SYSTEM FOR SPATIALLY TRANSFORMING IMAGES

Abstract: A system for electronically transforming input data samples corresponding to picture elements of an image includes a horizontal to vertical transposing memory (18) which receives a serial sequence of data samples corres­ ponding to source locations serialized by scanning in one direction and outputs the samples in a serial sequence either in the same direction or a second direction. A first filter (800) receives the data samples output from the first memory and to outputs a serial sequence of filtered data samples for target locations as a function of a plurality of the data samples corresponding to picture elements neighboring respective first source location coordinates. A second memory (900) receives the serial sequence of filtered data samples from the first filter and outputs the filtered data samples in a scan line sample sequence scanned in the second direction. A second filter (906) receives the filtered data samples from the second and outputs a serial sequence of additionally filtered data samples scanned in the second direction for target locations. Source address generators (912, 908) provide to the first and second filters serial sequences of respective first and second source addresses corresponding to respective serial sequences of coordinates in accordance with a desired transformation between the source and target locations.

Description: Background of the Invention 1. Field of the Invention This invention relates to systems for providing location transformations in a multi-dimensional co-ordinate system using separate transformations for each co-ordinate of the system and more particularly to a system providing spatial transformations of a two-dimensional video image in a raster scan television system. 2. Discussion of the Prior Art Methods of producing multi-dimensional spatial transformations have been developed and are discussed in references such as Principles of Interactive Computer Graphics by William M. Newman and Robert F. Sproull, McGraw-Hill Book Company, second edition 1979, Transmission and Display of Pictorial Information, by D.E. Pearson, A. Halstead Press Book, 1975 and "A Digital Signal Processing Approach to Interpolation", by Ronald W. Schaefer and Lawrence R. Robiner, Proc. IEEE, Vol. 61, pp. 692-702, June 1973. However, for transformations which involve rotation, perspective representations, or other transformations which involve more than simple unidirectional translations, or scaling the transformation process involves multi-dimensional spatial filtering and interpolation operations. Consequently, a video image transformation process requires complex and time consuming processing for each picture element of the transformed video image. Transformations are thus rendered impractical in terms of cost of data processing time for complex images such as raster scan television displays. The long processing times required further make the real time processing of a continuous stream of television frames virtually impossible with present day technology. Nevertheless, a practical system for transforming multi-dimensional visual images has an important demand for such diverse purposes as producing special effects in television programming or transforming a satellite picture of the earth which is distorted by the curvature of the earth into a flat pictorial representation. The present invention broadly provides a system for electronically transforming input data samples corresponding to picture elements of an image, said transformation corresponding to transformation of said picture elements of said image from a source location to a target location in a two dimensional co-ordinate system in which two co-ordinates indicate position in respective first and second directions, characterised by: a first memory coupled to receive a serial sequence of data samples corresponding to source locations serialized by scanning in said first direction, the first memory being selectively operable to output the data samples in the serial sequence in which they are received or in a serial sequence representing a scan in said second direction; a first filter coupled to receive the data samples output from said first memory and to output a serial sequence of first filtered data samples for target locations as a filtered function of a plurality of the data samples corresponding to picture elements neighbouring respective first source location co-ordinates, said sequence output by said first filter corresponding to scanning in the direction corresponding to the output of said first memory; a second memory coupled to receive the serial sequence of first filtered data samples from the first filter scanned in the respective said direction and to output the first filtered data samples in scan line data sample sequence scanned in the other said direction; a second filter coupled to receive the first filtered data samples output from said second memory and to output a serial sequence of second filtered data samples scanned in said other direction for target locations as a filtered function of a plurality of the first filtered data samples corresponding to picture elements neighbouring second source location co-ordinates; and first and second source address generators coupled to provide to the first and second filters serial sequences of respective first and second source addresses corresponding to respective serial sequences of co-ordinates in accordance with a desired transformation between the source and target locations. A system for spatially transforming images in accordance with the invention greatly reduces conventional processing time and demands by enabling separate and sequential transformation of the image for each dimension of the co-ordinate system in which it exists. The multidimensional filtering for the case of a video image can be accomplished on a real time basis one dimension at a time concurrently with the separate and sequential transformation operations. In an example represented by an image transformation system for real time television applications, each color component of the raster scan video signal is passed through a serial sequence of processing elements including a horizontal to vertical transposing memory, a vertical transformation system, a vertical to horizontal transposing memory, and a horizontal transformation system to generate as an output the transformed component of the video signal. Each video component of the video signal is operated upon separately and in parallel and the operations may be substantially identical except that in some cases it may be possible to utilize slower, less expensive circuitry in the case of a color component having a narrow bandwidth compared to other color components. The general principles of separating the image into unidimensional serial transformations is the same for all color components. Brief Description of the Drawings A better understanding of the invention may be had from a consideration of the following detailed description taken in conjunction with the accompanying drawings, in which: Fig. 1 is a block diagram representation of a spatial transformation system in accordance with the invention; Figs. 2A, 2B, 2C and 2D are pictorial representations that are useful in understanding transposition; Fig. 3 is a block diagram representation of the spatial transformation system; Fig. 4 is a block diagram of a transposing frame store for the spatial transformation system shown in Fig. 1; Fig. 5 is a memory map for the transposing frame store shown in Fig. 4; Fig. 6 is a schematic and block diagram representation of addressing circuitry for the transposing frame store shown in Fig. 4; Figs. 7A and 7B are block diagram representations of a deinterlace filter; Fig. 8 is a block diagram representation of a predecimator; Fig. 9 is a block diagram representation of a filter for the predecimator shown in Fig. 8; Fig. 10 is a schematic and block diagram representation of an interpolation decimation filter; Fig. 11 is a schematic and block diagram representation of a vertical source address generator; Fig. 12 is a schematic and block diagram representation of a horizontal source address generator; Fig. 13 is a block diagram representation of a digital special effects system in accordance with the invention; Fig. 14 is a block diagram representation of the control panel for the system shown in Fig. 13; Fig. 15 is a block diagram representation of a horizontal to vertical transposing memory shown in Fig. 13; Fig. 16 is a block diagram representation of a field store memory for the memory shown in Fig. 15; Fig. 17 is a block diagram representation of an address and timing circuit for the field store memory shown in Fig. 16; Fig. 18 is a block diagram representation of a motion sensitive de-interlace filter for the system shown in Fig. 13; and Fig. 19 is a block diagram representation of an advantageous embodiment of chroma predecimation and interpolation decimation filters for the system shown in Fig. 13. Detailed Description Referring now to Fig. 1, a spatial transformation system 10 in accordance with the invention which operates separately upon each dimension of a coordinate transformation is shown in the specific embodiment of a transformation system for a standard raster scan television video signal. The transformation system 10 includes three color component processors 12-14, one for each of the Y, I and Q components of a color television video signal. It will be appreciated that other representations for the television signal such as red, green, blue or Y, U, V could be used alternatively. Each of the component processors 13 and 14 may be implemented as duplicates of the component processor 12 which is shown in greater detail in Fig. 1 and which will be described in greater detail herein. The Y component processor 12 receives as an input a Y digital video component of a video image in raster scan television order. The Y component is passed serially through a signal processing path 16 which includes a horizontal to vertical transposing memory 18, a vertical transformation system 20, a vertical to horizontal transposing memory 22, and a horizontal transformation system 24 to produce a digital Y video output component which has been fully transformed in two dimensions, one dimension at a time. A transform compose and factorizor 26 receives operator input commands and in response thereto generates transformation information for the separate vertical and horizontal directions which is communicated to a vertical address generator 28 and a horizontal address generator 30 respectively. Because the image transformations for each of the color components are substantially identical, the vertical and horizontal transformation information may also be communicated to I component processor 13 and Q component processor 14 without need for duplication of the transform composer 26 for each color component. A timing and control circuit 32 develops basic timing and control signals for use throughout the spatial transformation system 10 in response to an incoming synchronization signal. Theory of Spatial Transformation We describe a procedure for spatially transforming a two dimensional sampled image. Common examples of spatial transformations are translation, contraction and expansion, rotation and perspective projection. The concept however is quite general and includes any odd warping of an image such as that produced by a fish-eye lens or a fun house mirror. Mathematically an image is determined by three functions of position that give the intensities of the three color components at each point within the boundary of the image. We denote our original or source image as s i (u,v) for i = 1,2,3 (2) where u and v are linearly independent coordinates that range over the area of the picture and i selects one of the primary color components. The transformed target image will be written as t i (x,y) (4) where x and y range over the area of the target. A spatial transformation is a relation that ties x and y to u and v such that the following is true t i (x,y) = s i (u,v) (6) The primary intensities at each point (x,y) in the target are determined by those at some point (u,v) in the source. For each (x,y) there should be only one (u,v) to avoid the possibility of specifying two intensities for the same primary at the same point; thus the relation between them is a function of (x,y): (u,v) = f(x,y) or u = f u (x,y) (8) v = f v (x,y) in component form. Any spatial transformation can be completely specified by giving its u and v components f u and f v . These functions simply tell where to look in the source to find the primary intensities at a point in the target. Many spatial transformations are invertible and are given by (x,y) = f⁻¹(u,v) x = f x ⁻¹(u,v) (10) y = f y ⁻¹(u,v) These functions tell where in the target to move each source intensity. Since a transformation is the same for each primary we will drop the subscripts and write one representative equation for what is actually a group of three. We then have t(x,y) = s(u,v) = s (f u (x,y),f v (x,y)) (12) If we are given a transformation in the form of eq. (10) we must first invert f⁻¹ to get a relation of the form in (8) to be able to compute target points with eq. (12). The problem of two dimensional spatial transformation is considerably simplified by the discovery that many transformations can be factored into a product of two one dimensional transformations. The factorization is derived as follows. What we seek is an intermediate r such that t(x,y) = r(u,y) = s(u,v) whereby t(x,y) = s(u,g(u,y)) (14) then t(x,y) = r(f u (x,y),y) (15) with g(u,y) = v The image r is produced from s by motion only in the second coordinate direction, since the first parameter in the equation relating the two is the same. Similarly r transforms into t by motion only in the first co-ordinate direction. To find g we have r(u,y) = s(u,v) = s(u,f v (x,y)) and f u (x,y) = u For every y we can define a one dimensional function f uy (x) = f u (x,y) = u (16) If this function is invertible we may write x = f uy ⁻¹(u) and substitute this into f v to get g(u,y) = v = f v (x,y) = f v (f uy ⁻¹(u),y) (18) Two important examples of spatial transformations are affine and projective. An affine transformation in two dimensions is given by f u (x,y) = a₁₁x + a₁₂y + a₁₃ f v (x,y) = a₂₁x + a₂₂y + a₂₃ (20) in three dimensions by f u (x,y,z) = a₁₁x + a₁₂y + a₁₃z + a₁₄ f v (x,y,z) = a₂₁x + a₂₂y + a₂₃z + a₂₄ f w (x,y,z) = a₃₁x + a₃₂y + a₃₃z + a₃₄ (22) and in general by It is known that affine transformation of dimension N are isomorphic to N + 1 dimensional matrices of the form therefore the composite of two affine transformations can be calculated by taking the product of their respective matrices. Thus a general affine transformation can be built out of a product of simpler ones. Also the inverse of a transformation is found by inverting its matrix. To use the matrix on an N-vector x, the vector is first mapped to an N+1-vector (x,1) by appending a 1 as its N+1 th coordinate. The matrix M is then applied to this new vector forming an N+1 th dimensional result. This is projected back to N space by dropping the N+1 th coordinate which was undisturbed by M. As a two dimensional example we have the transformation in (20). In matrix form this is the 3x3 array We map (x,y) to the three vector (x,y,1) and apply M Dropping the third equation, which is an identity, we are left with (u,v). If M is invertible we may express (x,y) as a function of (u,v) This is normally how transformations are specified. For calculation purposes though, we are given individual target coordinates (x,y) and must find what (u,v) in the source contributes intensity to that location. Translation, scaling, rotation and shearing are all special cases of affine transformation. These four taken together can produce all possible affine mappings. The matrices and formulas for these are shown below for the two dimensional case. The transformations are described verbally in the source to target direction and we first show the M⁻¹ that corresponds to that description. Translation of each source point (u,v) by a vector (T x ,T y ): Expansion by factors S x and S y : Clockwise rotation by an angle ϑ: Right shear of x coordinate by an angle ψ: Note the simple relationship between each of these matrices and its inverse. If we are given a sequence of operations specified in the source to target direction and need the M corresponding to the composite target to source transform, we may find this M by inverting each matrix in the sequence and concatenating in the reverse order according to the formula (AB)⁻¹ = B⁻¹A⁻¹ instead of inverting the composite directly. As an example, suppose we wish to rotate our source, then translate it. The M⁻¹ for this is the product or Then by direct calculation using cofactors, since det M⁻¹ = 1. This same result can be had by taking the reversed production of inverse Three dimensional affine transforms behave analogously except that there are three matrices for rotations about X, Y and Z and three for shears along those axes. Projective transformations are given by the general form These transformations are isomorphic to the set of all N+1 dimensional square matrices. Affine transformations are thus special cases of projective ones. The distortion of distance produced when a three dimensional scene is projected onto a flat plane by a lens can be modeled by a projective transformation. In fact, analysis of that distortion, called perspective, was the impetus for the creation of projective geometry. Perspective distortion is quite familiar to anyone involved in art, architecture, photography, drafting, computer graphics, etc. A two dimensional perspective projection of a three dimensional scene is produced by dividing X and Y coordinates of each point in the original by its Z value, where Z points in the direction of view of the lens. Thus X = X'/Z' and Y = Y'/Z' where (X', Y', Z') = coordinates of point in 3-D scene; and (x,y) = are the coordinates of image of point in 2-D view plane This mapping collapses all points lying on a line passing through the focal point of the lens onto a single point in the view plane. We can construct a two-dimensional projective transformation from a three dimensional affine one. The transformation models the image formed by a camera viewing a flat picture that has been rotated, sheared, scaled and translated to locations throughout 3-space. We start with an image in the u,v plane and map the points in it to the 3-space coordinate (u,v,0) and apply an affine transformation of the form (22) to obtain an (x',y',z'). Dividing by z' we have The a₁₃, a₂₃ and a₃₃ terms are missing since w is zero in this case. Equations (28) and (29) are specifications for an f x ⁻¹(u,v) and f y ⁻¹(u,v). We want to invert and factor this transformation to obtain the f u (x,y) and g(u,y) needed in equations (14) and (15). Since we are starting with inverses the procedure for factorization is somewhat different from that described above. We first solve (29) for v to get g(u,y) directly. Substituting for v in (28) and solving for u we have after some manipulation If the terms a₃₁ and a₃₂ are zero and a₃₄ equals one, the projection reduces to an affine transformation within the plane and we have A three dimensional affine transformation from a source array having three dimensional variables u, v and w to a target array having dimensional variables x, y and z would be defined by the generalized equation: x = a₁₁ u + a₁₂ v + a₁₃ w + a₁₄ (35) y = a₂₁ u + a₂₂ v + a₂₃ w + a₂₄ (36) z = a₃₁ u + a₃₂ v + a₃₃ w + a₃₄ (37) Although the actual manipulations become quite extensive and are therefore hereafter omitted, it will be appreciated that equation (37) can be solved for u to produce u = g₁ (v, w, z) (38) Determining u at each possible combination of values of v, w and z and using u as a source address to obtain data corresponding to each source address, a three dimensional first intermediate array of data is established having the coordinates v, w and z. The target dimension z has now been substituted for the source dimension u. Next, substituting equation (38) into equations (35) and (36) to eliminate u, the result is x = g₂ (v, w, z) (39) y = g₃ (v, w, z) (40) Equation (40) can now be solved for v to obtain v = h₁ (w, y, z) (41) Determining v for each possible combination of values of w, y and z and using the determined "a" values as array address locations to obtain data from the first intermediate v, w, z array, a second intermediate array of data is established having dimensions w, y and z and values at coordinate points thereof corresponding to the addressed locations in the first intermediate array. The final target matrix of data having dimensions x, y and z is obtained by substituting equation (41) into equation (39) to eliminate v. The result is x = h₂ (w, y, z) (42) Solving equation (42) for w we obtain w = i l (x, y, z) (43) The values of w can be determined for all possible combinations of values x, y and z and used as source address locations within the second intermediate w, y, z array to obtain data from the second intermediate array and establish the three dimensional target array T(x, y, z) as the values obtained from the second intermediate array at the locations defined by w, y and z for each possible combination of values x, y and z. Discussion of Real Time Video Image Transformation Systems The preferred embodiment of the device accepts separate digitized versions of the Y, I and Q color components of a horizontal left to right scan NTSC television signal. This signal is 525 line, 2 to 1 interlaced, 8 bits per pixel, with a field rate of 60 Hz. Vertical scan is from top to bottom. The Y or luminance signal is sampled at 4 times the NTSC color subcarrier frequency of 3.579545 MHz (f sc ). The I and Q signals are sampled at the subcarrier rate. We discuss the transformation of the Y signal first. I and Q are handled similarly. The period between Y pixels is 1/(4f sc ) or approx. 