FR2639740A1 - METHOD FOR PROCESSING AN IMAGE TO GIVE A ZOOMED CORRESPONDENCE, AND SYSTEM FOR CARRYING OUT SAID METHOD - Google Patents

Abstract

System for processing a medical diagnostic image in order to create a zoom image 31 by which the medical diagnostic image 21 comprises a matrix 27 of rows and columns of regions having input intensity values which are transferred from the specified regions for which a zoom must be carried out in order to designate the regions of a zoom matrix 28 separated by regions of unknown intensity. Stored or produced kernels 26 that are individual to regions of known intensity are convolved with the intensity values of selected neighboring regions of known intensity to obtain intensity values for regions of unknown intensity.

Description

The present invention relates to image processing for diagnosis

  medical and more particularly image processing which involves processing an image zoom. It is often desirable to enlarge the size of part of an image displayed in medical diagnostic image production systems. A displayed zoom image is made up of a certain number of pixels which are contiguous in an initial image now located in the zoom image with new ones.

pixels between the initial pixels.

  For example, a region of interest called ROI is chosen consisting of a given number of contiguous pixels. The region of interest is enlarged to enlarge the entire display screen. To achieve this, the initial contiguous pixels of the region of interest are separated by new pixels placed between the initial pixels. The new pixels placed between the initial pixels are provided with intensity data obtained by interpolation using the intensity values of the initial pixels. In general, interpolation is achieved using techniques such as extracting the intensity values of known pixels, say two pixels surrounding an unknown pixel, by arithmetically adding the intensity values and dividing them by two, in the case where there is only one unknown pixel between two known pixels. When there is only one unknown pixel between the pixel of known value, then weighting factors are used to account for the distances between the unknown pixels and the known pixels. A zoom is generally performed when you want to look at a particular ROI and display it on the entire screen. In the past, zooming has been done mainly by linear interpolation processes which include an arithmetic interpolation described

  previously or analytical interpolation processes.

  In an analytical interpolation, the interpolated value I, must be found by solving the linear equation: f (I) = mX + b, om is equal to the slope of the linear function, b is the value of the function when X is equal to zero, and o X is the location of the pixel in the horizontal direction. Thus, knowing the intensity values of any two pixels provides two points on an intensity graph relative to the location. The two points define a straight line which has a slope m and intersects the intensity axis at point b. The linear interpolation of the two-dimensional case (production of images) ensures linear adjustment in both the X and Y directions. A specific problem that occurs when using linear interpolation is that in real life there is locations where the slope m changes critically - the slope can, for example, reverse. Thus, the following two known pixels must define a line having a slope and the opposite of the slope of the initial linear function. The change in the slope of the line results in artefacts such as staircase artefacts in

the displayed image.

  There are now algorithms that smooth the results of deep changes in the direction of the slope that causes sharp angles in the linear function. However, these algorithms tend in general to smear the image and it is often doubtful whether the remedy for the artifact is not fatal to the quality of the image. A recommended method for improving the images for which a zoom has been carried out consists in performing the interpolation of the pixels using polynomial functions. or, more generally, binomial functions instead of the linear function. However, the processing for a polynomial interpolation becomes very complex and in general requires too much time and memory space because in a binomial and polynomial interpolation there are more arithmetic steps than in a

Linear interpolation.

  As a result, those skilled in the art are always on the lookout for useful interpolation methods for zoom images. This research is particularly intense with regard to the discovery of an interpolation process which will make it possible to carry out a "zoom" "in direct", that is to say the sufficiently rapid realization of the interpolations to process the data of incoming image during acquisition, or can allow operator to vary interactively

  zoom at speeds exceeding 10 frames per second.

  In accordance with the present invention, a method of processing a normal input image to provide

  an output zoom image is stated.

  The input image includes an input matrix of rows and columns of "regions" having input intensity values corresponding to the rows and

  columns of pixels in a normal displayed image.

