Quadtree-structured walsh transform coding
First Claim
1. A method for displaying an image which is represented by a quadtree code, the method comprising the steps of:
- storing a portion of a quadtree code in a memory, the quadtree code including values which indicate leaf nodes and values which indicate a fixed number of coefficients for each of the leaf nodes. wherein the leaf nodes correspond to blocks in a quadtree partition of the image. and for each leaf node, the coefficients for that leaf node are Walsh transform coefficients of a matrix of pixel values which represents a block corresponding to that leaf node;
determining, from the quadtree code, Walsh transform coefficients for a selected one of the leaf nodes;
performing an inverse Walsh transformation on a matrix containing the Walsh transform coefficients for the selected leaf node, to generate pixel values which indicate colors for pixels in a block that corresponds to the selected leaf node; and
displaying a portion of the image by displaying the pixels with colors as indicated by the generated pixel values.
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Abstract
Two dimensional data structures are represented by quadtree codes with embedded Walsh transform coefficients. The quadtree code permits both variable block size inherent in quadtrees, and the calculational simplicity of Walsh transform descriptions of nearly uniform blocks of data. Construction of the quadtree is calculationally simple for implementation in a digital system which does a bottom-up determination of the quadtree because Walsh transform coefficients and a measure of the distortion can be recursively calculated using only Walsh transform coefficients from the previous level in the quadtree. Uniform step size quantization, which is optimal for variable length coding and generalized gaussian distributions, permits fast encoding and decoding of quadtree code.
92 Citations
29 Claims
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1. A method for displaying an image which is represented by a quadtree code, the method comprising the steps of:
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storing a portion of a quadtree code in a memory, the quadtree code including values which indicate leaf nodes and values which indicate a fixed number of coefficients for each of the leaf nodes. wherein the leaf nodes correspond to blocks in a quadtree partition of the image. and for each leaf node, the coefficients for that leaf node are Walsh transform coefficients of a matrix of pixel values which represents a block corresponding to that leaf node; determining, from the quadtree code, Walsh transform coefficients for a selected one of the leaf nodes; performing an inverse Walsh transformation on a matrix containing the Walsh transform coefficients for the selected leaf node, to generate pixel values which indicate colors for pixels in a block that corresponds to the selected leaf node; and displaying a portion of the image by displaying the pixels with colors as indicated by the generated pixel values. - View Dependent Claims (2, 3, 4, 5)
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6. A method for representing a visual image as digital signals, the method comprising the steps of:
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representing the image as a two-dimensional array of values, each value indicating a color for a pixel within the image; partitioning the two-dimensional array to form a quadtree partition, the guadtree partition comprising blocks of data representing portions of the image; generating signals which identify the blocks in the quadtree partition; and generating, for each block in the quadtree partition, signals which indicate a fixed number of Walsh transform coefficients representing that block. - View Dependent Claims (7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21)
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22. A method for transmitting signals which represents an image, the method comprising the steps of:
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generating a representation of the image, the representation including a two-dimensional array of values; partitioning the two-dimensional array into 4I non-intersecting blocks, each block containing N2 values of an N-by-N matrix corresponding to the block, wherein I is a positive integer, and N is a non-negative power of two; selecting from the 4I blocks a set of four neighboring blocks which together include (2N)2 values that constitute a first 2N-by-2N matrix; determining, for each of the four neighboring blocks, M Walsh transform coefficients of the N-by-N matrix corresponding to the block, where M is an integer less than or equal to N2 ; determining M Walsh transform coefficients of the first 2N-by-2N matrix; measuring a differences between a second 2N-by-2N matrix and a third 2N-by-2N matrix, wherein the second 2N-by-2N matrix is generated by an inverse Walsh transform of four N-by-N matrices, each of which contains M Walsh transform coefficients for a corresponding one of the four neighboring block, and the third 2N-by-2N matrix is generated by an inverse Walsh transformation of a 2N-by-2N matrix containing the M Walsh transform coefficients of the first 2N-by-2N matrix; and transmitting digital signals which represent the image by indicating the M Walsh transform coefficients for the four neighboring blocks when the difference is greater than a threshold value. - View Dependent Claims (23, 24, 25)
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26. An apparatus for encoding an image, comprising:
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a memory; an input device coupled to the memory, the input device receiving a signal which represents the image as a two-dimensional data structure, wherein the input device stores the two-dimensional data structure in the memory; and a processor coupled to the memory, wherein the processor comprises; means for generating a quadtree partition of a two-dimensional data structure stored in the memory, the quadtree partition consisting of blocks from a series of partitions of the two-dimensional data structure, wherein the blocks in the quadtree partition are selected according to errors introduced by representing the blocks with a fixed number of Walsh transform coefficients per block; means for generating a code which indicates which of the blocks of the series of partitions are in the quadtree partition of the two-dimensional data structure; and means for generating the fixed number of Walsh transform coefficients for each block in the quadtree partition. - View Dependent Claims (27, 28, 29)
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Specification