70 nS. There are exactly 910 pixels per 63.5 uS horizontal scan line. Only 486 of the 525 lines in a frame contain active picture data, the rest are devoted to retrace blanking. The 8 bit parallel, byte serial, data stream enters the first transposing memory 18. This contains three memories, each large enough to hold one active field of data. Every field, the memory containing the oldest data is used as a buffer to store the current field while the previous two fields are read simultaneously from the other two for processing. This arrangement prevents timing conflicts that occur when trying to write new data to a memory that still contains parts of an old field not yet processed. Only that data representing visible picture is stored, thus each memory contains 243 lines of 768 pixels. The main function of the transposing memory 18 is to change the direction of scan of the fields stored within it. Each field memory is written in horizontal order as shown in Fig. 2A, but can be read in vertical order as 768 columns of 243 pixels as shown in Fig. 2B. This produces a digital data stream representing a vertically scanned version of the input data. The horizontal and vertical dimensions of the picture are interchanged by this means. What was the left to right direction in the original becomes top to bottom and what was top to bottom becomes left to right. The output data stream can be considered as a horizontal scan of the original image mirrored about its vertical center line and rotated about its Z axis 90° counterclockwise as illustrated in Figs. 2A-2D. In this manner vertical processing of the input data can be achieved by operating on the output data with a device only capable of transformation along the direction of scan. Vertical processing of the original horizontally scanned signal is difficult because vertically adjacent samples are separated widely in time. After transposition, however, vertically adjacent samples are close together in time while horizontal ones are far apart. Referring now to Fig. 3, two 70 nS data streams representing the two fields previous to the current input field leave the transposing memory 18 to enter a deinterlace filter 600. These two fields together contain information describing the entire spatial area of the image, except that one field was scanned 1/60 second earlier than the other. The deinterlace filter 600 blends the two fields to create a new frame that appears to have been scanned at a time midway between them. The filter effectively operates at twice the original data rate of 4f sc . The deinterlace filter 600 is implemented as two filters in parallel and data from these filters is carried in two 70 nS streams. Throughout the machine, paralleling of data paths, memory modules and computational elements is used to prevent the data rate required on any single path from rising above 4f sc , while still retaining the enormous total rates required for real time processing. The machine is built with commonly available Schottky TTL logic devices which can comfortably respond to a 70 nS clock. The predecimation filter 700 has a triple line buffer memory, one memory absorbs the present column of data while the previous column is read from another. The third stores intermediate predecimated results. The predecimator 700 provides coarse size change by powers of two in the direction of scan. Each column is processed by the filter multiple times. Every pass of the filter reduces the length of the column by a factor of two until it is only one pixel long. Each pass takes half the time of the previous one and produces half as many pixels, therefore the total amount of pixels produced including the original is twice the length of a column since the sum of 1 + 1/2 + 1/4 + 1/8 + ... = 2. The predecimator output rate is thus twice its input rate and we require four 70 nS streams to carry its output to the interpolator-decimator filter. An interpolator 800 has a double line buffer, each side of which is long enough to contain a column and all of its predecimated copies. The filter can interpolate between two pixels to a resolution of 1/64 of a pixel and vary its low pass frequency response on a point by point basis over a range appropriate for the smooth compression of a column to half its normal size. Compressions to less than half size are done by selecting one of the predecimated versions for interpolation and filtering. For example, if it is desired to compress the picture to 1/15 normal size the interpolator would select the 1/8 size decimated copy and interpolate and filter it to shrink it further by a factor of 8/15, a number between 1 and 1/2. Referring now to Fig. 4, the transposing frame store 18 includes three field buffer components 50-52 designated respectively field buffer 0, field buffer 1, and field buffer 2. Two multiplexers 54, 56 are coupled to output bytes of video field information from one of the field buffer components 50-52 in response to selection signals from a memory address and control circuit 58. Memory address and control circuit 58 also provides address and control information to each of eight components of each of the frame buffer stores 50-52. The field buffer stores 50-52 operate on a continuous revolving basis in which one of the three field buffers receives an incoming field of data while the other two field buffers provide a newest complete field of data and a next oldest complete field of data to the newer and older field multiplexers 54, 56 respectively. A frame start signal provides the identification of the beginning of a frame interval while the pixel clock signal provides a basic clock signal at the incoming data rate. The revolving nature of the field buffers 50-52 and the multiplex selection can be better understood by looking at what happens at three successive field time periods beginning with an arbitrarily selected field time N. At field time N field buffer 0 is selected to have incoming bytes of video data written therein while field buffer 1 outputs the oldest field through older field multiplexer 56 and field buffer 2 outputs the newer field through newer field multiplexer 54. At the next field time, N+1, field buffer 1 becomes the write field buffer while field buffer 2 outputs the older field through older field multiplexer 56 and field buffer 0 outputs the newer field through newer field multiplexer 54. At the next field time N+2, field buffer 2 becomes the write buffer while field buffer 0 outputs the older field through older field multiplexer 56 and field buffer 51 outputs the newer field through newer field multiplexer 54. At the next field time, N+3, the cycle repeats itself with field time N+3 being identical to field time N. It will be appreciated that during each cycle of three field times each field buffer is written into once and then read out through newer field multiplexer 54 and then read out through older multiplexer 56. As a result, the older field multiplexer 56 always outputs field N-2 while newer field multiplexer 54 always outputs field N-1 where field N is considered to be the field which is currently being written into one of the field buffers 50-52. The two most recent stored fields are thus continuously output to the next stage and are updated for each new field time. Read and write accessing of the field buffers 50-52 is complicated somewhat by the fact that practically available memory storage chips cannot read and write at the 70 nanosecond pixel clock rate. In order to accommodate the required bandwidth, each of the field buffers is implemented as 8 modules of 32K x 8 memory. By sequentially accessing the 8 modules, each individual module has 8 pixel clock periods to read and write a byte of data corresponding to a sampled pixel location. However, in order to assure proper sequencing of the memory modules for both the horizontal and vertical accessing which are required to obtain a horizontal to vertical transposition, care must be taken in implementing the addressing scheme. One advantageous addressing scheme is shown by way of example for field buffer 50 in Figs. 5 and 6. Fig. 5 illustrates the lower number addresses of an address map for field buffer 50. The 1 byte memory components 0-7 are represented vertically in ascending order from top to bottom while hardware memory word addresses ascend from left to right as indicated immediately above the map. However, for convenience of address implementation these memory addresses may be further divided into row and column addresses which are indicated above the chip address in Fig. 5. Horizontal accessing of the first row is the most straightforward. Horizontal accessing begins with address 0 of component 0 and proceeds through the components in sequence. After address 0 has been written in module 7 the column address is incremented with pixel (row, column) position (0,8) being accessed at word 1 of module 0. The 768 pixels of the first row of a field are written into the first 96 word positions of the memory modules in sequential order. In the event of a vertical access, it must be remembered that the 2 pixels located at column 0 and rows 1 and 2 will be accessed in sequential order. Care must therefore be taken that these two pixels are stored in sequential memory modules and not in the same memory module. This is accomplished by storing pixel 1,0 in module 1 with the word address being skipped to address 128 which corresponds to a resetting of the column address to 0. The memory modules are then again accessed in sequence with a wraparound to component 0 before the word address is incremented to column address 1 which corresponds to chip address 129. Similarly, for the second row the first pixel of the second row must be stored in module 2 and the modules then continue to be accessed in sequence with a wraparound until the word address is incremented after module 1 has been accessed. The starting module for the first pixel of a row continues to be incremented in similar fashion until all 8 components have received the first pixel of a row. The process then recycles with component 0 receiving the first pixel of row 8. When making vertical accesses to the frame buffer, the components are again accessed in sequence except that the row address is now incremented for each pixel. At the beginning of each new column, the row address is returned to 0 and the column address is incremented to 1. It will be observed that pixel 0,0 occurs at row 0 column 0, component 0; pixel 1,0 occurs at row 1, column 0, component 1 and pixel 2,0 occurs at row 2, column 0, component 2. This addressing arrangement thus meets the requirement that the components of the field buffer can be accessed sequentially for both vertical and horizontal accessing. An advantageous implementation of this addressing scheme is shown in Fig. 6 wherein the frame buffer 50 includes eight 32K x 8 storage modules designated module 0-7. Each module has a corresponding data latch and an address latch. The least significant address bits 0-6 are provided by a 7 bit column counter 70 while the most significant 8 address bits 7-14 are presented by an 8 bit row counter 72. Row counter 72 is reset at each field start and incremented for each pixel in a vertical mode and at row start in a horizontal mode. The column counter 70 is reset to 0 at field start and at row start when in a horizontal mode and is incremented in response to the maximum count output of a 3 bit counter 74. Counter 74 is coupled to be reset at field start and is clocked by the pixel clock signal. The count enable input to counter 74 is continuously enabled in a horizontal access mode and is enabled at column start for a vertical mode. Consequently, the column counter 70 is incremented for every eighth pixel clock in a horizontal mode and for every eighth column in a vertical mode. Selection for the 32K x 8 modules 0-7 is controlled by a 3 bit counter 80, a 3 bit counter 82, and a 3 to 8 module select decoder 84. Three bit counter 82 is incremented at the pixel clock rate to control the sequential accessing of the individual memory modules. The output of counter 82 is decoded by decoder 84 to select one of the eight modules in sequence for the simultaneous loading of the data latch and address latch for the selected module. Three bit counter 80 provides the required staggered module offset at row or column start. Counter 80 is reset at field start and is incremented in a horizontal mode at row start and in a vertical mode at column start. Three bit counter 82 is loaded at column start or row start with the contents of 3 bit counter 80 immediately prior to incrementing. It should be noted that the addressing of the field buffers 50-52 is described in terms of vertical mode accessing and horizontal mode accessing. Under most circumstances these field buffers provide a transposition by being accessed in a horizontal mode for writing and in a vertical mode for reading. However, under some circumstances the field buffers may be accessed in a horizontal mode for both reading and writing. The failure to provide a transposition at frame store 18 coupled with a transposition at frame store 22 effectively imposes a 90° rotation upon the video image. As an image is rotated toward 90° the image effectively becomes mapped into a line of zero width and resolution is lost. However, the resolution of the video image can be better preserved for large angle rotations by transposing the image at only one of the frame stores 18 and 22 and then imposing a negative rotation of between 0 and 45° to account for the difference between the desired rotation angle and the 90° rotation imposed by failing to provide a transposition at frame store 18. Transposing frame store 22 of Fig. 1 is implemented in a manner substantially identical to frame store 18 except that frame store 22 requires only two field buffers. A field of data is written vertically into one buffer while a previously written field is read horizontally out of the other buffer. The two buffers are then interchanged with the one buffer being read horizontally while the other buffer is written vertically. The deinterlace filter 600 of Fig. 3 is illustrated in Figs. 7A and 7B. Filter 600 includes a 2 byte wide three stage shift register 602, a filter component 604, and multiplexers 606, 608. The even and odd line data from the transposing field buffers 50-52 is clocked at the pixel rate through the shift register 602 having stages R0-R5 which are numbered in scan sequential order for interlaced vertically scanned data from the transposing frame store 18. Although the connections are not explicitly shown for simplicity, the purpose of the shift register 602 is to make the contents of each stage R0-R5 available to filter 604. Multiplexers 606, 608 respond to a vertical scan signal to select odd and even outputs respectively from filter 604 when data is being output from frame store 18 in vertical scan order. When data is being output in horizontal scan order multiplexer 608 selects the output of register stage R2 to drive the even byte data stream while multiplexer 606 selects the output of register stage R3 to drive the odd data byte stream. In the event of horizontal accessing of the frame store 18 a similar deinterlace filter subsequent to the vertical to horizontal transposing frame store provides deinterlace filtering. The filter 604 contains substantially identical components for the even and odd data streams each of which provide a -1/8, 2/8, 6/8, 2/8 and -1/8 filtering function. Each of the two odd and even components of filter 604 is advantageously implemented as shown in Figure 7B with multiply by two functions 610, 611, a multiply by four function 612, four addition functions 614-617, one subtraction function 618 and a divide by eight function 620. It will be noticed that the multiply and divide functions are implemented as powers of two and that they can therefore be easily accomplished by merely shifting the relative positions of the data bit lines for incoming and outgoing data streams. The inputs to the even and odd data stream filters are indicated by the information shown in the even and odd columns of the Table shown in Figure 7B for the outputs of the shift register 602. Each element in the table refers to a shift register stage within shift register 602 whose output is connected to a filter input as indicated. Referring now to Fig. 8, the predecimator 700 includes five line buffers designated line buffer 0 through line buffer 4, each of which has a 256 word x 32 bit storage capacity. Line buffers 0-3 each receive two 8 bit data streams from multiplexers 702-705 respectively. Each of the multiplexers 702-705 is capable of selecting one of four input signals and placing the selected input signals on one of the 8 bit buses to its corresponding line buffer. In some modes of operation the two 8 bit bus inputs to the line buffers are driven in parallel. The multiplexers 702-705 must thus be capable of either selecting two of the four input byte streams or one of the four input byte streams depending upon the mode of operation. Line buffer 4 receives two 8 bit data streams as even and odd outputs from a filter 708. A 32 bit wide 5 to 1 multiplexer 710 provides a 32 bit output which is split into four 8 bit data streams and communicated to a 4 byte wide 3 stage shift register 712. Data is loaded into the line buffers and in such an order that it may be read out to fill the 12 bytes of shift register 712 with a serial sequence of pixel information for a scan line. That is, each register stage of shift register 712 stores 1 pixel of information and the pixel information is arranged in raster scan order as designated by the numbering of the registers R0-R11. Registers R8-R11 provide data output to the next stage of the transformation system as well as data output to the second stage of the shift register containing registers R4-R7. The purpose of shift register 712 is to make available to filter 708 12 bytes of sequential pixel information in a predetermined order. Although not explicitly shown for simplicity, the outputs of each of the registers R0-R11 are communicated to filter 708. Filter 708 actually contains two separate filters operating in parallel. One of the filters generates even numbered pixel data at the pixel rate while the other generates odd numbered pixel data at the pixel rate. The even and odd outputs 716, 718 thus in combination provide feedback data at twice the pixel rate A disable signal may be utilized to drive an output disable input to multiplexer 710 at the end of the processing for a scan line to cause zeros to be loaded into shift register 712. This loading of zeros creates an aesthetic blending by filter 708 at the end of a scan line and prevents information from the end of a scan line from affecting information at the beginning of the next scan line. Six extra clock signals are provided at the end of each scan line pass through the filter 708 before data is input