  The output zoom image includes a matrix of rows and columns of regions having intensity values corresponding to the rows and columns of pixels in a displayed zoom image (here "regions" are often also referred to as "pixels") said method comprising the operations of: specifying a zoom factor and a region of interest containing input intensity values by which a zoom must be carried out, transferring the input intensity values from the specified regions for which a zoom must be

  performs at designated regions of the zoom matrix.

  said designated regions with known transferred intensity values separated by regions of known intensity values, convolving known intensity values including intensity values close to those of designated regions of the zoom matrix to obtain intensity values for regions of known intensity values, and said convolution operation including the operation of choosing a kernel memorized individual to each region of the zoom matrix, said kernel being selected as a function of the location of the row and of the column of the region of values of unknown intensity and being fed with values of intensity known for convolution as a function of zoom, allowing that the values of intensity are

  applied to each region of the zoom matrix.

  A feature of the invention includes an arrangement of a plurality of kernels stored in the form of individual look-up tables for each region of the zoom matrix as a function of the row and of

the region column.

  An additional feature of the invention comprises the step of dividing the zoom matrix into subdivisions between regions of known intensity, each subdivision providing a pointer to the look-up tables, the look-up tables thus designated being convolved with neighboring regions of known intensity and in which the regions of known intensity used in the convolution are

  incremented as a function of the number of sub-

  divisions divided by the zoom factor.

  Yet another feature of the invention includes the step of determining

  an increment value based on the number of sub-

  divisions divided by the zoom factor each time the increment value is used to "step & step" through the kernels lookup tables at

memorized convolution.

  An additional feature of the invention includes the use of kernels based on

polynSms.

  Another characteristic of the invention uses the

kernels based on binomials.

  Another characteristic of the invention is that it is necessary to find the values for the lookup tables only once for each image production system since the kernels used in the convolution process are independent of the format

  image, zoom factor and matrix format.

  Thus, the kernels are calculated once and are memorized on a disk to be loaded in the memory each time the zoom function is called. As a result, an interactive image zoom is practical with this system. An additional characteristic in connection with the invention is the use of the convolution operation characterizing the kernels obtained from a polynomial which are a function only of the location of the region requiring an interpolated value in connection with any processing of any image that might require interpolation, instead of the well-known linear interpolation, in order to improve image quality by

  minimizing artifacts such as stage artifacts.

  Yet another characteristic of the invention used the interpolation method described to translate an image of matrix format (i.e. 340 x 340) into another image of matrix format (i.e. 512 x

  512) with a zoom equal to one (no zoom is performed).

  The above mentioned and other features and objects of the invention will be best understood when

  will be considered in light of the following description

  of a main aspect of the present invention taken in conjunction with the following drawings, in which: Figs. la, lb are illustrative block diagrams of two linear interpolation systems of

the prior art.

  Fig. lc is a representative graph of a

  analytical linear interpolation process.

  Fig. 2 is a block diagram representative of the present inventive interpolation system used for a

zoom.

  Fig. Z is a graphical representation of a function of polynomials defined by four values of known intensity by adapting a curve to the best: known values to allow the determination of

  unknown values at selected locations.

  Fig. 4 represents a consultation table (: ernel) used with the polynomial to convolutional interpolation of the present invention, FIG. 5 is a zoom matrix representation representing grids between regions of known intensity values covering the regions to be provided with intensity values in accordance with the invention, and

  Figs. 6a, 6b, 6c and 6d represent a single pro-

  gram of effective interpolation zoom for computer in language

  Fortram and follow each other.

  Zooming is a well-known image processing procedure in which a region of interest is enlarged, such as for example a region smaller than the image

  displayed whole spread over the complete displayed image.

