</mi><mo>⁢</mo><mn mathvariant="normal">1.1</mn></mfenced><mo>⁢</mo><mfenced><mn mathvariant="normal">1</mn><mo mathvariant="normal">-</mo><mi mathvariant="normal">d</mi><mo>⁢</mo><mn mathvariant="normal">2.1</mn></mfenced><mo>⁢</mo><mfenced><mi>px</mi><mn mathvariant="normal">.2</mn></mfenced><mo mathvariant="normal">+</mo><mfenced><mn mathvariant="normal">1</mn><mo mathvariant="normal">-</mo><mi mathvariant="normal">d</mi><mo>⁢</mo><mn mathvariant="normal">1.1</mn></mfenced><mo>⁢</mo><mfenced><mn mathvariant="normal">1</mn><mo mathvariant="normal">-</mo><mi mathvariant="normal">d</mi><mo>⁢</mo><mn mathvariant="normal">2.1</mn></mfenced><mo>⁢</mo><mfenced><mi>px</mi><mn mathvariant="normal">.1</mn></mfenced></math><img file="EP1523730B1_D0003.tif" /></maths>or any other higher order relationship.

0097During step ET8, the digital pixel block BPNUM.i containing the point resulting from the mathematical projection of the transformed pixel PXTR.i on the digital image is located from the previously calculated proportionality relations.

0098During the step ET9, with the same proportionality rules, the position pxnum.i, in the block BPNUM.i, of the point resulting from the mathematical projection of the transformed pixel PXTR.i on the digital image is determined.

0099At this stage the use of the proportionality rules applied to the set of points of the image is economical in computation time compared to the use of the formatted information.

0100As before, the position of the pxnum.i point can be quantized and expressed on a limited number of bits. We can take the same quantization basis as that adopted when calculating the values ​​of the initial transformed pixels so as to use the same coefficient tables to be applied to the block of digital pixels to obtain the value of the pixel PXFIC and therefore that of the transformed pixel PXTR .i (step ET10).

0101It will be noted that:<ul id="ul0018" list-style="dash" compact="compact"><li>the initial transformed pixels can be arranged in a regular matrix, that the pitch of the matrix can be a power of two to be able to benefit from the parallel instructions of a processor, in particular the instructions MMX, SSE, SSE2 of Intel or 3DNow of AMD.</li><li>the location of a block of pixels (step ET8) and the location of a point in the localized block of pixels (step ET9) can be done by bilinear interpolation.</li></ul>

0102According to an alternative embodiment of the invention, it is possible to provide the method of calculating the pixel value in several steps in order to reduce the size of the blocks and the final number of addition and / or multiplication performed by the computer. For certain values ​​of the coefficients Cj representing a interpolation operator said mathematically separable for a person skilled in the art, it is possible to perform the general algorithm and / or optimized for a horizontal geometric transformation in a first time and again for a vertical geometric transformation on the intermediate result, so that the number of multiplications and / or additions necessary to process a block is theoretically divided by two.

0103It should also be noted that:<ul id="ul0019" list-style="dash" compact="compact"><li>quantizing the positions of the transformed pixels and the digital pixels makes it possible to produce constant and limited size coefficient tables, which makes it possible to use a much smaller cache memory and to have a lower main memory bandwidth. This is possible because the calculations of steps ET3 and ET10 depend only on the digital position in the pixel block.</li><li>the coefficient tables can be realized once and for all in the system. Of course, it is possible to have several types of tables of coefficients of different sizes corresponding to blocks of digital pixels of different sizes. Thus, it will be possible by modifying the precision of the quantization to modify the rate of the approximation of the processing and thus to modify the quality of the transformed image obtained. It is also possible to have several types of coefficient tables of the same size but in which, for the same position of a point in a block of digital pixels, the different types of tables contain coefficients of different values, if necessary. to compensate for the choice of different types of distinct defects (distortion, vignetting, blur ...).</li><li>An interesting dimension of the coefficient tables can be 4 x 4 without this being mandatory.</li><li>The coefficients can be those of a bi-cubic interpolation and the calculations of the steps ET3 and ET10 can be done in the form of a dot product.</li></ul>

0104The approximation of the processing resulting from the quantization over a limited number of bits of the pixel positions, as just described, leads to having a transformed image that may differ from an image obtained entirely by mathematical transformation. In these conditions it may be decided to limit this approximation by providing, in the method, a threshold selection step. This step will include the choice of a quantization threshold by deciding that the quantization will not fall below a threshold determined so as to have a number of digital positions of a point in a block of pixels that is not below this threshold. It will thus be possible to optimize the calculation time for a given transformed image quality.