through multiplexer 710 for the next scan line to clear the pipeline of the predecimator system, and particularly the shift register 712. While the wide distribution of the four scan line signals stored by the line buffers 0-4 in order to accommodate different operating modes makes the predecimator 700 appear complex, its operation is actually quite straightforward. In the normal mode of operation vertical scan line information from corresponding vertical scan lines of a pair of sequential fields is received over the even and odd input lines and gated into line buffer 0. Because these even and odd input lines represent data from consecutive fields, they each carry alternate pixels for a frame. That is, for a given scan line column, the pixel information for rows 0 and 1 appear on the even and odd buses respectively followed by pixel information for rows 2 and 3 on the even and odd buses respectively followed by the pixel information for rows 4 and 5 on the even and odd buses respectively and so forth. Multiplexer 702 connects the upper output stream 720 to the even input bus and simultaneously connects output stream 722 to the odd input bus. Gating at the input latches to line buffer 0 directs the first or row 0 pixel information to byte position 0 of the input data latch while the row 1 pixel information on bus 722 is gated to byte position 1 of the input data latch. At the next pixel clock period the pixel information for frame row 2 appearing on bus 720 is gated to the position 2 input data latch and the frame row 3 pixel information appearing on bus 722 is gated to the position 3 input data latch. The first four pixel bytes are thus stored in the input data latch in sequential scan order at the end of 2 pixel clock times with the data being written into address word location 0 and the input data buffer being reloaded with pixel information for row positions 4-7 during the third and fourth pixel clock times for storage at address word location 1. It is thus seen that a vertical scan column from a pair of sequential fields is deinterlaced and stored in line buffer 0 in raster scan order during a vertical line scan time period which will be designated scan time N to provide a frame of reference. During this same vertical scan time and simultaneously with the writing of a frame scan line into buffer 0, previously written vertical scan line information is read from line buffer 2 four bytes at a time and output through 5 to 1 multiplexer 710 to the first stage of shift register 712 comprising registers R8-R11. Subsequent 4 byte words are read from line buffer 2 and shifted through shift register 712 at each pixel clock time. Since the data read out of line buffer 2 and shifted through shift register 712 contains a 4 byte parallel data stream, the effective bandwidth of this data transfer operation is four times the pixel rate. Filter 708 responds to the data content of the individual byte registers R0-R11 in shift register 712 to output 2 bytes of data designated even and odd on bus lines 716 and 718 at the pixel rate. Since the input scan line information to line buffer 0 and the even and odd output information from filter 708 each contain 2 bytes in parallel while the information being read from line buffer 2 contains 4 bytes in parallel, the line buffer output information has twice the effective bandwidth of the other two data streams. Line buffer 4 is qated to provide to its input data latch alternate bytes from the even and odd data streams from filter 708 in a manner similar to the gating of even and odd frame data into line buffer 0. Consequently, as 4 byte sequences of input pixel information are loaded into line buffer 0 four byte sequences of filtered information from filter 708 are loaded into line buffer 4. At the point in time during a scan line cycle where half of the pixels for the incoming vertical scan line has been loaded into line buffer 0, half of a scan line of pixel information from filter 708 will have been loaded into line buffer 4 since the bandwidth of the two data stream inputs to line buffer 0 and line buffer 4 are the same, i.e. twice the pixel rate. However, while line buffers 0 and 4 are being loaded at twice the pixel rate, line buffer 2 is being output at four times the pixel rate so that as half lines of pixel information are loaded into line buffers 0 and 4 a complete line of pixel information is being passed through shift register 712 and processed by filter 708. The half line of data stored in line buffer 4 thus represents a 2:1 compression ratio since the processing of a full line of information has resulted in the storage of a half line of information. It will be noted that during the first half of the scan line period the full, uncompressed pixel information was transferred through shift register 712 and presented to down path circuitry for possible use thereby by the outputs of shift register stages R8-R11. Thus, even though a 2:1 data compression has taken place the original data may be stored and preserved for further use by the down path circuitry. During the next one-fourth of the scan line time period (time one-half to three-fourths) line buffer 0 continues to receive pixels of video input information in scan line order while line buffers 2 and 4 are interchanged. The 2:1 compressed data is read out of line buffer 4 at four times the pixel clock rate, passed through shift register 712 to filter 708 for compression processing and written into line buffer 2. As the 2:1 compressed data is read from line buffer 4 and passed through shift register 712 it also is made available for storage and later use by down path circuitry through the data outputs from registers R8-R11. At the end of three-quarters of the vertical scan line period, a scan line of 4:1 compressed data has been loaded into line buffer 2. During the next one-eighth of a line scan period the 4:1 compressed data is read out of line buffer 2 and in response 8:1 compressed data is stored in line buffer 4. This process of sequentially further compression by two with alternate storage in line buffer 2 and line buffer 4 is continued to the end of vertical scan line time period at which a complete vertical frame line has been loaded into buffer 0 and the scan line being circulated through filter 708 has been compressed to a single pixel or byte. This predecimating thus provides down path circuitry with a selection of scan line information which has been processed in a high quality filtering process and has compression ratios in powers of two. This predecimating performs much of the burden which would otherwise be incurred by the vertical transformation circuitry to provide an improved final fully transformed video image for a given data resolution of the data transformation system. For example, if a compression ratio of 17:1 is required, the transformation system may select from the predecimated data having a compaction ratio of 16:1 and provide only a very small additional compaction required to increase the ratio to 17:1. At the end of vertical scan line time period N a new vertical scan line time period N + 1 begins with multiplexer 704 gating a next vertical scan line pair of even and odd field data into line buffer 2 in sequential order just as the previous scan line had been written into line buffer 0. At the same time, a flip-flopping data exchange begins between line buffer 0 and line buffer 4 with the scan line data being predecimated to provide sequential compressions by factors of two as the scan line data is recirculated through shift register 712 and filter 708 as previously done for the data stored in line buffer 2 during vertical scan line time N. For the next vertical line time period N + 2 the cycle is repeated with the incoming scan line pixel data stream being loaded into line buffer 0 while the contents of line buffer 2 are predecimated. In the mode of operation wherein data is received on the even and odd input buses in horizontal rather than vertical scan line order the data buffering process must be slightly different because each even and odd input carries a complete sequence of pixel row information by itself rather than information for alternate pixel locations as was the case for the interlaced vertical scan line information. Complete even row data is on the even line while complete odd row data is on the odd line. For this mode of operation multiplexers 702 and 703 operate to select and gate the even and odd incoming horizontal data streams to line buffer 0 and line buffer 1 respectively. Multiplexer 702 causes the even line incoming data stream to be alternately gated onto upper bus 720 and lower bus 722 to permit the loading of the incoming pixels into the 4 byte input data buffer for line buffer 0 in sequential scan order. Similarly, multiplexer 703 operates to alternately gate the incoming odd horizontal scan line information onto upper bud line 724 and lower bus line 726 to permit the loading of the odd horizontal scan line information into line buffer 1 in sequential scan order. While each of the line buffers 0 and 1 are now loaded at the pixel rate instead of twice the pixel rate for the vertical scan mode of operation, the total incoming data rate remains at twice the pixel rate since two line buffers are used in parallel instead of one. As the horizontal scan time interval continues previously loaded data is read out of line buffer 2 at four times the pixel rate, passed through shift register 712 and filter 708 to be stored by line buffer 4 with a 2:1 compaction ratio. Since the data is read out of line buffer 2 at four times the rate that data is being written into each of the line buffers 0 and 1, a full scan line of data will have been read out of line buffer 2 and passed through filter 708 by the time one-fourth of a line of data has been stored in each of the line buffers 0 and 1. The original contents of line buffer 2 will have been fully predecimated by the time line buffers 0 and 1 are each loaded with one-half of a line of information. During the second half of the horizontal line time interval the previously written contents of line buffer 3 are predecimated. During the next horizontal scan line time period interval horizontal scan line information is written sequentially into line buffer 2 and line buffer 3 for even and odd scan line row information respectively while the previously stored contents of the line buffer 0 are predecimated during a first half of the scan line time period interval and the previously stored contents of line buffer 1 are predecimated during the second half of the scan line time period interval. It is thus apparent that the predecimation process is substantially the same for both vertical and horizontal scanning although the buffering of the incoming data must be somewhat different to account for the differences in the interlaced and non-interlaced incoming video data streams. Filter 708 contains two parallel filters providing a -1/16, 0, 5/16, 1/2, 5/16, 0, -1/16 filtering function and are identical except for their input connections within shift register 712. A highly advantageous implementation for filter 708 is illustrated in Fig. 9 to which reference is now made. While only one filter 708 is shown, it will be appreciated that duplicate even and odd filters are employed with their inputs connected to the respective even and odd registers indicated by the table at the inputs to the filter. It will be seen that the filter is very conveniently implemented with four adders 730-733 and a single subtractor 734. No actual multiplication or addition is required since the multiply blocks 736 and 737 and the divide block 738 are implemented in powers of two to permit the operations to be accomplished by merely shifting the relative bit positions of the incoming and outgoing data information. Because of the elimination of actual multiply and divide operations, the filter 708 can be implemented at far less expense than conventional seven point filters and can operate at the 70 nanosecond pixel clock rate. Interpolation decimation filter 800 and 906 (Figure 3) are essentially the same and are representatively illustrated by interpolation decimation filter 800 as shown in Fig. 10 to which reference is now made. Filter 800 provides the ultimate functional relationship between the source or input video data and the target data in the vertical dimension. Vertical source address generator 912 (Fig. 3) calculates and supplies to interpolation decimation filter 800 a sequence of vertical pixel source addresses corresponding to a sequence of output target video data points in response to the vertical target address counter 914 and transform composer and factorizer 916. The addresses supplied by vertical source address generator 912 have a resolution of 1/64 pixel and include a 4 bit magnification factor parameter of between 0 (for a 1/1.99 sized image or larger) and 15 (for predecimated data compressed by 2¹⁵ or more). Interpolation decimation filter 800 supplies a video data value calculated from four pixel locations appearing on each side of the source address. Sixteen filter functions are available for calculating the output video data value. One is selected in response to a four bit parameter alpha in accordance with the desired compaction ratio provided by interpolation decimation filter 800 in addition to a selected predecimation compaction. A two line double buffer 809 is implemented in 8 segments 801-808 and receives video data 4 bytes parallel from the R8-R11 data outputs of predecimator 700 (Figs. 3 and 8). For each vertical scan line of a frame the received data includes a full line of video data plus all of the predecimated copies of the full line which copies occupy a second full line of data. Hence, there is a need for storing two lines of data in each half of the double buffer 809. The double buffering permits a new two lines of video data to be received while the immediately preceding two lines of data are operated upon to provide one line of target image video data. As video data is received by double buffer 809 the first four bytes are stored respectively in the four segments 801-804, the second four bytes are stored respectively in the four segments 805-808, the third four bytes are stored respectively in the four segments 801-804 and so forth. The eight part segmentation of the double input buffer 801-808 thus assures that the pixel data for the four adjacent pixel locations on each side of an address point (8 total) can be read in parallel from the double input buffer. A barrel shifter 810 receives the 8 bytes of pixel data from double input buffer 809, circulates the data to a desired position in response to the three least significant bits of the nonfractional portion of the source address and presents the circulated video data to an eight segment multiplier 820 having segments 821-828. The data is circulated such that the pixel data corresponding to the nonfractional portion of the source address is presented to a central multiplier segment 824. The pixel data for the three pixels sequentially to the left thereof are presented to segments 823, 822 and 821 while the pixel data for the four pixels to the right are presented to segments 825-828 respectively. The eight multiplier segments 821-828 thus receive as first inputs 8 bits of video data for each of 8 sequential pixel locations centered about the source address point. Multiplier segments 821-828 each receive as a second input an eight bit coefficient or weighting function from an 8 segment coefficient memory 830 having segments 831-838. Each segment is configured as 1024 words of eight bits each. The coefficient memory 830 receives as a partial address the six bit fractional part of the source pixel address. These six bits provide a phase factor  which defines the one of 64 subpixel points for the 1/64 pixel resolution of the source address. A filter function may thus be centered about the subpixel source address with the pixel data being weighted in accordance with its position on a filter function curve relative to the subpixel address. The coefficient memory 830 further receives four bits of address in accordance with the parameter alpha which is related to the magnification produced by interpolation decimation filter 800. Coefficient memory 830 may thus contain 16 different filter functions for each of the 64 subpixel source addresses. The filter function may thus be tailored to the degree of magnification (compaction) provided by interpolation decimation filter 800. For example, if the output target image is to be at least as large as the selected original or predecimated copy of the source image, it may be desirable to use a filter function which heavily weights video data for pixel locations very close to the source address. On the other hand, if compaction approaching 1/2 is desired, a filter function giving at least some weight to all eight pixel locations near the source address may be desirable. It will be recalled that the predecimator 700 provides compaction by all practical powers of 1/2 so that the further compaction provided by interpolation decimation filter 800 can always be by a magnification factor greater than 1/2. An addressing circuit is illustratively represented by a segment 841, which is one of eight segments providing address inputs to the eight double buffer memory segments 801-808 respectively. Address segment 841 includes an adder 851, a magnification factor ROM 861 and a carry ROM 871. Adder 851 receives as a first input the nonfractional part of the source address divided by eight. Division by eight is of course accomplished by merely shifting off the three least significant bits of the integer portion of the source address. The four bit magfactor parameter is presented as an address input to ROM 861 which generates an address shift in accordance with the magnification factor. If the target image is to be larger than half the size of the source image magfactor is zero and the full size copy of the source image is output to barrel shifter 810. For a target image compressed to between 1/4 and 1/2 the size of the source image the ROM 861 translates the source address to the half size predecimated copy of the source image and so forth. Carry ROM 871 receives the three least significant bits of the integer part of the source address and selectively provides a carry output to increment the translated buffer memory 809 word address when the three least significant bits designate a number between 4 and 7 inclusive. This selective incrementing accommodates situations where the desired eight pixels cross a word boundary for buffer memory 809. It will be noted that the addresses for segments 806-807 must be selectively decremented rather than incremented. As an example, assume that the source address is 25 5/64 (binary 00011001.000101) for a full size target image. The divide by 8 pixel address input to adder 851 thus becomes 3 (Binary 00011). Magfactor = 0 will designate a full size image and the output of ROM 861 to adder 851 will be zero. For the given address it is desired to read from buffer memory 809 video data for pixel locations 22-29. The data for pixels 24-29 is stored at word location 3, buffer segments 801-806, while data for pixel locations 22 and 23 is stored at word location 2 in buffer segments 807 and 808 respectively. The carry ROM 871 thus outputs a zero in response to a 1 (binary 001) input and buffer address word 3 is presented to segment 801 by adder 851. Similarly segments 802-806 will receive address word 3 from their respective address circuit segments 841 and segments 807 and 808 will receive a decremented address word 2. Data for the pixel defined by the integral portion of the source address (pixel 25) is output from segment 802 and is circulated downward (as shown) two places by barrel shifter 810 in response to the three least significant address bits (001) so that data for the designated source pixel is presented to multiplier segment 824. Coefficient memory 830 can thus be programmed with the assumption that the video data for the eight pixels about a source point will always be presented in ascending order to multiplier segments 821-828. The same effect could be accomplished by eliminating barrel shifter 810 and adding three address inputs to coefficient memory 830 with each of the segments receiving additional programming to accommodate the eight possible locations where the data for the designated source pixel might occur. The multipliers 821-828 of