  To achieve the enlargement, values of known intensity of the regions for which a zoom has been carried out are interpolated to fill the intensity values of the new regions inserted between the regions of known intensity values. More particularly, the acquired input image data is arranged in a matrix form, that is to say in rows and columns of S regions containing intensity values measured before the zoom processing. To zoom, a region of interest of the input image matrix is processed by symmetrically placing the known intensity values of the matrix region in the region of interest on an enlarged matrix having many more matrix regions than 'it is not included in the region of interest. This leaves blank regions in the rows and columns between the regions of known intensity taken from the region of interest of the input image. In the prior art, regions with unknown intensities are fed with intensity values by "linear" interpolation between the

  regions of known intensity values.

  There are many ways to perform linear interpolation. One way is shown in fig. which can be called an analytical process. More particularly, in fig. there is shown a zoom arrangement at 11. The zoom arrangement comprises an input image 12 includes rows il, i2, i3, ... in and columns jl, j2, j3.

  in. In general, such matrices can include 512 rows by 512 columns. To zoom the image, the operator selects a region of interest on an operator input device such as a rolling ball keyboard unit 13 for example. As a variant, the operator can select a central point such as i3, j3 and a zoom factor, say 8. The central processor of the system determines the dimension of the region of interest (ROI), that is to say how much of the matrix region should zoom. The pixel intensity values in the ROI are extracted from the input image data by the extraction unit..DTD: 14 and written in an interpolation operator 16.

  The interpolation operator then performs interpolation using linear interpolation between the selected pixels of a matrix 12 to provide intensity values for the pixels between the

  ROI pixels that are extracted from the input image.

  A writing unit 17 transfers the intensity values here in the pixels of an output image 18 which

  are extracted from the ROI of the input image 12.

  Interpolation is done mathematically. So, for example, if there is a blank region between a pixel having an intensity value of 5 and a pixel having an intensity value of 3, then the interpolated value of the

  region between this will be 5 + 3 divided by 2 or by 4.

  If there are two empty regions between regions with known intensities, then a weighting factor can be used to account for the distance of a

  virgin region from the region with known intensity.

  If the blank region falls between both rows and columns of known pixels, the linear interpolation is performed by weighting in accordance with the distances between four known neighboring pixels. In this way, the zoom image at 18 is made up of regions which all have intensity values to provide a complete image. In the arrangement of the prior art of FIG. lb, an analytical solution is used. Here of 350 new, there is an input image 12a. An operator input device such as a rolling ball keyboard 13a allows the selection of a central point of interest region and a zoom factor. The extraction unit 14a operates in response to information received from the selected region of interest and extracts the data of the selected region of interest from the input image 12a. Only two regions with known intensities should be used to develop the linear equation f (I) = mX + b (represented in fig. Lc o X is the distance at which the region is on the left side of the matrix, m is the slope of the straight line defined by the two points (il, jl) and (i3, j3) and ob is the intensity value of the line when X is zero, in other words, when the line intersects the intensity axis I. From the two data points, the slope m can be determined and b can also be determined.The graph f (I) in Fig. lc represents the intensity I with respect to the horizontal distance X from the intensity axis I. Any value on the function can be determined from the function A similar approach is used to determine the intensity I with respect to the vertical distance Y. A problem presented by linear interpolation is that it often leads to art efacts known as "mixed" artefacts. Mixed artefacts appear

  when discontinuities occur on slopes.

  For example, when on the right side of a known pixel the slope is positive and when on the left side the slope

is negative.

  As a result, an interpolation method using higher order analysis which provides a continuously varying slope is presented. The interpolation process is shown by way of example in the block diagram of FIG. 2. In the past, interpolations of a higher order have not been performed due to the large number of computations required exerting a constraint on the computer and on the system memory. However, the system described here which) performs a convolution in order to interpolate using kernels independent of the image size, the zoom factor and the intensities makes it possible to

higher order interpolations.

  The system 20 comprises an image as input of an acquired data item represented at 21. A data item can be acquired by any of the acquisition modes

  used by the medical diagnostic field, for example.

  The input image again consists of a matrix

  rows and columns that are not shown.

  Means such as a rolling ball keyboard 22 are provided for operator interaction with the input image which the operator uses to select the region of interest or the center of the region of interest plus a factor zoom. In interactive mode, the output image is presented almost instantly on the screen and the operator can modify

  zoom, pan and scroll directly.