0105The <figref idref="f0007">figure 8</figref> represents an improvement of the invention to save memory exchange time and therefore the processing time. It is easy to imagine that the calculation of the value of two neighboring transformed pixels leads to the use of two blocks of digital pixels having common pixels and thus to read twice (according to this example) the values ​​of these common pixels. The improvement of the invention aims to avoid this double reading. For this purpose it is expected to sort the positions of the transformed pixels so as to treat them in a certain order. For example, we can decide to process the transformed pixels of the transformed image, line by line and in each line, pixel by pixel by describing each line from left to right. This is how on the<figref idref="f0007">figure 8</figref>, we can first treat the pixel PXTR.1, then the pixel PXTR.2, etc.

0106The processing of the pixel PXTR.1, according to the method described above, gives rise to:<ul id="ul0020" list-style="dash" compact="compact"><li>when selecting a block of digital pixels BPNUM1,</li><li>to the positioning of a point in this block of pixels,</li><li>calculating the value of the transformed pixel PXTR.1 as a function of the position of this point and the value of the pixels of the block.</li></ul>

0107According to the improvement of the method and system of the invention, the values ​​of the pixels BPNUM.1 are kept in a temporary memory. In practice, the storage of the values ​​of these pixels can be done, for example, in cache memory.

0108The processing of the pixel PXTR.2 gives rise to the selection of the block of digital pixels BPNUM.2, for example, which has pixels in common with the BPNUM.1 block previously used. Since the values ​​of these pixels have been kept in temporary memory, the system needs only to fetch the values ​​of the BPNUM.2 pixels that are not common with the BPNUM.1 block; on the<figref idref="f0007">figure 8</figref>, these are the pixels in the right column of the BPNUM.2 block. After the processing of the pixel PXTR2, the values ​​of the pixels of the block BPNUM.2 are stored in temporary memory so as to prepare the processing of the transformed pixel according to PXTR.3.

0109According to a variant of the invention, it is possible to keep in temporary memory only the values ​​of the pixels common to the two blocks of pixels used successively. In general, only the values ​​of an average number of pixels common to two blocks of pixels used successively will be memorized in temporary memory.

0110The preceding description has been made in the context of the distortion correction, but the invention is also applicable to the correction or the attenuation of the blur, so that it is possible to carry out several image transformations while consuming less energy and less time.

0111This same description is also applicable for the case of a string of devices where one or more devices have defects such as distortion. A combination of formatted information would be translated into the distortion space by a simple vector summation and would treat the entire fault on the device chain in a single pass.

0112It is also possible to combine in the same transformation, several types of corrections such as the filling of the discrete values ​​RGB and / or CMYK on a color image sensor, the removal of vignetting of the image, the addition of a function magnification or zoom, a change of perspective.

0113The <figref idref="f0005">figure 6</figref>, schematizes the calculation steps (ET4 or ET10) in which it is possible to provide, in order to calculate the value of each transformed pixel, additional coefficient tables making it possible to perform other corrections. This is how, on the<figref idref="f0005">figure 6</figref>, the coefficient tables Ca to Cn make it possible to calculate the corrected pixel values ​​after correction of the distortions. The CA and CN coefficient tables are used to correct other defects such as blurring, vignetting of the image, etc. The multiplication of the tables between them, as indicated on the<figref idref="f0005">figure 6</figref>, or any other operation to combine the coefficients of a table, allows to combine several corrections of different types and thus to save processing time and energy consumption. Such a provision allows discretion to make any correction, or all corrections if the user wishes.