arithmetic network 812 thus receive the 8 pixels of video data from barrel shifter 810, multiply the pixels by their appropriate coefficient factor from coefficient memory 830 segments 831-838 and output the results to a summing network 881-887 which sums the eight products to generate the pixel of video data corresponding to the input source address. The resulting stream of pixel data from interpolation decimation filter 800 is fully processed in the vertical dimension and is then presented to the vertical to horizontal transposing memory 900 for the initiation of processing in the horizontal dimension separately from the processing in the vertical dimension. Referring now to Fig. 3, interpolation decimation filter 800 receives vertical lines of the source image. Even if the video data is read out horizontally from H to V transposing memory 18, the video data is still treated as a vertical scan. The net effect is a 90° rotation and mirror imaging which is compensated by transform composer and factorizor 916. It will be recalled that x and y are used to identify pixel locations within the target or output image while u and v are used to identify pixel locations within the source image. At interpolation decimation filter 800 each vertical scan line corresponds to a constant u value with the u value being incremented for each sequential vertical scan line starting with zero and moving from left to right. For each vertical scan line interpolation decimation filter 800 receives a sequence of v address inputs from vertical source address generator 912 specifying a sequence of pixel addresses within a scan line for a sequence of video data pixels. Interpolation decimation filter 800 responds to each v address received by outputing a pixel of video data as a function of the pixels positioned about the v point in the vertical scan line. Equation (30) defines v as a function of u and y and a number of constants from an "a" matrix (Table I) which defines the desired relationship between the target and source images. During each vertical retrace time between fields the transform composer and factorizor 916 calculates the required matrix constants in response to operator input commands and supplies them to vertical address generator 912. Vertical address generator 912 itself generates the u and y terms by in effect starting at zero for the first pixel of the first scan line and incrementing y for each successive pixel and incrementing u for each successive vertical scan line. Similarly, for the horizontal dimension horizontal address generator 908 receives the appropriate "a" matrix constants from transform composer and factorizer 916 and calculates the horizontal source addresses u for each horizontal scan line in accordance with equation (31) as a function of x and y. X and y are, in effect, established by starting at 0,0 for the first pixel of each field and incrementing x for each pixel and incrementing y for each horizontal scan line. While the vertical and horizontal addresses v and u could of course be generated from the equations therefor by microprocessors, it would be very difficult to accomplish this at the 70 n sec pixel rate. The vertical source address generator 912 and horizontal source address generator 908 are special purpose circuits for calculating the v and u equations 30, 31 at the pixel rate. It is of interest to note that video data enters interpolation decimation filter 800 at twice the pixel rate because of de-interlacing but passes through the remainder of the system at the pixel rate. The vertical and horizontal source addresses need therefore be generated at only the pixel rate and not twice the pixel rate. Referring now to Fig. 11, the vertical source address generator 912 includes a numerator calculation circuit 915, a denominator calculation circuit 917, a divider circuit 918 to divide the numerator by the denominator and a timing and control circuit 920 for generating the various timing and control signals used throughout the vertical source address generator 912. A previous v register 924 receives and temporarily stores each vertical address v. A subtractor 926 subtracts the stored previous v address from the current v address to generate an 18 bit difference parameter on signal path 928. The most significant bit of the 18 bit difference parameter is a sign bit while the six least significant bits represent a fractional part. The difference parameter is used as an estimate of the derivative of v with respect to time from which terms Magfactor and Alpha are derived. A magfactor ROM 930 receives the integer portion of the difference parameter and outputs the term magfactor as the integer part of the log base 2 of the absolute value of the difference parameter. Magfactor equals 0 for difference parameters of 0-1.99, 1 for difference parameters 2.00-3.99, 2 for difference parameters of 4.00-7.99 and so forth. Only absolute values are considered. Magfactor commands interpolation decimation filter 800 to use a particular predecimated copy and is communicated to a barrel shifter 934 which shifts (divides) the vertical source address by a number of bit positions equal to magfactor to produce an adjusted source address. When a predecimated copy of a line of data is selected having compaction by a given power of 2, the source address must be divided by the same power of 2 for compatibility and barrel shifter 934 performs this function. The difference parameter is the reciprocal of the magnification of the target image relative to the source image. For example a double size target image will produce difference parameters of 0.5 while a half size target image will produce difference parameters of 2.0 and so forth. The difference parameter is thus a measure of the magnification (including compaction) of the target image relative to the source image. Barrel shifter 936 receives the difference parameter and shifts it toward less significant bit positions by a number of bit positions indicated by the parameter magfactor to generate an interpolator difference signal in signal path 938 which represents the magnification (compaction) which must be performed by interpolation decimation filter 800 over and above that performed by a predecimated copy selected by the parameter magfactor. A parameter interpolator difference is used as an address input to alpha ROM 932 which responds by generating a 4 bit parameter, alpha, which selects one of 16 filter functions for use by interpolation decimation filter 800. To improve target image quality it is desirable to use different filter functions for different degrees of magnification (compaction) of the target image by the interpolation decimation filter. Filtering of the predecimated copies is handled by predecimation filter 700 so that only the additional filtering by interpolation decimation filter 800 is of interest at this point. For example, if the target image is to be full size or larger, a high peak, narrow filter function should be used which places great weight on the source pixels nearest to the vertical source address point. As the target image is compacted by greater and greater amounts, the filter function should become flatter and broader, thus putting less weight on pixels immediately adjacent the source address point and more weight on pixels farther from the source address point. Interpolation decimation filter 800 provides all degrees of image enlargement but a maximum compaction by a factor of 1.99. Any additional compaction would be accomplished by selecting a smaller predecimated copy. For example, compaction of the target image by a factor of 16 would be accomplished by selecting the fourth predecimated copy (magfactor equal to 4) and by introducing a compaction factor of 1 in the interpolation decimation filter 800 (no further compaction). The term magfactor would be 4, the difference parameter would be 16 and the interpolator difference parameter would be 1. For compaction of the original image by 32 the fifth predecimated copy would be selected, magfactor would be 5, the difference parameter would be 32 and the interpolator difference parameter would be 1. For compaction of the original image by the factor of 15.4, the third predecimated copy would be selected, magfactor would be 3, the difference parameter would be 15.4 (binary 1111.011001), and the interpolator difference parameter would be 1.92 (binary 1.111011). The integer part of the interpolator difference parameter on signal path 938 has a maximum value of 1 and its fractional part has 6 bits of accuracy. The interpolation difference parameter thus has 7 bits and alpha ROM 932 can have a size of 128 by 4. Since a single filter function is adequate for all degrees of image enlargement, full size and slight compaction, it is desirable to divide the range of the interpolation difference parameter between 1.00 and 1.99 into 16 equal parts along a logarithmic scale with each part being assigned a different alpha parameter and a corresponding filter function. The alpha ROM 932 is thus loaded to output 0 for addresses 0-1.04 (binary 1.000011), 1 for input addresses 1.05-1.09 (Binary 1,000100 to 1,000110); 2 for input addresses 1.10 to 1.14 (binary 1.000111 to 1.011001) and so forth up to 15 for input addresses 1.91 to 1.99 (binary 1.111010 to 1.111111). A different filter function can thus be provided for each of the 16 values of alpha ranging from narrow and steep for alpha equal 0 to broad and flat for alpha equal 15. The same filter function is thus used for full size images, enlarged images and the largest sized group of compacted images. The vertical source address generator 912 includes a numerator circuit 915, a denominator circuit 917, and a divider and denormalization circuit 918 which divides the output of the numerator circuit 915 by the output of the denominator circuit 917 and then denormalizes the quotient before outputing the vertical address, v, to barrel shifter 934. A timing and control circuit 920 responds to commands received from vertical target address counters 914 on signal paths 940 which indicate the end of a frame interval as well as information from transform composer and factorizer 916 received on a communication bus 942 to generate the various timing and control signals used throughout the vertical source address generator 912. It will be appreciated that the actual circuitry of the source address generator has been represented in a simplified form for clarity of explanation. For example, multiplexers 944, 946 and 948 can be implemented through selective gating of tristate logic circuits rather than as separate integrated circuits called multiplexers and data can be sequentially loaded one byte at a time into 32 bits (94 byte) data registers 950, 951, 952, 953, 954, and 955 where the communication bus 942 includes for example an 8 bit data bus from an 8 bit microprocessor. Data register 956 is also a 32 bit register while bias data register 957 may be implemented as an 8 bit register. It will be recalled that vertical source address generator 912 solves equation (30) to generate vertical source addresses at the pixel rate. During each vertical retrace time interval transform composer and factorizer 916 loads the constants for equation (30) into corresponding registers of vertical source address generator 912 over communication bus 942. For example, the numerator constants a₃₁, a₃₄, a₂₁, and a₂₄ are loaded respectively into 32 bit registers 950, 951, 952 and 953. Timing and control circuit 920 renders the select A inputs of multiplexers 944 and 946 at logic zero during this interval to permit the data to be communicated to the inputs of registers 951 and 953. Thereafter the select A inputs are set to logic 1 so that register 951 receives data from a 32 bit adder 960 through A input of multiplexer 944 while register 953 receives data from a 32 bit adder 962 through the A input of multiplexer 946. Similarly, during the vertical retrace vertical constant a₃₂ is loaded into 32 bit register 954 and constant -a₂₂ is loaded into 32 bit register 955 through the B input to multiplexer 948. Thereafter, the select A input to multiplexer 948 is set to logic 1 so that data may be communicated from 32 bit adder 964 through the A input of multiplexer 948 to the input of data register 955. It will be appreciated that adder 960 receives inputs from the output of a₃₁ register 950 as well as register 951 to present the sum of these inputs to the main input of multiplexer 944. Similarly, adder 952 adds the output of a₂₁ register 962 to the output of register 953. Numerator circuit 915 further includes an adder 966 which adds the output of register 951 to the output of register 956 and presents the sum back to the input of register 956. A subtractor circuit 968 subtracts the output a register of 956 from the output of register 953 to generate a difference signal which is the solution to the numerator portion of equation 30 and which is presented to divider circuit 918. Adder circuit 964 adds the output of a₃₂ register 954 to the output of register 955. The output of register 955 becomes the solution to the denominator portion of equation (30) and is also presented to divider circuit 918. As a frame of reference pixel time intervals will be defined as a function of u and y corresponding to the vertical addresses, v(u,y), such that at the output of numerator circuit 915 and the output of denominator circuit 916 data for a given pixel address shall be valid at the occurrence of a corresponding pixel clock transition. For example, at pixel clock time t 0,0 , data shall be valid for the pixel corresponding to vertical source address v 0,0 and at pixel clock time 2,2 data shall be valid for pixel source address v 2,2 and so forth. It will be appreciated that at the vertical source address generator 912 vertical addresses are measured in terms of the target image pixel locations y while horizontal addresses are measured in terms of the first image pixel locations u. During the vertical retrace interval register 956 is cleared while constants are loaded into the other registers. Looking at equation (30), it will be observed that for the first pixel clock time t 0,0 , the variables u and y will both be 0 so that the solution to v is a₂₄ divided by -a₂₂. Since register 953 has been preloaded with constant a₂₄ while register 956 has been cleared during the vertical retrace interval, at time t 0,0 subtractor 968 generates the appropriate numerator term a₂₄ as the output of numerator circuit 915. Similarly, register 955 has been preloaded with the constant -a₂₂ and outputs this term as the proper denominator term for equation (30). Clock signal CK3 loads register 956 with the output of adder 966 at each pixel clock time. Thus, at pixel clock time t 0,0 register 956 is loaded with the sum of 0 + (1) (a₃₄). The output of register 956 thus represents the proper value of u = 0 and y = 1 for the first portion of the numerator of equation (30) at the second clock time t 0,1 . Clock signal CK3 is active at this time and at each additional pixel clock time so that the constant a₃₄ stored in register 951 is added to the contents of register 956 at each pixel clock time. Since y is incremented at each pixel clock time, the next result is multiplication of a₃₄ by y by means for successive additions. That is, the output of the first portion of the numerator of equation (30) for y = 0, 1, 2, 3, 4 etc. is generated at the output of register 956 by adding to register 956 the value (a₃₁ u + a₃₄) 0 times, 1 time, 2 times, 3 times, 4 times, and so forth respectively. In a similar manner, the register 951 is clocked with clock signal CK2 during an interval between successive line scans so that register 951 stores the constant a₃₄ during the first line scan for line 0, the value a₃₄ + (1) (a₃₁) during the second line scan for vertical line 1, a₃₄ + (2) (a₃₁) for the third line, vertical line 2, and so forth. The output of register 951 thus continually represents the term a₃₁u + a₃₄. This value is added to the contents of the register 956 at each pixel clock time so that the effect is the same as multiplying the output of register 951 by y as y is incrementally stepped through successive pixel locations within a vertical line scan. Between each successive line scan the register 956 must be cleared or reset to reflect the new vertical line scan starting position of y = 0. This general concept of repeatedly adding or accumulating a term at the pixel clock rate to accomplish multiplication by y and repeatedly adding a term at a line clock rate to accomplish multiplication by u is used throughout the vertical source address generator 912. In the horizontal source address generator 908 a similar technique is used with successive additions at the pixel clock rate being utilized to accomplish multiplication by x and successive additions at the horizontal line clock rate being utilized to accomplish multiplication by y. It will be observed that the second term of the numerator is generated at the output of register 953 which is initially loaded with a constant a₂₄ before the beginning of each field time and then clocked with signal CK5 at the vertical line clock rate between each successive vertical line scans so that the output of register 953 represents a₂₄ + a₂₁u. Similarly, the clock signal input to register 955, CK7, is activated to initially load the constant -a₂₂ to register 955 and then to add the term a₃₂ to the contents of register 955 at the pixel clock rate so that the output of register 955 represents the value a₃₂y- a₂₂. This is the denominator of equation (30). A barrel shifter 970 receives the successive 32 bit words of video data for successive pixel addresses and operates in conjunction with an exponent detector 972 to convert the numerator into a floating point form with the output of barrel shifter 970 providing 16 bits of data representing the mantissa of the numerator and exponent detector 972 outputing 8 bits representing the exponent of the numerator term. Conversion to the floating point representation eliminates the need to carry leading 0's and permits the 16 bit output of barrel shifter 970 to carry the most significant 16 bits of actual numerical data. In a similar manner the barrel shifter 974 and exponent detector 976 convert the denominator term to a floating point representation. A reciprocal circuit 978 receives the 16 bit mantissa of the denominator term and outputs the reciprocal thereof. One suggested approach for accomplishing this reciprocation at the 70 ns pixel clock rate is to utilize the most significant 8 bits of the denominator term to address a conversion table storing reciprocal values and to utilize the least significant 8 bits of the denominator term to generate a linear interpolation between adjacent values in the reciprocal table. The reciprocated mantissa of the denominator is multiplied by the mantissa of the numerator in a hardware multiplier 980 and the product is presented to a barrel shifter 982. A subtractor 984 subtracts the exponent of the denominator from the exponent of the numerator to accomplish the division function and an adder 986 adds the difference to a bias term which is stored in bias register 957 before the beginning of each field scan time. The A constants are selectively shifted for optimum utilization of the 32 bit capacity of numerator circuit 915 and denominator in circuit 917 prior to loading into the corresponding register 950-955 before the start of each field scan time. A constant corresponding to the number of shift places of these constants is loaded into bias register 957 for addition to the output of subtractor 984 to denormalize the exponent term to correctly represent the actual value of the vertical address. This denormalized exponent term is output by adder 986 to barrel shifter 982 for a proper shifting operation to provide a conversion back to a 16 bit fixed point number representation at the output of barrel shifter 982. This output of barrel shifter 982 is the actual fixed point representation of the actual vertical address without adjustment for predecimation. As explained above, barrel shifter 934 receives this vertical address and adjusts it by division by a selected power of 2 to provide an adjustment to accommodate a particular selected predecimated copy of the video data. It will be appreciated that the bias term stored in bias register 957 can be either positive or negative, depending upon the values of the terms from the a matrix. These values will vary