  The unit 22 causes an extraction unit 23 to extract intensity values from the appropriate regions of the input image. The appropriate regions are the neighboring pixels necessary for the convolution process. In a polynomial example, four horizontal values and four neighboring vertical regional values (i.e. a minimum of 16 pixels) are extracted. The extracted information is supplied to a memory 25 in a zoom convolution processor 24. It is the function of the convolution processor 24 to supply intensity values to the matrix regions between the extracted X: 0 regions which are part of the image zoom out. This is done using the selected kernels of a plurality of kernels stored in the processor.

  convolution of zoom to the memory of kernels 26.

  The kernels memory is shown in greater detail; detail in 27 although in a preferred embodiment the kernels memory is an integral part of the zoom convolution processor. The plurality of kernels in a preferred embodiment is established in a plurality of look-up tables such as look-up table 28. Means are provided for producing look-up tables which contain the "weights" to be used in the convolution with pixel values

  known to provide missing pixel values.

  In a preferred embodiment, the lookup tables (kernel) are independent of the image data. zoom factor and matrix format. Means are provided for producing such independent look-up tables and for selecting the appropriate look-up table to be used in the convolution operation. The means involve the establishment of a system of independent grids extending between the regions of known intensity for which a zoom has been made. In a preferred embodiment, the grid comprises 16 horizontal lines and 16 vertical lines between each of the regions of the ROI which are for which a zoom has been carried out. The number of grid lines is usually

indicated here by isubX and isubY.

  The weights for the look-up tables are determined using a weight table provided for each grid line intersection. Thus, the input matrix is developed to provide a number of selected lines between each zone of known intensity transferred to the output zoom matrix. In one embodiment, 16 lines are used extending from the middle of one of the pixels of known intensity to the middle of the next pixel of known intensity of the output zoom matrix. Depending on the zoom factor, there is a fixed number of regions that are inserted between regions of known intensity. The intersection of the grid lines closest to the inserted region center is the pointer to (or selects) the desired kernel before being used, the kernel is a lookup table of 16 weights (in our example) which is convoluted with 16 neighboring pixels of known intensity to provide the intensity value of the inserted region for

the output matrix.

  The weights of each intersection of the grid are precalculated IC) as shown in fig. 3. It is assumed that there are 4 points of known value such as f1, f2, f3 and f4 between which the interpolated values such as the intensity value of point X must be determined located between points f2 and f3 (an interpolation

is characterized).

  A function f (X) connecting the points fi, f2, f3 and f4 can be approximated by a third order polyn8me f (X) p (X) = f1 + rjfl + r (r-1l) / 2_t2f, + [r 'r-, <r-2) / 63 f .... <. 1)) o: X = X1 + rh (h is represented in fig. 3) r = (X-X1) / h, 0 <r <3 A fm = f (m + l) - fm (m is a index = 1, 2, 3 ... n) 42fm = / f (m + 1) --bfm 13fm = A 2f (m-1) --jfm In fig. 3, the number of interpolation lines between the known points (input matrix area) Isub is 16 as shown between f and f. A redefinition of the variables using Isub gives: r = [(isubX-1) / Isub] + 1 A = r (r-1) B = A (r-2) Consequently, equation (1) can #tre rewritten as: P (isubX) = f1 + r (f2-f 1) + (A / 2) (f3 - 2f2 + fl) + B / 6 (f4 - 3f3 + 2f2 - fl) ..... (2 ) which can be factored into: P (isubX) = f1 + (1-r + R / 2 - B / 6) + f2 (rA + B / 2) + f3 (A / 2-B / 2) + f4 (B / 6) ..... (3) Equation (3) gives four weighting coefficients as a function of the interpolation location in the horizontal direction: Wxl1 (isubx) = 1-r + A / 2 B / 6 wx2 (isubx) = rA + B / 2 wx3 (isubx) = A / 2 - B / 2 Wx4 (isubx) = B / 6 where the interpolated value of f (X) is: P (isubx ) = Wxl fl = Wx2 f2 + Wx3 f3 + Wx4 f4 .. (4) Thus, the third order interpolation according to a vector of points (ie in the direction X) is

  simply a dimensional convolution kernel.