0114The application of the exemplary embodiments of the methods and system described above to the treatment of a color image will now be described.

0115It can be considered that a color image comes from several channels and provides several image planes or color planes.

0116As represented in <figref idref="f0006">figure 7</figref>, a color image is considered to consist of an INUMR red image, INUMV green image and INUMB blue image.

0117The methods described above are executed up to the step of calculating the value of a transformed pixel, that is to say up to the step ET3 of the <figref idref="f0002">figure 3</figref> or ET9 of the <figref idref="f0003">figure 5a</figref>. The position of a block of digital pixels (BPNUMR, BPNUMV, BPNUMB) is thus known in each INUMR, INUMV and INUMB image, as well as the position in these blocks, of a point corresponding to the transformed pixel for which it is desired to calculate the value. The value of the different pixels constituting the blocks BPNUMB, BPNUMV and BPNUMB is also known.

0118The position of the point corresponding to the transformed pixel to be calculated, makes it possible to access a table of coefficients, for example the table C1 on the <figref idref="f0006">figure 7</figref>. As before, we perform the calculation<maths id="math0004"><math display="block"><mi mathvariant="normal">Σ</mi><mfenced><mi>vxnum</mi><mn>.</mn><mi mathvariant="normal">i</mi><mo>×</mo><mi>cj</mi></mfenced></math><img file="EP1523730B1_D0004.tif" /></maths>realizing the sum of the products of the value of a pixel of the block by the corresponding coefficient of the coefficient table. This is done for the BPNUMR block of the red image, then for the BPNUMV block of the green image and finally for the BPNUMB block of the blue image. This gives the value of a transformed pixel in its red, green and blue components.

0119Such a method and system allows, for the color, to save time and energy consumption. Such treatment can be integrated into a digital camera. It can then be considered to add to the processing of geometric transformations.

0120The invention is applicable to the processing of color images in which the numbers of pixels of different colors or numbers of color channels (r, v, b) are equal. For example, a trichrome image IMrvb, as represented in<figref idref="f0007">figure 9a</figref>, may have two green pixels for a red pixel and a blue pixel which is generally the case of color sensors where the eye is very sensitive to wavelengths of green. Moreover, a color image is considered from the point of view of the software processing of the image as comprising as many images (or color planes) as there are basic colors in the image. This is how the IMrvb image of the<figref idref="f0007">figure 9a</figref> is considered to have the three color planes IMr, IMv, IMb. In the method and system described above, each color plane will be processed independently so as to obtain three transformed images. In addition, it may be interesting to give a value to each pixel of each of these transformed images. The<figref idref="f0008">figure 9b</figref> represents three transformed image planes ITRr, ITRv and ITRb corresponding to the three color image plans IMr, IMv and IMb of the <figref idref="f0007">figure 9a</figref>. The calculation of the value of each pixel of the different transformed image planes is done by applying the method described above and by taking for each transformed color pixel (red, for example) a digital pixel block of the corresponding color digital image plane (the IMr plane according to the example taken).

0121Moreover, in the application of the method and system to a color image, to save time and electrical energy, it will be possible to combine the treatments of the three color planes.

0122In particular, it will be possible to apply the same geometrical transformation between a transformed color image plane and a digital color image plane to compensate, for example, for the distortion.

0123Different geometrical transformations can also be applied to different color planes in order to correct chromatic aberrations and / or distortion.

0124Note that in an RGB (three-channel) image, the transformed color planes can be obtained by taking one pixel out of three.

0125In the description which precedes the transformed image and the digital image correspond by geometrical transformation. It is possible to combine a first determined geometrical transformation resulting in particular from the fixed and known characteristics of the devices used with a second geometrical transformation such as a variable geometrical transformation which is a function of the digital image and in particular, for example, capture conditions. of the image (zoom for example), so that it is possible with a little extra cost in time and energy, to apply to the digital image the other geometrical transformation, the zoom according to the example taken, at the same time as the first geometrical transformation and that it is possible to apply the variable geometric transformation on a digital image having undergone the first geometric transformation.