with the particular manipulation of the video image which is being commanded. An advantageous arrangement of the horizontal source address generator 908 for solving equation (31) is shown in Fig. 12. Horizontal source address generator 908 includes a numerator circuit 1002, a denominator circuit 1004, a divider circuit 1006 which may be identical to divider circuit 918, and a timing and control circuit 1008. Horizontal source address generator 908 also includes an adjustment circuit 1010 which is substantially identical to the adjustment circuit for vertical source address generator 912 and converts the horiziontal source address, u, output from divider circuit 1006 into an adjusted horizontal source address, uadj. Adjustment circuit 1010 also generates the parameter magfactor and alpha for the horizontal interpolation decimation filter 906. The numerator circuit 1002 includes registers 1012, 1014, and 1016 which are preloaded with data from the transform composer and factorizer 916 prior to a field scan time. The data is received over communication bus line 942. A multiplexer 1018 permits register 1016 to be loaded alternatively from an adder 1020 or from the communication bus 942. A register 1024 is selectively loaded with the output of an adder 1026. The numerator of equation (31) has the general form Ax + By + C where A = a₂₂ a₃₄ - a₂₄ a₃₂; where B = a₁₄ a₃₂ - a₁₂ a₃₄ and C = a₁₂ a₂₄ - a₁₄ a₂₂. During prefield scan time initiation the parameter C is loaded into register 1016 while B is loaded into register 1014. Clock signal CK21 is generated by timing and control circuit 1008 at the horizontal line clock rate so that the output of register 1016 continually presents the value of C + By which is the last two terms of the numerator of equation 31. Register 1024 is clocked by clock signal CK23 from timing and control circuit 1008 at the pixel clock rate so as to be continually updated to generate the quantity Ax which is added to the quantity C + By by an adder 1028 to output the numerator portion of equation 31 to the divider circuit 1006. The denominator circuit 1004 has exactly the same form as numerator circuit 1002 except that the constant A, B and C are replaced by the constants D, E and F where D = a₂₁ a₃₂ - a₂₂ a₃₁; E = a₁₂ a₃₁ - a₁₁ a₃₂ and F = a₁₁ a₂₂ - a₁₂ a₂₁. An adder 1030 outputs the denominator value to division and normalization circuit 1006. Since denominator circuit 1004 is essentially identical to numerator circuit 1002 it will not be further described. It is thus apparent that the divider circuit 1006 outputs the denormalized horizontal source address u to the adjustment circuit 1010. Adjustment circuit 1010 in turn generates signal uadj, the horizontal magfactor parameter, and the horizontal alpha parameter in a manner analogous to the operations of the vertical source address generator 912 which has been described above. Returning to Fig. 3, a vertical to horizontal transposing memory 900 is substantially the same as transposing memory 18. It requires only two field buffers and always writes vertically and reads horizontally. A horizontal deinterlace filter 902 is normally inactive as deinterlacing is performed by filter 600. However in the event of horizontal reading from transposing memory 18, deinterlace filter 902 must perform the deinterlace function. It requires only one filter component which may be the same as either of the two filter components of the deinterlace filter 600. A predecimation filter 904 receives an 8 bit stream of video data from deinterlace filter 902 and performs a predecimation operation substantially in the same manner as that performed by predecimation filter 700. Predecimation filter 904 requires only 3 line buffers. Interpolation decimation filter 906 receives a two byte stream of information from predecimation filter 904. It is substantially the same as vertical interpolation decimation filter except for adjustments that result from receiving data at one-half the data rate of filter 800. The data rate through the system is reduced by one-half at the interpolation decimation filter 800. Up to this point the system is processing two fields at once to maintain a composite frame available for interpolation. Interpolation decimation filter 800 need only produce a single field each 1/60 of a second. Horizontal source address generator 908 implements a function defining the source address along a horizontal scan line as a function of the target pixel row and column location. Horizontal target address counter 910 provides target position information in horizontal raster scan order. This enables processing of an intermediate image stored in transposing memory 900. Vertical address generator 912 defines source addresses along a vertical scan line. Vertical target address counter 914 provides target position information for the vertical scan into the intermediate transposing memory 900. Transform composer and factorizer 916 receives transformation commands and implements the equation shown in Table I to produce transform parameters to control the horizontal and vertical source address generators 908, 912. These parameters are calculated by a data processor within factorizer 916 once every field. Horizontal interpolator decimator filter 906 implements the function: where s is a source data value at discrete sample points, i is the integral part of the source address of the point to be interpolated,  is the fractional part of the source address of the point to be interpolated, and h is the impulse response of the interpolating function. h is determined according to the equation where α is a number between 1/2 and 1 representing the cutoff of this lowpass response. The horizontal address generator calculates the function listed in eq. (31) where x is the target pixel number and y is the scan line address. The vertical source address generator 912 calculates the function of equation (30). Referring now to Fig. 13, a digital special effects system 1300 for color television video signals includes an array processor 1302 for channel 1, as well as array processors 1304 for channels 2, 3 and 4 coupled to receive an input video signal for each channel. A video switcher 1306 receives the transformed video signals for each of the four channels and outputs them in a commanded combination. For example, all four channels might be combined to form a single output channel A, channels 1 and 2 might be combined to form output channel C while channels 3 and 4 are combined to form output channel D, or each transformed channel input to switche 1306 might be output as separate channels. A panel processor 1308 is implemented as a Z8000 microcomputer based microprocessor system and operates in conjunction with the control panel 1310 to receive operator commands. These commands are communicated to high level controller 1314 which is also a Z8000 microprocessor based processor and which has a multiplier 1316 coupled thereto to enhance its arithmetic capabilities. High level controller 1314 receives and stores sequences of transformation states from panel processor 1308. During operation, high level controller 1314 provides transformation commands to the respective transform composer and factorizer 1318 at the field rate. High level controller 1314 outputs the stored command states at the appropriate set times corresponding thereto and between the set times interpolates between the immediately preceding and succeeding states for each control parameter. High level controller 1314 thus permits the digital special effects system 1300 to provide a smooth, controlled and repeatable special effect that could not be obtained by operator manipulation on a real time basis. By defining special effect states at the set points, and interpolating between the set points, a smooth image manipulation effect can be realized while defining only a relatively few set points and without the need for separately defining the special effect parameters at each field. High level controller 1314 receives from panel processor 1308 and stores, data for a plurality of set points. Twenty-five or more set points are available and they will be referred to herein as knots. At each knot there is stored a parameter specifying the state at that knot for each image manipulation variable. There is also stored at each knot a number indicating the relative time between that knot and a next knot. Initially, this number represents a number of field times. However, an overall effect run time can be modified. The interpolation equation for each parameter is a function of a single independent variable. When an effect is run, the value of this single variable is passed to the high level controller 1314 from the panel processor 1308. The value of this variable is modified in each field. It is by adjusting the amount of this modification that the overall run time of an effect is controlled. The high level controller 1314 provides to transform composer and factorizer 1318 for each field time,data commanding each variable for each access of the variable for the given field time. At the knots, the stored parameter conditions are commanded. Between knots, each parameter is interpolated between its state at the preceding and succeeding knots with a third degree polynomial equation, the coefficients of which are computed in terms of the value of the parameter at the current and succeeding knots and the value of the slope or first derivative of the parameter with respect to time at the current and succeeding knots. The slopes at each knot for each parameter are determined by first testing to see if the value is changed relative to the immediately succeeding knot. If not, the slope is set to zero and the parameter is assumed to be constant between the current and succeeding knots. In the event that the parameter changes, the cubic spline interpolation technique is utilized to obtain the slope. A discussion of cubic spline interpolation is provided by Carl de Boor, A Practical Guide To Splines , pp. 49-57, Springer-Verlag (New York, 1978). In addition, the slope for each parameter is set to zero at the first and last knots of an effect. The use of knots with interknot interpolation permits a user to specify a highly complex and continuously changing video effect by merely specifying desired video transformation states at a relatively few key knot points and without need to specify each field transformation condition. Furthermore, pre-establishment of exact states and times provides a precision far superior to that which could be obtained through real time operator control while the specification of the overall run time permits the effect to exactly match a given time slot such as 15, 30 or 60 second commercial. This preprogramming also permits a plurality of video channels to be precisely synchronized. Unless otherwise specified, a parameter at a given knot assumes the value of the corresponding parameter at the preceding knot unless the current knot is the first knot in which case the value of the parameter is set to its nominal value and the time between knots is assumed to be zero. In practical applications it may be desirable to implement two adjacent knots with zero time between them. For example, it may be desirable to implement an image rotation over a given time interval and to then implement a sudden and stepwise change of the axis of rotation without a corresponding sudden change in the video image. This could be implemented for example by specifying first and second knots with a given gradual rotation function between them. A third knot could then be established at the same time as the second knot by specifying zero time for the second knot with a translated axis of rotation. A smooth transition could then occur about the new axis of rotation between the third knot and a fourth knot establishing a terminal or intermediate condition of rotation. The channel 1 array processor is generally similar to that shown in Fig. 3 with certain modifications being implemented which have been found to reduce cost without seriously degrading transformation quality. In particular, the I and Q chroma components of the video signal are sampled at 1/4 the approximately 70 nanosecond sampling rate of the Y or luminance component. This enables certain economies such as less expensive, lower speed integrated circuits to be utilized as well as less data storage capacity so long as care is exercised to assure consistency of the processing of the different video components. The channel 1 array processor includes a luminance or Y processing system 1320, a first chrominance or I processing system 1322, and a second chrominance or Q processing system 1324. A vertical source address generator 1326 and a horizontal source address generator 1328 provide common addresses to the Y, I and Q processing systems 1320, 1322 and 1324 respectively. The address generators 1326 and 1328 may be substantially identical to the corresponding vertical and horizontal source address generators 912 and 908 as shown in Fig. 3. A horizontal-to-vertical transposing memory 1330 includes five field stores which operate on a cyclical rotating basis with one of the stores receiving and storing incoming video luminance data while the other four stores output the four most recently received fields of video data on output paths A, B, C and D with the most recent field appearing on path A and the fourth most recent field appearing on path D. The individual field buffers of memory 1330 are written into as data is received in a normal horizontal raster scan order and may be read in either the same order or alternatively in an order providing a vertical raster scan of the data from top to bottom and from left to right. During normal operation data is written into memory 1330 horizontally and read out vertically and this mode will be assumed unless otherwise specified. A deinterlace filter 1332 receives the four streams of data from transposing memory 1330 and continuously converts the most recent field to a deinterlaced complete frame of data by outputing a second field of data which completes the alternate missing lines of the most recent field of data. Deinterlace filter 1332 includes a motion detector which causes the second most recent field of data to be output as the intermediate lines of the most recent field in the absence of detected motion. If motion is detected, the average of the pixel locations in the most recent field immediately above and below a given intermediate line of the most recent field is used to define the intermediate line. This interpolation or averaging of data between lines of the most recent field has the effect of decreasing the spatial resolution of the output frame of video data but eliminates a double image effect which occurs when two successive fields of data are combined to form a single frame of data which is deemed to occur or have occurred at a single instant in time. In contrast to the arrangement of Fig. 3, deinterlace filter 1332 operates whether or not H to V transposing memory 1330 is operated in a transposing mode. It will be recalled that the nontransposing mode is utilized for rotations about the Z axis of 45° to 135° and 225° to 335°. Predecimation filter 1334 receives the video data from deinterlace filter 1332 and makes available to vertical interpolation decimation filter 1336 a full size copy thereof as well as 1/2, 1/4 and 1/8 sized copies thereof. A vertical interpolation decimation filter 1336 receives an appropriate size copy of each field of video data from predecimation filter 1334 and responds to vertical source addresses from vertical source address generator 1326 to either select vertical data points or interpolate between data points in the vertical direction to output a video image which has been transformed in the vertical dimension. Vertical interpolation decimation filter 1336 utilizes the full size copy of each field when specified magnification in the vertical direction results in an output image greater than the incoming image, the same size as the incoming image, or greater than 1/2 the size of the incoming image. The half size copy is used for 1/4 to 1/2 size images, the 1/4 size copy is used for 1/8 to 1/4 size images and the 1/8 size copy is used for images less than 1/8 normal size. In the event that transposing memory 1330 is operating in a non-transposing mode, vertical interpolation decimation filter 1336 treats the image as though it had been vertically scanned even though it in fact was horizontally scanned. Operation is thus substantially the same for both modes of operation except that an image which has been truly vertically scanned will have only 425 pixels per line while the horizontally scanned image will have 768 pixels per line in the NTSC format. Filter 1336 may be implemented substantially as filter 800 (Fig. 3) although an economically advantageous arrangement for the lower bandwidth chroma components is described below in conjunction with Fig. 19. A vertical-to-horizontal transposing memory 1338 receives the partially transformed image array data from vertical interpolation decimation filter 1336 and imposes a vertical-to-horizontal transposition. Data is read into transposing memory 1338 in a vertical raster scan order and read out in a horizontal raster scan order at a single field rate of about 70 ns per pixel. A predecimation filter 1342 may be implemented substantially identically to filter 1334. It receives data from V to H transposing memory 1338 and outputs both a full size copy and 1/2, 1/4 and 1/8 size copies to a horizontal interpolation decimation filter 1344. Horizontal interpolation decimation filter 1344 responds to horizontal source addresses from horizontal source address generator 1328 to complete interpolation decimation filtering in the horizontal direction to output the luminance conponent of the transformed video image. Horizontal interpolation decimation filter 1344 may be implemented substantially identically with vertical interpolation decimation filter 1336. An advantageous arrangement of control panel 1310 is illustrated in Fig. 14 and includes a three axis rate-control joystick 1410, two status displays 1412, 1414 providing feedback to a panel operator, and several groups of pushbutton or key switch controls. By utilizing the key switch groups to specify modes, channels, and functions, a relatively complex set of controls can be implemented with a single three axis rate-control joystick 1410. With the joystick in the return or neutral position, no change of status occurs. With the joystick pushed to the right the selected X parameter is increased and continues to increase so long as the joystick is held to the right. The farther to the right the joystick is moved the faster the parameter increases. Similarly, the parameter decreases as the joystick is pushed to the left. The Y and Z axes operate in a similar manner. Motion of the joy-stick upward towards the top of Fig. 14 as shown represents an increase in the Y axis parameter while motion downward commands a decrease. For the Z axis control, counterclockwise rotation commands an increase in the parameter while clockwise rotation commands an increase. While electrical connections have been omitted for clarity, it will be appreciated that the joystick as well as each of the key switches and the status displays is connected for communication with the panel processor 1308. A channel select group of switches 1418 permits selection of one of four available channels for control of the associated video image. The last channel key selection determines the channel to which the transformation commands pertain. A clear group of switches 1420 permit the clearing of selected axes or alternatively a master clear for all axes back to the normal or input video state for a currently selected parameter. For example, if positioning (translation) has been selected and the joystick is moved to the right to cause the video image to move to the right, actuation of the clear X key will cause the image to return to its normal location. A mode select group of keys 1422 determines the overall operating mode of the transformation system and also facilitates the implementation of special features. Selection of the program key places the system in the program mode to permit the entry of transformation commands at each of the available knots starting with the first knot. Actuation of the rightward pointing arrow causes the selected knot number to be incremented while selection of the leftward