  Because the graphic zoom involves two-dimensional interpolation, weighting factors are obtained identically in the vertical direction. The result is a kernel of 2) 4 x 4 convolution shown in fig. 4 constructed using: w (isubx, isuby) = wij (isubx, isuby) = wxi (isubx) * wyi (isuby) It should be noted that there are ISUB * ISUB such convolution kernels, in which each is used to find the value at a specific grid intersection for example, if the value of the interpolated point (grid intersection) occurring in isubx = 3 and isuby = 10 is necessary for the output image of the appropriate kernel to be found wij ( 3.10) and be convoluted with the 16 matrix zones adjacent to the matrix

  input to produce the zoom matrix as output.

  With ISUB equal to 16, there are 4K words required

to memorize the kernels.

  In this way, the lookup tables (convolution kernels) provide weights for a convolutional interpolation of the known area value in order to obtain values for the number of zooms located between them as imposed by the zoom factor. A convolution with the look-up tables on the data coming from the input image provides data for the output zoom image represented at 31. The look-up tables are chosen by the location of the grid line intersection la closer to the center of the region for the region looking for an intensity value. In order to facilitate the location of the nearest grid line intersection, an increment value

  is selected by a sub-increment unit 29.

  This value is added to the lookup table pointer for each new region with a generated value. A line from the unit 22 is shown going towards the reading unit 23 to extract the y ROI zone values selected from the input image matrix 21. The zones read are exploited by the kernels which are selected in accordance with the zoom factor determining the 16 neighboring areas of

  known value that are used in convolution.

  So a line from the sub-

  increment 29 is plotted to the zoom convolution processor to determine which areas of

  known values must be convolved with the kernel.

  For example, in fig. 5, the regions between the initial zones O0 of known values (f2.2, f2.3, f3.2 and f3.3) are subdivided into a fixed grid. The fixed grid in a preferred embodiment is a 16 x 16 grid starting at the start of a known area and extending to the beginning of the next known area. It should be understood that other schemes of cyclic grids can also be used in the context of the invention. Grid intersection values are provided using kernels for each intersection. The convolution process begins at the starting positions X, Y defined as: Start X = center X - (matrix format / 2) (1 / zoom) Start Y = center Y (matrix format / 2) (1 / zoom) the center X, center Y and zoom factor are user defined. The matrix dimension is generally that of the input image, but can be

other formats.

  The subdivision pointers (grid intersection) start in subx = suby = 1 and are incremented by: subinc = ISUB / zoom in the X and Y directions as the convolution progresses. So, when the subdivision points become greater than ISUB), then the kernel is shifted and the rest (ISUB-SUBx or ISUB-SUBy is used as the

  new subdivision pointer).

  The convolution process can be carried out either row by row or column by column. However, the process should be cyclical. In other words, if the convolution is carried out row by row, four rows must be stored in the memory of the processor 25 to provide the intensity value of the four zones of neighboring rows necessary to provide the value of each single row inserted in the image zoom out. If one of the rows is no longer necessary, ie when isubY is greater than ISUB, only one row needs to be replaced by the row of the next input image in memory 25 and the process continues without require that an entirely new network be entered into memory 25. For example, in fig. 5 f2, 25 f2.3, f32 and f3.3 are areas with known intensity values transferred from the input image. The zoom factor is 4 and ISUB is 16. There are three areas requiring interpolation values between f2.2 and f2.3 and between f3.2 and f3.3 mime as the following three sets of five areas f2.2, f2.3 and above

f3.2 and f3s, 53-

  Assuming that an intersection t is made row by row, then the memory 25 will have four columns and four rows coming from the initial image which is stored therein to supply the 16 values of intensity necessary for the neighboring areas required for the process of convolution. Thus, in order to obtain the i5 value of area A, the kernel for the grid intersection 19, 24 is used at the same time as the values of the region with four neighboring rows and four neighboring columns: f1, 1, f1 , 2, fl, 35 fl, 4 - {f2,1 'f2,2, f2,35, f2,4 f3,15 f3,25 f3,35 f3,4

f4.1, f4.2, f4.3, and f4.4.