0126The second geometrical transformation can be notably:<ul id="ul0021" list-style="dash" compact="compact"><li>a rotation,</li><li>a rotation of a quarter or a half-turn,</li><li>a translation,</li><li>a zoom,</li><li>a resize,</li><li>a change of perspective,</li><li>a change of reference,</li><li>a projection,</li><li>a geometric transformation represented by a function making it possible to calculate x 'and y' coordinates from x and y coordinates,</li><li>identity</li><li>a combination of these examples,</li><li>any geometric transformation linear or not.</li></ul>

0127The combination between the two geometric transformations can be done for various purposes:<ul id="ul0022" list-style="dash" compact="compact"><li>to apply to the digital image the second geometrical transformation including a zoom, at the same time as the first geometrical transformation for, for example in the case where the geometrical transformation is linked to a distortion, to be able to obtain a transformed image of the same size as the digital image, despite the resizing necessary to have straight image edges;</li><li>combine the distortions of several devices in a chain to correct them in one step;</li><li>in the case for example of a digital camera producing images of various sizes by applying a zoom, and where the geometric transformation is related to the geometric distortions of the apparatus, the combination of the geometric transformation with the zoom makes it possible to correct the distortions; information relating to the history of the treatments applied to the digital image may be useful for this purpose.</li></ul>

0128The combination between the two geometric transformations can be done in various ways:<ul id="ul0023" list-style="dash" compact="compact"><li>by calculation on the parameters,</li><li>by calculation on the mathematical functions, for example if it is about vector field by addition of vectors, if it acts of polynomials by combination of the polynomials; mathematical functions can be functions calculating x 'and y' coordinates from x and y coordinates,</li><li>by calculating at each iteration of the processes of the steps ET2 and ET3, in this case the implementation of the optimized algorithm makes it possible to make the extra cost in calculation time of the application of the second geometrical transformation to the initial transformed points the method of <figref idref="f0003">figure 5a</figref>.</li></ul>

0129The invention is applicable in any image processing system but also in the cameras, camcorders, surveillance cameras, webcam type computer cameras.

0130The embodiments of the invention thus described may be implemented in software form or in the form of wired components.

0131The <figref idref="f0009">figure 11</figref> represents an example of a system according to the invention. The system comprises calculating means MC. The calculation means MC implement the method according to the invention for calculating the transformed image ITR from the digital image INUM, the value of the variable characteristics VCV and the formatted information IF relating to a transformation. geometric, including formatted IF information relating to the distortions and / or chromatic aberrations of the P3 appliance chain.

0132The system may comprise IT processing means MTI, in particular to implement the method according to the invention for:<ul id="ul0024" list-style="dash" compact="compact"><li>quantify the numerical positions so as to obtain quantized numerical positions, and / or</li><li>to correct the chromatic aberrations by applying to each color plane a different geometrical transformation, to combine the geometrical transformation with another geometrical transformation variable according to the digital image, notably a zoom,</li><li>determine the value of the variable characteristics VCV, for the digital image concerned, for example by using the data recorded in Exif format in the file containing the digital image INUM,</li><li>sort the transformed positions.</li></ul>

Application of the invention to cost reduction

0133Cost reduction is a method and system for decreasing the cost of a P25 apparatus or P3 appliance chain, including the cost of the optics of a device or appliance chain; the process of:<ul id="ul0025" list-style="dash" compact="compact"><li>decrease the number of lenses, and / or</li><li>simplify the shape of the lenses, and / or</li><li>design or choose in a catalog an optical lens with P5 defects greater than those desired for the device or the appliance chain, and / or</li><li>use less expensive materials, components, processes or manufacturing processes for the appliance or appliance chain, adding P5 defects.</li></ul>

0134The method and system according to the invention can be used to reduce the cost of a device or a chain of devices: digital optics can be conceived, IF formatted information relating to the device's P5 defects or the appliance chain can be produced, using this formatted information to allow image processing means, integrated or otherwise, to modify the quality of the images from or intended for the apparatus or the appliance chain, so that the combination of the apparatus or the appliance chain and image processing means make it possible to capture, modify or restore images of the desired quality at a reduced cost.