pointing arrow causes the current knot number to be decremented. Actuation of the run key places the system in a run mode with a stored sequence of knots being executed. Actuation of the test key places the system in a test mode of operation in which diagnostic programs within the various microprocessor subsystems test for and indicate error conditions. Actuation of the duration key followed by one or more keys from a number key group 1424 specifies a total time in fields for an operating sequence. In program mode, the duration function specifies the transition time in fields from the current to the succeeding knot. A pair of keys labeled "store effect" and recall effect permit an entire effect or sequence of knots to be stored on a floppy disk and then recalled. The number group 1424 also includes enter and recall keys. This enter key permits a selected number to be entered in storage and terminates number entry. The recall key zeros the number being entered to allow erasure of errors. A parameter selection group 1426 determines the meaning of the various axes of the joystick. An aspect/skew skew key causes the video image to be selectively enlarged or decreased in size in the horizontal and vertical directions in response to motion of the joystick in the X and Y direction respectively. At the same time, the Z axis control of joystick 1410 may be utilized to introduce a skewing of the video image. That is, the top of the image is translated relative to the bottom of the image so as to turn squares into parallelograms. The axis select key positions in three dimensions the point about which image rotations occur. When this function is selected, a cursor is displayed to assist the user in positioning the point of rotation. All rotations occur about one of three mutually perpendicular axes passing through this center of rotation. The locate key permits positioning in three dimensions of the incoming image. A blur key permits the video image to be selectively defocused. Only the Z or ⊘ axis control of joystick 1410 is effective upon actuation of this key. A position/size key permits horizontal and vertical translation of the output video image relative to the input video image using the X and Y axes while the Z axis control of the joystick controls the size of the output video image relative to the size of the input video image. A rotate key permits control of three dimensional rotations of the image about the center point. Each of the joystick axes controls a corresponding axis of rotation. Vertical movement controls rotation about the X axis, horizontal movement controls rotation about the Y axis and rotation of the joystick causes rotation of the image about the Z axis. Any reasonable number of rotations may be specified. For example, zero rotations may be specified at one given knot with ten rotations being specified at the next knot. The interpolating capability of the high level controller 1314 will then cause ten rotations to occur between the given and the next knot. Multiple rotations are accomplished by actuating the joystick to cause rotation about a desired axis and maintaining the joystick actuated until the desired number of rotations have been counted. A depth of perspective key is effective only with the Z axis of the joystick to control the rate at which objects become smaller as they move rearward of the plane of the initial video image or larger as they move forward of this plane, as by rotation about the X axis. This can be visualized by imagining the video image rotating about an X axis at the bottom of the image. As the image rotates away from the viewer the top portion of the image becomes farther from the initial plane and hence appears smaller. The depth of perspective key permits control over the rate at which the image becomes smaller relative to the angle of rotation. A LUM HUE SAT key permits specification of the background color of the output video image in regions not occupied by the initial image. For example, in the above perspective rotation example, as the top of the image rotates away from the plane of the viewing screen, the top of the image becomes smaller and the upper right and upper left hand corners of the viewing screen are no longer occupied by the initial image. The LUM HUE SAT key permits the Y, Z and X axes respectively of the joystick 1410 to control the corresponding components of the background video image. This control over the background image can be especially useful when used in conjunction with a switcher 1306 (Fig. 13) which is programmed to respond to color or luminance keys to substitute video data of one channel for video data of another channel when putting together a composite image for a single channel. A programming group of keys 1428 facilitates the programming of the various knots for a given video effect. Actuation of an insert knot key permits a new knot to be inserted between the current and previous knots while the remove knot key similarly permits a preprogrammed knot to be deleted from a sequence of knots. Actuation of a save knot key causes all of the parameters at a given knot with the exception of the rotations to be stored for a later recall by actuation of the recall knot key. This save and recall feature is useful where the parameter state at a given knot is to be duplicated at a subsequent knot. Some or all of the parameters can of course be changed after duplication. Actuation of the pause knot key causes execution of the effect to halt at the current knot during run mode and await further user commands. A loop key actuation followed by selection of a duration number through the number key group 1424 causes a loop back from the last knot to the first knot of an effect. The duration Of the transition from last to first knot is taken to be the number entered by the user after selecting the loop key. The loop back causes the intermediate sequence of knot states to be continuously and sequentially executed until the actuation of the stop key terminates the continuous loop sequence. A freeze update rate key permits the specification through the number key group 1424 of the number of fields that a frozen video image will be held before being updated. That is, if the freeze update key is followed by the number 8 key, on every 8th field two new video fields will be sampled and held until the next update time. In effect, the horizontal-to-vertical transposing memory 1330 is inhibited from receiving a new input video field until the specified number of input video fields have occurred. As an example of entering an effect for a given channel, assume an example in which the full size picture is to shrink to one-half size at midscreen, rotate 360° about the Y axis with perspective and then return to full size. After selecting the desired channel with switch group 1418, for example channel 1, the program switch in group 1422 is actuated to set all conditions to an initialized state yielding a full size picture, without any manipulation supplied. This initial picture condition is now the first knot point of the effect. The save knot key in group 1428 is now actuated to preserve the initial condition for later use at the end of the effect where the effect is to be returned to the initial condition. A duration time is now specified through the number keyboard 1424 to define the time to the next or second knot. For example, the number 600 will cause the first knot time to be 600 field times or ten seconds. During this first 10 second interval the "zoom" from full size to half size will occur. The knot number is displayed on status display 1412 and as the knot time duration number is entered it appears on status display 1414. In general, the status display reflects the present knot as well as the state of a selected parameter. The forward or rightward pointing arrow in group 1422 is now actuated to cause incrementing to the next or second knot state. Actuation of this key closes the programming for the events of the first knot and opens the second knot for programming. The 2D position size key is now actuated from group 1426 and the joystick can now be used to position the picture on the screen according to the XY movements of the joystick or can change picture size according to movement of the rotating knob atop the joystick in the Z or ⊘ axis. For the present example the XY position is to remain constant while the joystick knob is rotated until the picture reaches one-half size. A duration time is now specified for the time to the next or third knot, which in this case will specify the time of the size reduction. The duration button is actuated and a time such as 300 field times or 5 seconds is entered. With the programming of the second knot complete, the forward key is again actuated to close the second knot and open the third knot. The third knot is to define a 360° rotation of the half-size picture about its Y axis with some three dimensional perspective effects added. The rotate key in group 1426 is now actuated to make the joystick active in rotating the picture about any of its three axes. In the present example the joystick is moved in a horizontal direction to the right to rotate the picture about its Y axis. Moving the joystick in a vertical direction would cause rotation about the X axis while rotation of the joystick knob in the Z or ⊘ axis would rotate the picture about its Z axis. In the present example, the joystick is moved to the right and held until the image has rotated through a sufficient angle to permit observation of the perspective effect, for example 30-45°. It should be appreciated that the rotation is required since the perspective effect is not observable until the image is rotated out of the plane of the viewing screen. With the image partially rotated, the joystick is released and the depth of perspective key is actuated in group 1426. The joystick ⊘ control is now active in controlling the amount of perspective desired and the desired amount of perspective is added to the picture. The rotate button is now again actuated and the picture rotation through the desired full 360° is completed by holding the joystick to the right until the rotation has occurred as viewed on the screen. A duration time is now specified for knot 3 by actuating the duration key and a set of number keys within group 1424. In this example let us assume that the time is entered as 600 field times corresponding to 10 seconds. In this case the 10 seconds will specify the time to knot 4 which is the unity or unaltered picture state. Thus during the final 10 second interval the picture will zoom back to full size. The advance arrow key is now selected to close knot 3 and open the final knot 4. The recall knot button is actuated from programming group 1428 to store the previously stored initial full size or unity parameters in the current knot point 4. The effect is now complete and can be stored on disk by selecting the store effect button from the mode control 1422. Further editing of the effects in terms of durations and manipulation changes or additions can also be made by returning to other knots, inserting additional knots at selected locations, or deleting knots. Alternatively, the total run time of the total effect can be modified without changing the relative time durations between each knot point. For example, the commanded run time of the effect is 25 seconds. However, the total run time can be easily increased to 30 seconds, as for a 30 second commercial, by actuating the duration key in group 1422 and then entering 1800 through keyboard 1424. Effectively each of the individual knot times is consequently increased by 30/25. That is, the first knot time will be effectively increased from 600 field times to 720 field times, the second knot time will be effectively increased from 300 field times to 360 field times and the third knot time will be effectively increased from 600 field times to 720 field times. This will result in a total run time for the effect of 30 seconds as commanded. Referring now to Fig. 15, the horizontal-to-vertical transposing memory 1330 includes a distributor 1502, five field stores 1510-1514 labeled 0-4, a 5:4 multiplexer 1520, and an address and control circuit 1522 connected to provide address and control signals to the other components of transposing memory 1330. Although the field stores 1510-1514 are shown separately for the luminance component, they advantageously function synchronously and with common addressing with the I and Q chrominance component field stores as explained hereinafter. Distributor 1502 receives a component of standard color television video data such as the Y or luminance component as an input and stores successive fields of the input data in successive ones of the field stores 1510-1514 on a cyclic basis. After all five field stores have been filled distributor 1502 continues to direct the incoming field of data to the field store storing the oldest field of data. As a result, the five field stores 1510-1514 always store the most recent four fields of data while the fifth most recent field of data is overwritten by incoming new data. Multiplexer 1520 receives the outputs of the five field stores and in turn outputs the data from the four most recently stored fields on four output lines on a cyclic basis such that the most recent field is output on path A, the second most recent field is output on path B, the third most recent field is output on path C, and the fourth most recent field is output on path D. The four most recent fields of video data are thus made available on a continuous basis to deinterlace filter 1332. As with horizontal to vertical transposing memory 18, transposing memory 1330 always receives data for storage in a horizontal scan direction. In a normal mode of operation the stored fields of data are transposed and output in a vertical scan direction and in a special mode of operation the memory 1330 may operate in a nontransposing mode to output the video data in a horizontal scan direction just as it has been read in. An example of an advantageous arrangement of the memory 1600 for field store 0 corresponding to store 1510 in Fig. 15 and corresponding stores for the I and Q processing systems 1322, 1324 is illustrated in Figs. 16 and 17. The memory for the luminance signal component contains eight memory components designated Y0-Y7. Each of these components is 32 words deep by 1 pixel or 8 bits wide. The memory 1600 operates on a 140 nanosecond cycle to store two luminance pixels during each cycle. During each memory cycle an early pixel is stored in one of memory components Y0, Y2, Y4, or Y6 while a next subsequent or late pixel is stored in one of four late components Y1, Y3, Y5 or Y7. Prior to writing into memory a first luminance pixel of data is stored in Y input early register 1602 in response to the Y input early strobe signal YIES. And the following pixel is stored in Y input late register 1604 in response to the Y input late strobe signal YILS. During this same two pixel time period the row and column addresses are strobed into the memory components Y0-Y7 to prepare the memory for immediate writing of the two pixels of data upon receipt of the late pixel by Y input late register 1604. Because the cycle time for economically available memory components is longer than 140 nanoseconds, the memory components are utilized in a four phase rotating configuration. During a first 140 nanosecond memory cycle phase 1 signals cause the storage of data in components Y0 and Y1. During a second phase data is stored in components Y2 and Y3, during a third phase data is stored in memory components Y4 and Y5 and during a fourth phase data is stored in memory components Y6 and Y7. For the fifth cycle the address inputs are incremented and the rotating cycle repeats itself beginning with components Y0 and Y1 storing information during phase 1. It is thus seen that for each of the memory components a time period of 4 x 140 nanoseconds or 560 nanoseconds is available for each data access cycle and this is well within the capabilities of economically available memory chips. During readout the memory components are operated in substantially the same way except that during a 140 nanosecond memory cycle data from one of the early memory components Y0, Y2, Y4 or Y6 is stored in Y output early register 1606 in response to Y output early strobe signal YOES and data from one of the components Y1, Y3, Y5 or Y7 is stored in Y output late register 1608 in response to Y output late strobe signal, YOLS. Subsequently, the two pixels of data are serialized to make them available sequentially on a Y output signal line YO by first enabling the output of Y output enable register 1606 with a Y output early enable strobe signal, YOEES and then 70 nanoseconds later enabling the output of Y output late register 1608 with a Y output late enable signal YOLES. During readout the memory components Y0-Y7 continue to operate on the same four phase rotating basis. If readout is to be in a row scan direction, operation is substantially identical to writing except that the memory components receive a read command rather than a write command. The memory arrangement shown in Fig. 16 further includes two memory components I2 and I7 for the I chrominance video signal component and two memory components Q2 and Q7 for the Q chrominance video signal component. Since the chrominance signal components are sampled at one-fourth the rate of the luminance components, only two memory modules are required for each of the chrominance signal components compared to eight memory modules for the luminance signal components. The I and Q chrominance components operate exactly in parallel except for the data which is received or read out and further, the I2 and Q2 components operate in parallel with the Y2 luminance memory component while the I7 and Q7 components operate synchronously in parallel with the Y7 luminance memory component. This synchronous parallel manner of operation permits the chrominance memory components to share the address and timing signals which are generated for the luminance components. Because the I2 and Q2 components are synchronized with the phase two Y2 component while the I7 and Q7 components are synchronized with the phase four Y7 memory component, the effect is that each of the chrominance field stores appears to operate as two 1120 nanosecond memories phased 180 degrees apart. In any event, the net result is that one pixel of I and one pixel of Q chrominance data is stored for each fourth pixel of luminance data. It is essential for proper operation of the field store 0 that the chrominance memory components be synchronized with the proper luminance memory components so that in both the horizontal scan and vertical scan readout modes chrominance data will be output at a uniform rate at one-fourth the luminance 70 nanosecond rate. That this goal is accomplished can be seen by looking at Table II. Table II is an address table illustrating the manner in which data is stored in the Y memory components. Although not separately indicated for each chrominance component, it will be appreciated that for each pixel of luminance data stored in Y memory components Y2 and Y7, corresponding pixels of chrominance data will be stored in chrominance memory components I2, Q2 and I7, Q7 as indicated collectively for the two components by the chrominance pixels C0,0; C0,1, etc. at the two righthand columns of the table. For synchronizing and timing purposes it is convenient to sometimes start operations prior to the initial address storage location. Therefore, in order to avoid the recognition of negative addresses, data is stored beginning with address location 16 x 112 = 1,792. As data is written into field store 0 in a horizontal row scan mode, data for pixels P0,0 and P0,1 arrive sequentially on Y input line Y1 and are stored in Y input early register 1602 and Y input late register 1604 respectively. As these first two pixels of data are written into registers 1602 and 1604, the row and column addresses are strobed into phase 1 memory components Y0 and Y1. As the first phase 1 memory cycle continues pixels P0,2 and P0,3 are sequentially strobed into Y input early register 1602 and Y input late register 1604 respectively. A phase 2 memory cycle then begins with the two pixels being stored respectively in component Y2 and Y3. The process continues through the first raster scan line with the memory phases being recycled back to phase 1 to store pixels P0,8 