  Similarly, to obtain the value of area B, the kernel for the grid intersection 27, 34 is used at the same time as the values of the mimes 16

neighboring areas.

  In order to obtain the zone intensity value i5, j3, the kernel for the grid intersection closest to the center of the region is used at the same time as the values of the newly incremented known regions: f2.1- f2 , 2, f2.35, f2.4 f3.1, f3.2, f 3.3, f3.4 f4.1, f4.25 f4.3, f4.4

f5.1, f5.2, f5.3, and f5.4.

  So the fifth row was taken and the first

was rejected.

  The program of effective computerized zoom interpolation in Fortram language is illustrated in

Figures 6a, 6b, 6c and 6d.

  Thus, a new and unique zoom interpolation system is created which, thanks to the kernels which are only a function of a location of the interpolation, allows a convolution intended to obtain intensity values on an inserted zone using consultation tables. This leads to very fast interpolation which ensures image quality comparable to reconstruction with a zoom and provides effectively

  "real time" zoom image production.

  While the invention has been described using an embodiment by way of example, it should be understood that this embodiment is described by way of example only and not as a limitation of the

scope of the invention.

Claims (15)

CLAIMS:   1. Method for processing a normal input image (21) to provide a zoomed output image (31), the input image (21) comprising an input matrix (28) of rows and columns of regions having input intensity values corresponding to the rows   and pixel columns in a normal displayed image.   said output zoom image (31) comprising a zoom matrix (28) of rows and columns of regions having intensity values corresponding to the rows and columns of pixels in a displayed zoom image (31), said method comprising: specifying a zoom factor (15) and regions of input intensity values for which a zoom must be carried out, the transfer of the input intensity values to the specified regions for which a zoom is to be carried out towards the regions designated from the zoom matrix (28), said designated regions being separated by t: 0 regions of known intensity values, selecting the individual stored kernels for each of said regions of known intensity from the zoom matrix (28), said stored kernels being selected according to the location of the region of unknown intensity of the zoom matrix (28), the selection of neighboring regions & from determined locations s by the location of the unknown intensity region and the zoom factor (15), and the convolution of said selected stored kernels with intensity values of said selected neighboring regions of known intensity values including the designated regions of the zoom matrix <28) to obtain intensity values for the value regions of unknown intensity.   2. Method according to claim 1, comprising means for selecting 16 neighboring regions in order to   satisfy a polynomial function.   The method of claim 1, wherein said selecting step comprises selecting 9 neighboring regions to satisfy a binomial function. 4. The method of claim 1 wherein the step of selecting said stored kernels comprises the operations of: covering a grid on the zoom matrix (28), said grid comprising a plurality of horizontal lines between said regions of known intensity in said rows and a plurality of vertical lines between said regions of known intensity in said columns, a kernel being associated with each intersection of said horizontal and vertical lines, and selecting said kernel closest to the center of said region of unknown intensity for Be used in the convolution step (24) to obtain a value   of intensity for said region of unknown intensity.   5. Method according to claim 4, comprising   the step of using a 16 x 16 grid.   6. The method of claim 1, wherein said kernels are independent of the image data, the   zoom factor (15) and matrix format.   The method of claim 4, including the step of incrementing the kernels based on the number of grid lines in said specified regions of known intensity values divided by the zoom factor (15) so that when '' there are 16 grid lines and a zoom factor of 8 only each second kernel be used.   8. The method of claim 1, wherein   said kernel is based on a polynomial function.   S5 9. The method of claim 1, wherein   said kernels are based on a binomial function.   