and P0,9 in memory address location 17 x 112 = 2016 after pixels P0,6 and P0,7 are stored in components Y6 and Y7 at address 1792 during phase 4. An address map allocates 112 x 8 = 896 pixels for each horizontal scan row in memory module address space. This is sufficient to accommodate the 768 pixels in an NTSC horizontal scan line as well as the greater number of pixels in a PAL scan line without changing the memory design. It will be appreciated that I and Q chrominance pixels are simultaneously stored along with luminance pixels P0,2, P0,7, P0,10 and so forth. After all pixels for the first raster scan row have been stored, preparations are made during the horizontal retrace interval for storage of the second raster scan row. Phasing is returned to phase 1 regardless of which phase stored the last pixel of the first row. However, field store sequencing begins one pixel time early for row 2. As a result, the Y input early register 1602 is strobed one pixel time before actual video data is available and is loaded with don't care information designated X in Table II. 70 nanoseconds later Y input late register 1604 is strobed to receive data for pixel P1, 0. Data storage thereafter continues in a normal manner with the chrominance portions of the field store storing data at phase 2 and phase 4 operating times. As data for the third raster scan row is received, the timing cycle begins two pixel times early so that don't care data is written into memory components Y0 and Y1 during phase time 1. During phase time 2 pixels P2,0 and P2,1 are written into components Y2 and Y3. During the same phase 2 chrominance pixel P2,0 is written into chrominance memories I2 and Q2. This same manner of operation continues with the memory starting time being advanced by one pixel time for each additional row until the eighth raster scan row has been stored. As the ninth raster scan row (row 8) is received the address inputs are incremented to 2,688 and the starting times are returned to the initial timing relationship so that only valid picture data is stored with pixels P8, 0 and P8, 1 being stored in modules Y0 and Y1 during time phase 1. The time staggering process then repeats itself with one pixel of don't care data being written at the beginning of row 9, two pixels of don't care data being written at the beginning of the tenth row and so forth. The staggering of the starting times on a modulo 8 basis for sequential raster scan rows during reading assures that pixels of video data for different rows of a single column are stored in the eight memory components on a module 8 staggered basis so that they can be sequentially available during readout in a column scan mode. For example, during the first vertical scan memory cycle time address 1792 is provided to Y input early component Y0 while address 1904 is provided to Y output late component Y1. During the phase 2 memory cycle time addresses 2016 and 2128 are provided respectively to the early and late components with pixel P2,0 being read from component Y2 and pixel P3,0 being read from component Y3. During the next phase time pixels P4,0 and P5,0 are read and so forth. Upon reading the seventh and eighth vertical column pixels, the cycle repeats itself as there is a return to phase 1 to read pixel P8,0 from component Y0 and pixel P9,0 from component Y1. For the second column memory operation begins one pixel time early just as for the second row. As a result, during the first phase 1 cycle time don't care information is read from component Y0 while pixel P0,1 is read from component Y1. During the following phase 2 time interval pixel P1,1 is read from component Y2 while pixel P2,1 is read from component Y3. This process continues within a modulo 8 recycle manner until all data for column 1 has been read. Reading of the third column, which is designated column 2, then begins two pixels times early with don't care data being read from components Y0 and Y1 during phase time 1 with pixels P2,0 and P2,1 being read from components Y2 and Y3 during phase time 2. It will be appreciated that the proper synchronous phasing of the chrominance storage components at phase times two and four will cause a chrominance pixel to be read for every fourth luminance pixel to maintain the proper chrominance one-fourth sampling rate during both row scan and column scan memory operations. At the same time, the selected field store configuration makes hardware implementation of the address and control circuitry relatively easy. The phase times are merely reset to one at the beginning of each row or column scan readout and then recirculated on a modulo 4 basis (modulo 8 basis for the memory components since they are operated two in parallel). By starting memory operations for each successive row or column one pixel time earlier on a modulo 8 basis, the staggering of the pixel storage locations is automatically accomplished to permit proper sequential access of the memories for stored pixel data on either a row scan or a column scan basis. One slight complication which must be accounted for is the crossing over of an address boundary at staggered phase intervals during readout in a column scan mode. When reading column 0, each successive pixel occurs in a successive module location in a corresponding memory address location for a row group of addresses. That is, each successive address is incremented by 112 to provide addresses 1792, 1904, 2016, 2128, 2240 and so forth. As column 1 is read out, however, this successive incrementing of the addresses by 112 is proper only until pixel P1,7 must be read from module Y0 at address location 1905 instead of location 1904. This is a departure from the straight-forward addressing scheme which requires an incrementing of the otherwise normal address for reading the 7th, 15th, 23rd, and so forth pixels. Similarly, for column 2, the address must be incremented for reading the 6th and 7th, 14th and 15th, 22nd and 23rd etc. pixels. For column 3, the address must be incremented for the 5th, 6th, and 7th pixels, the 13th, 14th, and 15th pixels, the 21st, 22nd and 23rd pixels and so forth. It is thus seen that for each progressive column the incrementing of the address must begin one pixel time earlier on a modulo 8 basis and continue until an eighth, sixteenth, twenty-fourth, etc. pixel has been read. No incrementing is required for columns 0, 8, 16, etc. As described below, this staggered incrementing is accomplished with the address and control circuitry 1522 by establishing an increment signal during vertical scan memory operations which is set progressively one pixel time earlier on a modulo 8 basis for successive columns and always terminated at a modulo 8 address boundary. Referring now to Fig. 17, there is shown the address and timing circuitry 1700 for field store 0. It will be appreciated that field stores 1-4 are substantially identical to field store 0. The address and timing circuitry 1700 includes a timing generator 1702, timing and control circuit 1704, a 7-bit horizontal address counter 1706, a 9-bit vertical address counter 1708, and an address map circuit 1710. Synchronization of the field store with incoming data is provided by a line blank clock signal which goes high shortly after the last pixel of each vertical or horizontal scan line and goes low again shortly before the first pixel time of the next scan line and a vertical clock signal, V CLOCK which produces a one pixel wide pulse immediately after the last pixel of a field. Consequently, at the end of a field signal V CLOCK asynchronously resets a 3 bit modulo 8 counter 1720 during the vertical retrace interval following each field. The zero o output is communicated to a read only memory 1722 which responds by outputing a 4 bit count to the 4 load inputs to a presettable counter 1724, which responds to a 70 ns pixel rate clock signal 70 NSCK. Counter 1724 is loaded with count 5 in response to signal Line Blank CK until this signal terminates shortly before the beginning of each scan line. Counter 1720 then immediately begins counting toward 15. At count 15 the terminal count output generates a timing and control enable signal T&C ENBL which disables further counting until counter 1724 is reloaded during the next line blank interval. The termination of the line blank signal is synchronized with the incoming video data such that the 10 pixel clock times required to count from 5 to terminal count 15 equals the system pipe line delay times required by timing and control circuit 1704 before activating field store 1600 with register strobe signals and phase 1 row and column address strobe signals. Store 1600 is thus properly synchronized to receive and store the first and subsequent pixels of data for the first scan line. After the end of the first scan line signal line blank clock goes high to increment counter 1720 to count 1 and load counter 1724 with count 6 which is now output by ROM 1722 in response to count 1 from counter 1720. Because counter 1724 starts 1 count higher its terminal count output is generated one pixel time sooner and memory 1600 begins operation one pixel time prior to valid data. If data is being stored, don' t care data is written into component Y0 of memory 1600. If data is being read, the output data is simply ignored because it arrives prior to the time at which valid video data is recognized. Following the second scan line counter 1720 is again incremented and ROM 1722 causes a count of 7 to be loaded into counter 1724 so that two pixels of don't care data are written into or read from memory 1600 prior to the valid data time. This manner of operation continues until counter 1720 is incremented to count 7 prior to the 8th scan line (scan line 7 when starting at 0) to cause count 12 to be loaded into counter 1724. This causes 7 pixels of don't care data to be written into or read from memory 1600 with the first valid pixel then occurring in association with module 7 during phase 4. After the 8th scan line and before the 9th scan line, counter 1720 is clock, causing it to overflow to count zero and repeat the above cycle. This process of starting one pixel time earlier for each scan line on a repeatable modulo 8 basis automatically accounts for the stepping or staggering of memory locations required for transposition on a high speed basis whether readings or writing, in a vertical scan mode or a horizontal scan mode. The operation of the address counting and timing circuitry remains essentially the same as timing generator 1702 provides the accounting for the required stepping of starting address locations. Because the 8 modules of field store memory 1600 store 8 pixels for each address location, horizontal address counter 1706 is incremented in a horizontal direction once every eighth column position. It is clocked by signal CKH which in the horizontal mode occurs every 560 ns at 1/8 the pixel rate. In the vertical mode the signal CKH is derived as the Line 4-7 output of counter 1720 which means that counter 1706 is incremented after every eighth vertical scan line. This is the equivalent of every eighth pixel in a horizontal scan mode. Horizontal address counter 1706 has its D inputs connected to logic zero and its load input connected to provide reset to zero in response to signal LDH which is V CLOCK in the vertical mode and Line Blank CK in the horizontal mode. Hence, in the vertical mode horizontal counter 1706 is reset at the end of each field and in the horizontal mode it is reset after each line. Vertical address counter 1708 is a 9 bit counter having its clock input connected to signal CKV, which is derived from the 70 ns Input Hold CK signal in the vertical mode and from the Line Blank CK signal in the horizontal mode, It is thus incremented for each new horizontal line (vertical position) regardless of the mode. A signal LDV causes counter 1708 to be periodically reset with the four least significant bits being derived from ROM 1722 and the more significant bits being reset to zero. At the beginning of a field vertical counter 1708 is preset to 16 to provide a small offset which avoids the use of negative numbers under some circumstances. In the horizontal mode ROM 1722 responds to an address input signal H Mode to always preset counter 1708 to count 16. However, in the vertical mode the preset state of counter 1708 depends upon the column count stored by counter 1720. For the first column vertical address counter 1708 is preset to 16. For the second column it is preset to count 15. It will be recalled that for the second column in the vertical mode the first pixel represents don't care data. Since counter 1708 is clocked at the pixel rate, by the time the second pixel arrives (representing the first pixel of video data), vertical address counter 1708 has been incremented to starting address count 16. This manner of operation continues in the vertical mode with the counter 1708 being preset to incrementally smaller counts for each new vertical scan line until count 9 is loaded before the start of the eighth scan line. By the start of the 9th scan line, counter 1720 recycles to zero and the process repeats. An address map 1710 receives the counts for counters 1706, 1708 and corrects for the failure of the number of pixels in a line to fall on a modulo 2 boundary in order to reduce wasted address space. The address map is readily implemented with adders to produce the function address = H/8 + 128V - 16V + C = H/8 + 112V + C. The multiplications fall on modulo 2 boundaries and can therefore be accomplished with binary shifts. The C or carry input is connected to occasionally increment the least significant address bit to accommodate a special situation in the vertical mode. The spacing of 112 in the vertical direction allows 8 x 112 or 896 pixels per horizontal scan line. This is sufficient for the PAL standard as well as NTSC. The carry input is generated by the Q output of a flip-flop 1726 which has its D input connected to signal H Mode, the preset input connected to the output of a decoder 1728, the clock input connected to a 560 ns (8 pixel time) clock signal which is synchronized with the starting address for each scan line memory operation, whether don't care or actual video date. Flip-flop 1726 is active only in the vertical mode and remains inactive in the horizontal mode. In the vertical mode flip-flop 1726 is loaded with logic zero to generate a carry every eighth pixel starting with the beginning of storage. It is preset to terminate the carry input every eighth pixel as vertical counter 1708 crosses a modulo 8 boundary. Decoder 1728 is enabled for every pixel time in the vertical mode by CKV which is driven by the 70 ns input hold CK signal. In the horizontal mode encoder 1728 is enabled by the Line Blank CK signal during each blanking time. As column zero is scanned in the vertical mode the 560 ns signal Pixel CK/8 clocks flip-flop 1726 but counter 1708 is at count 16, a modulo 8 boundary, and decoder 1728 immediately presets flip-flop 1726 before its output is effective to cause an address increment. This is repeated for every eighth pixel. For column 1 flip-flop 1726 is clocked at cycle start while counter 1708 is set to 15. The carry input is thus active while the don't care pixel read during the blanking interval. At the next pixel time counter 1708 is incremented to 16 and flip-flop 1726 is preset to terminate the carry command. However, after pixel P7,1 (8 pixel times (560 ns) after start is read, flip-flop 1726 is clocked to reset it and cause an address increment for pixel P7,1. Looking at Table II it will be seen that this address increment properly addresses the data for this pixel. For column 2, memory 1600 operation begins 2 pixels early and the last two pixels of each block of 8 receive an incremental address. For column 3 the last three pixels in each block of 8 receive an incremented address until for column 7 (the eighth column) the last 7 pixels in each group of eight receive an incremented address. The cycle then repeats itself with no increments being commanded for column 8. While the memory 1600 operates at a 2 pixel parallel 140 ns clock rate, the addresses for each of the two active memory modules during a memory cycle can be different. Address map 1710 must therefore provide alternate early and late addresses at the pixel rate. During each 140 ns cycle the early address is loaded into an early address hold buffer 1730. Seventy nano-seconds later the late address is loaded into the early address hold buffer 1730 and a late address buffer register 1132. At the same time, the early address previously loaded into hold buffer 1730 is loaded into an early address buffer 1734 for presentation to memory 1600. During the next 70 NSEC clock period the late address loaded into hold buffer 1730 is simply lost as the next early address is loaded into buffer 1730. In this way the correct address is presented to memory 1600 for each of the two modules which are active during a 140 NSEC phase time. In the horizontal mode there are relatively few scan lines with a large number of pixels per line. In the vertical mode there are more scan lines but with fewer pixels per line. Consequently there are also more blanking intervals, but with a shorter duration for each interval. As a result, it has been found to be advantageous when implementing memory 1600 with dynamic memory chips to perform 1 refresh cycle during each blanking interval in the vertical mode but 2 refresh cycles in the horizontal mode. Referring now to Fig. 18, deinterlace filter 1332 includes a motion detector 1802 and a deinterlacing or frame generating circuit 1804 which outputs a complete frame of data at the field rate. For each field time, the newest stored field is always output as half of the video data and the intermediate lines of the frame are supplied from the second most recent field if no motion is detected by motion detector 1802. The occurrence of motion tends to create a double image of the moving object when two different fields sampled 1/60 of a second apart are merged into a frame representing a single instant in time. Hence, in response to the detection of motion by motion detector 1802, the intermediate lines of the frame which are output on the data path designated old field are taken as the average of the pixels above and below each successive pixel in an intermediate line. This averaging of upper and lower pixels to generate an intermediate line of pixels has the effect of reducing bandwidth by approximately 1/2 in the vertical direction, but presents a more pleasing image than the double image effect which occurs when two successive fields are combined during the occurrence of motion. A subtractor 1810 receives the newest field on input A and the third newest field on input C and subtracts the data of the third newest field from the data representing the newest field on a sequential pixel by pixel basis with the difference being stored in an 8-bit register 1812. A threshold detector 1814 responds to the difference outputs of register 1812 and outputs a logic 1 signal whenever the difference exceeds a selected threshold such as 8 out of 256 possible states. A 1 bit register 1816 stores the motion indication output from threshold detector 1814 for presentation to an OR gate 1820 and for further presentation to a 1 pixel delay circuit 1818 whose output is also presented to OR gate 1820. Similarly, a subtractor 1830 subtracts the pixel data for the fourth newest field on input D from the pixel data for the comparable second newest field on input B and presents the difference to an 8 bit register 1832. A threshold detector 1834 responds to the difference output stored by register 1832 and outputs a logic 1 signal whenever this difference exceeds a given threshold such as 8 out of 256 states. This threshold output represents an indication of motion which is stored by 1 bit register 1836, the output of which is passed through a 1 pixel delay circuit 1838 to OR gate 1820. The 12 pixel time delays through registers 1812, 1816 and 1832, 1836 plus the extra time delays through delay circuits 1818 and 1838 are synchronized with delays inserted in the video data path such that the detection of motion at a pixel location in the newest field causes the pixels thereabove and therebelow to be generated as the average of the two pixels in the newest field vertically above and below the pixel being generated. If motion is detected at a pixel location in the second newest field, only that single pixel location is generated as the average of the pixels immediately above and below the generated pixel. Delay circuits 1818 and 1838 respond to a pixel signal during a vertical scan to provide a 1 pixel delay and to a line signal during a horizontal scan to provide a 1 line delay since vertically adjacent pixels will be separated by a line scan time in the horizontal scan mode. The pixel data for the newest field on input A is passed through two 8 bit registers 1840, 1842 which compensate for delays of registers 1812 and 1816 in the motion detector, to a delay circuit 1844. Delay circuit 1844 responds to a pixel/line delay input from a trming and control circuit 1850 to provide a 1 pixel delay during a vertical scan normal mode of operation. The output of delay circuit 1844 represents the video data for the new field portion of the frames of data which are output at the field rate. An adder circuit 1846 adds the input and output to delay circuit 1844, deletes the least significant bit of the sum to effectively divide it by 2 and provide an average, and communicates the average to the A input of a multiplexer 1848. The B input is coupled to the output of a multiplexer 1866. The select A input to multiplexer 1848 is coupled to the output of OR gate 1820 to receive the motion detection signal. Hence, in the presence of the motion signal the alternate lines of the output frame of data are output by multiplexer 1848 as the average of the video data above and below the pixel of data which is being synthesized. This output of multiplexer 1848 is designated old field. The second newest field of data appearing on input B is shifted by two 8 bit registers 1860 and 1862 which compensate for the delays occurring in corresponding 8 bit registers 1832 and 1836 of the motion detector circuit 1802 and applied to the input of a delay circuit 1864. During a normal vertical scan mode of operation delay circuit 1864 provides a 1 pixel delay in response to the pixel/ line signal from timing and control circuit 1850. The output of delay circuit 1864 is communicated to the A input of multiplexer 1866. Consequently, in the absence of a motion signal from OR gate 1820, the old field video data which interlaces the lines of the new field video data to form a complete frame of data is taken from the second newest field of data coming in on input B. During a special mode of operation in which the transposing memory 1330 outputs data in a horizontal scan rather than a vertical scan direction, the pixel/line signals must command the delay circuits 1818, 1838, 1844 and 1864 to store or delay a complete line of data in order that an incoming pixel of data may be matched with the pixel immediately above it in the incoming field (the incoming pixel will be matched with a pixel two lines above it in a frame). The proper corresponding vertically juxtaposed pixel data may thus be averaged in adder 1846 for presentation to the A input of multiplexer 1848. Delay line 1864 provides a one line delay during the horizontal scan mode of operation to provide compatibility with the one line delay which must occur in decay circuit 1844. Deinterlace filter 1332 thus outputs complete frames of data at the field rate with the newest field of data being continuously output on the new field path and with the intermediate horizontal lines of data appearing on the old field output path as either the second oldest field of data when motion is not detected or the average of the two vertically adjacent pixels in the new field of data when motion is detected. It will be appreciated that in a vertical scan mode the time sequential new field and old field outputs will represent vertically adjacent pairs of pixel data. That is, when an even line field is the newest field being received, the new field and old field lines will carry respectively data for pixels P0,0 and P1,0 followed by P2,0 and P3,0 followed by P4,0 and P5,0 and so forth. In a horizontal scan mode of operation the new field and old field will carry data for vertically adjacent complete lines of data. That is, when the newest input field is an even field the sequence of data will be for pixel locations 00 P0,0 and P1,0 for the newest and second newest field data followed by P0,1 and P1,1 followed by P0,2 and P1,2 and so forth until the first two lines of a frame of data have been output. After the 0 and first lines have been output the second and third lines will be output and so forth. When the newest field is an even field representing lines 0, 2, 4, etc., the old field contains lines 1, 3, 5, etc. with the old field pixel representing data one line below the corresponding new field pixel. The timing relationship of adder 1846 is such that when motion is detected the old field is generated as the average of data in the current line and the subsequent line. For example, in the vertical mode the new field pixel P0,2 is output with pixel P0,3 formed as the average of pixels P0,2 and P0,4. However, were the new field to be an odd field, this timing relationship would result in a pixel P0,3 being output with pixel P0,2 formed as the average of pixels P0,3 and P0,5 rather than pixels P0,1 and P0,3 as would be desired. This relationship is corrected by bypassing delay circuits 1838 and 1864 when the newest field is an odd field. This in effect produces output data pairs for row pairs don't care, 0 and 1, 2 and 3,4 etc. As a result the proper timing relationship is restored such that the old field data is one line below the corresponding new field data and the old field data is properly derived by averaging the current pixel and the pixel for the line below it in the new field. A multiplexer 1866 is connected to selectively bypass delay 1864 with the A input connected to the output of delay 1864 and the B input connected to the input of delay 1864. The select A input is connected to signal Even Field to select the A input for an even field and the B input for an odd field. Referring now to Fig. 19, the chroma predecimation and interpolation decimation filters 1900 are essentially the same for both the vertical and horizontal portions of the system. While the chroma system could utilize filters constructed similarly to predecimation filters 1334, 1342 and vertical interpolation decimation filter 1336, the bandwidth for the chroma data is only one-fourth that of the luminance data and the arrangement of Fig. 19 takes account of the corresponding lower data speed to provide a lower cost implementation. Chroma predecimation and interpolation decimation filters 1900 include a pair of line buffer memory segments 1902, 1904, a write address circuit 1906 which provides write addresses to the buffer segments 1902, 1904 as data is received from the preceding transposing memory corresponding to the H to V transposing memory 1330 or V to H transposing memory 1338 in the luminance data path. Write address circuit 1906 also supplies addresses as data is written back into line buffer segments 1902, 1904 after having been stored and then read out and predecimated by a predecimation filter 1908. Line buffer segments 1902 and 1904 operate in parallel to double the speed of memory 1600. Line buffer segments 1902, 1904 actually store three lines of video data with the storage for each line including both a full size copy and a predecimated partial sized copies thereof including half size, one-fourth size and one-eighth size. The filters 1900 operate continuously on the three lines of data in an interleaved fashion. At one line storage locations an incoming line of video data is stored so as to replace the oldest line of video data. At the same time the newest complete line of video data is predecimated by predecimation filter 1908 and the second newest line of complete data which, represents the newest line of completely predecimated data, is output by interpolation decimation filter 1910. Memory segments 1902, 1904 operate on a 560 nanosecond cycle consisting of eight 70 nanosecond subcycles. During a given memory cycle incoming data is received and stored in registers 1920 and 1921. During the first half of the next cycle and before the early pixel of data is received for the next cycle, the two pixels stored in registers 1920 and 1921 are written into the line buffer segments 1902, 1904. Similarly, two pixels of data processed by predecimation filter 1908 are stored by early and late registers 1924, 1925 pending the writing of the predecimated data stored therein back into line buffer segments 1902, 1904. The eight subcycle repeating sequence for each cycle of each 560 nanosecond cycle of line buffer segments 1902, 1904 occurs as follows. 1. Interpolate. That is, read out two pixels of video data to early and late pixel interpolation decimation buffer registers 1928, 1929 for use by interpolation filter 1910. 2. Readout two pixels of data for predecimation filter 1908 and store a pixel of predecimated pixel data in early predecimated data buffer register 1924. 3. Interpolate. Readout a second pair of pixels for storage in registers 1928, 1929. 4. Write the two pixels of incoming data stored in registers 1920 and 1921 into line buffer memory segments 1902, 1904 at the next sequential address location in the current incoming line section of the memory address space. 5. Interpolate, with two more pixels of video data being written into buffer registers 1928, 1929. 6. Readout a pair of pixels for predecimation filter 1908 with a pixel of predecimated data being written into late predecimated data buffer register 1925. 7. Interpolate by reading out two more pixels of data for storage by interpolation buffer registers 1928, 1929. 8. Write two pixels of predecimated data which have previously been stored in early and late predecimation registers 1924, 1925 into buffer memory segments 1902, 1904. It will be noted that the clocking and output enabling of the buffer registers shown in Fig. 19 have been omitted for clarity. However, such clocking and gating can be readily implemented according to the schedule indicated above. Predecimation filter 1908 provides a 2:1 compaction for each passage of the data therethrough. It is operated on a cyclic basis much as in the manner of operation of predecimation filter 700. First the full size copy of a line of data is passed through filter 1908 and reduced to half size. Then the half size copy is reduced to one-fourth size followed by the reduction of the one-fourth size copy to one-eighth size. Further size reductions would of course be possible but are not implemented in the present embodiment of the invention. The predecimation filter 1908 may be advantageously implemented as a 5 point filter utilizing the sequential weighting factors of 3/32, 8/32, 10/32, 8/32, and 3/32. Operation of the interpolation decimation filter 1910 is substantially the same as that of the interpolation decimation filter 800 as shown in Fig. 10 except that coefficient store 1932 outputs a weighting coefficient to multiplier 1933 which is varied according to the relative position of a pixel of data within all of the pixels which are being weighted to provide the filter function rather than using the barrel shifter 810 to prealign the video data to match a predetermined filter function weighting. In effect, this shifting of relative pixel data positions is accommodated through the addressing of coefficient store 1932 rather than through the actual shifting of the video data. A read address processor 1934 provides the read addresses to line buffer memory segments 1902, 1904. As data is read out for predecimation by filter 1908, the addresses are merely sequentially advanced first through the full size data, then through the half size data, and then through the one-fourth size data as the one-eighth size predecimated data is formed. For interpolation, the read address processor 1934 receives source addresses from source address generator 1326 and responds to each source address by addressing four pixels of data which surround the source address. The principle of implementation is essentially the same as the address circuitry for line buffer 809 except that a 4 point filter is utilized instead of an 8 point filter. The addresses for the line buffer segments 1902, 1904 must be selectively incremented or decremented as necessary to accommodate the actual address location of the required pixel of video data for a given source address. Interpolation decimation filter 1910 operates on single pixels of video data being interpolated on a 70 nanosecond cycle which matches the rate of two pixels of data received by buffer registers 1928, 1929 from line buffer segments 1902, 1904 every 140 nanoseconds. Filter 1910 is a 4 point filter and thus outputs one pixel of data every 280 nanoseconds, which is consistent with the one-fourth sampling rate and bandwidth of the chroma data. After the storage of two pixels of video data in buffer registers 1928, 1929 at the end of the first memory subcycle, during the second memory subcycle multiplier 1933 multiples the value of the pixels stored in register 1928 times a coefficient value from storage 1932 with the results being stored in register 1940 at the end of subcycle two. Simultaneously, at the end of subcycle two an accumulating register 1942 is cleared. During memory subcycle three the line buffer segments 1902, 1904 output two more pixels of interpolation decimation data and multiplier 1933 multiplies the value of the pixel data stored by register 1929 by a new coefficient provided by coefficient store 1932. At the end of subcycle three, the two new pixels of data are clocked into buffer registers 1928, 1929 as the output of multiplier 1933 is clocked into register 1940 and the output of adder 1944, which represents the sum of the contents of register 1940 and accumulator 1942, are clocked into accumulator 1942. Since accumulator 1942 had been previously cleared, in this case the contents of register 1940 are stored in accumulator 1942. This represents the first pixel of a 4 point filter cycle. During memory subcycle four, multiplier 1933 multiplies the third pixel of the cycle in register 1928 by a proper coefficient and adder 1944 adds the first pixel of the cycle stored in register 1942 to the second pixel of the cycle stored in register 1940. At the end of memory subcycle four the third pixel is stored in register 1940 and the sum of the first two pixels is stored in accumulator 1942. During memory subcycle five the line buffers 1902, 1904 readout another pair of pixels as multiplier 1933 multiplies the pixel previously stored in register 1929 by its proper coefficient and adder 1944 produces the sum of the first two pixels stored in accumulator 1942 plus the third pixel stored in register 1940. At the end of the fifth memory cycle the three pixel sum at the output of adder 1944 is stored in accumulator register 1942, the fourth weighted pixel is stored in register 1940 and the first two pixels for the next filter cycle are stored in buffer registers 1928, 1929. During memory subcycle six multiplier 1933 multiplies the pixel data in register 1928 by an appropriate coefficient from store 1932 while adder 1944 adds the three pixel sum accumulated in register 1942 to the fourth weighted pixel stored in register 1940. At the end of memory cycle six the four pixel sum output from adder 1944 is loaded into an output buffer register 1946, accumulator register 1942 is cleared and the first weighted pixel for the second output pixel is stored in register 1940. The above described interpolation decimation filter cycle thus continues to repeat itself with two 280 nanosecond filter cycles occurring for each 560 nanosecond memory cycle. The weighting factors provided by coefficient store 1932 are selected to provide a desired filter function which depends upon the particular full size or partial size predecimated copy which is being utilized as the source data, the amount of further size reduction or enlargement provided by interpolation filter 1910, and the location of the source address point relative to the pixel.

Claims: A system for electronically transforming input data samples corresponding to picture elements of an image, said transformation corresponding to transformation of said picture elements of said image from a source location to a target location in a two dimensional co-ordinate system in which two co-ordinates indicate position in respective first and second directions, characterised by: a first memory (18, 1330) coupled to receive a serial sequence of data samples corresponding to source locations serialized by scanning in said first direction, the first memory being selectively operable to output the data samples in the serial sequence in which they are received or in a serial sequence representing a scan in said second direction; a first filter (800, 1336) coupled to receive the data samples output from said first memory and to output a serial sequence of first filtered data samples for target locations as a filtered function of a plurality of the data samples corresponding to picture elements neighbouring respective first source location co-ordinates, said sequence output by said first filter corresponding to scanning in the direction corresponding to the output of said first memory; a second memory (900, 1338) coupled to receive the serial sequence of first filtered data samples from the first filter scanned in the respective said direction and to output the first filtered data samples in scan line data sample sequence scanned in the other said direction; a second filter (906, 1344) coupled to receive the first filtered data samples output from said second memory and to output a serial sequence of second filtered data samples scanned in said other direction for target locations as a filtered function of a plurality of the first filtered data samples corresponding to picture elements neighbouring second source location co-ordinates; and first and second source address generators (912, 908; 1326, 1328) coupled to provide to the first and second filters serial sequences of respective first and second source addresses corresponding to respective serial sequences of co-ordinates in accordance with a desired transformation between the source and target locations. A system according to claim 1 further characterised by a third filter (700, 1334) interposed between said first memory and said first filter for producing a sequence of data samples corresponding to picture elements of a fractional-size reproduction of the image that is a fraction of the linear size of the image corresponding to the data samples input thereto, and a fourth filter (904, 1342) interposed between said second memory and said second filter for producing a sequence of data samples corresponding to picture elements of a fractional-size reproduction of the image that is a fraction of the linear size of the image corresponding to the data samples input thereto. A system according to either one of claims 1 and 2 characterised in that the data samples correspond to two-field interlaced raster scan television images, further comprising a deinterlace filter (600, 1332) disposed between the first memory and the first filter to deinterlace interlaced two-field images into respective deinterlaced single-frame images. A system according to any one of claims 1 to 3 characterised in that said pluralities of data samples corresponding to picture elements neighbouring respective first and second source location co-ordinates correspond to respective pluralities of picture elements disposed on each side of respective source location co-ordinates. A system according to any one of claims 1 to 4 characterised by further means (1304) for transforming data samples corresponding to at least one other image at the same time, and a switcher (1306) coupled to receive transformed data samples corresponding to respective images and to output said transformed data samples in a selected combination. A system according to any one of claims 1 to 5, in which the or each image has three components representing a color television picture, characterised by a said first memory and a said second memory in respect to each of said components, respective memories being addressed in parallel by said first and second address generators. A system according to claim 6 wherein the said components are a luminance component and two chrominance components.

Inventors: GABRIEL, STEVEN ALLEN
Applicants: AMPEX CORPORATION
Application year: 1981
Main classification: G06F15
IPC codes: G06T1, G06T3