li. The method of claim 1. comprising the steps of producing a kernel, said steps of producing a kernel comprising the steps of: a) establishing a polynomial function which joins the specified regions of known intensity into a row as a function of the lines grid between said specified regions, said convolution being: P (isubX) = fi (ir + A / 2 - B / 6) + f2 (rA + B / 2) + fE (A / 2-B / 2) + f4 (B / 6) ..... (3) where fl f2, f3s f4 are neighboring regions of known intensity in a row, the multipliers fi, f2, f3 and f4 are the kernels in the direction X, r = isubX-1) / ISUB +1 A = r (r-1) B = A (r-2> isubX is the number of vertical grid lines, and 201 ISUB is the total number of grid lines between the specified regions d intensity known; b) obtain weighting factors using the polynomial function P (isubY) in order to obtain kernels in the X direction leading to a convolution kernel not   4 x 4 for each grid intersection.   11. A method of interpolation in a matrix to obtain interpolated values from known values, said method comprising the operations consisting in producing kernels which are independent of the known values or the dimension of the matrix, but are a function of the location separating pixels of known value with pixels requiring interpolated values, to convolve neighboring pixels of known value with a kernel determined by;; 5 location of the pixel needing an interpolated value to obtain values for the pixels requiring the interpolated values.   12. A normal input image processing system for providing an output zoom image (31), the input image (21) comprising an input array (27) of region row and column having values of input intensity corresponding to the row and column of pixels in a normal display image, said output zoom image (31) comprising a zoom matrix (28) of rows and columns of regions having intensity values corresponding to the rows and columns of pixels in the displayed zoom image (31), said method comprising: means for specifying a zoom factor and regions of input intensity values for which zooming has been performed, means for transferring the input intensity values to the specified regions for which a zoom must be performed in order to designate regions of the zoom matrix (28), said designated regions being separated by regions of values of unknown intensity, an average in to select individual stored kernels for each of said regions of unknown intensity in the zoom matrix (28), said stored kernels being selected as a function of the location of the region of unknown intensity in the zoom matrix (28>, a means for selecting neighboring regions from locations determined by the location of 0C} the region of unknown intensity and the zoom factor (15), and means for convolving said selected stored kernels with values intensity of said neighboring regions selected with -_. values of known intensity including the designated regions of the zoom matrix (28) in order to obtain intensity values for the regions of values of unknown intensity.   135. The system of claim 12. comprising a medium S (24) for selecting 16 neighboring regions   to satisfy a polynomial function.   The system of claim 12, wherein said selection means (24) comprises means (26) for selecting 9 neighboring regions to satisfy a binomial function.   15. The method of claim 12, wherein the means for selecting (24) said stored kernel comprises: means for covering a grid on the zoom matrix (28), said grid comprising a plurality 1 'of horizontal lines between said regions of known intensity in said rows and a plurality of vertical lines between said regions of known intensity in said columns, a kernel associated with each intersection of said horizontal and vertical lines - being present, and means for selecting said most kernel neighbor of the center of said region of unknown intensity for use by the means to perform a convolution in order to obtain the intensity values for   said regions of unknown intensity.   16. The system of claim 15 comprising a grid 16 x 16.   17. The system of claim 12, wherein said kernels are independent of the image data 3o <21), the zoom factor (15) and the matrix dimension. 18. The system of claim 15, comprising means for incrementing the kernels based on the number of grid lines divided by the zoom factor * _ i (15).   19. The system of claim 12, wherein   said kernels are based on a polynomial.   -. The system of claim 12, wherein   said kernels are based on a binomial function.   21. A system for interpolation making it possible to obtain an interpolated value from known values in a matrix of pixels, said system comprising means (24) serving to produce kernels which are independent of the matrix data or of the format of the matrix, means for separating pixels of known value using pixels requiring an unknown value, means for carrying out a convolution of pixels of known value with said produced kernels in order to obtain values for pixels requiring interpolated values.