HP Inc. The method of claim 1, wherein k is determined from the following relationship: EQU The method of claim 1, wherein k is determined by: a. The method of claim 1, wherein each pixel value is a member of a first alphabet of values, further comprising the step of: mapping each pixel value of said image to a value in a second alphabet, wherein said second alphabet is a subset of said first alphabet.

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HP Inc. The method of claim 1, wherein k is determined from the following relationship: EQU The method of claim 1, wherein k is determined by: a. The method of claim 1, wherein each pixel value is a member of a first alphabet of values, further comprising the step of: mapping each pixel value of said image to a value in a second alphabet, wherein said second alphabet is a subset of said first alphabet.

The method of claim 6, wherein after decoding said mapping introduces an error of uniform bound E and each pixel value xi is mapped to a value yi according to the relationship: EQU A method of operating a computer to losslessly compress digitized images comprising the steps of: a. The method of claim 10 further comprising the step of computing the context by determining values of gradients between pixels adjacent to the pixel. The method of claim 11 further comprising the step of computing the context by quantizing the gradients into approximately equiprobable regions.

The method of claim 13 wherein the alphabet extension is a length of consecutive constant values. The method of claim 23 wherein the constant values are constant pixel values.

The method of claim 23 wherein the constant values are constant prediction residuals. The method of claim 14 farther comprising the step of ranking the lengths of consecutive constant prediction residuals by occurrence counts; and for an occurrence of a length r of consecutive constant prediction residuals, encoding the length as a Golomb code for the rank of the length, i r.

The method of claim 14 further comprising the steps of: definining a second special context; when encoding a pixel immediately following the encoding of an event in the first special context: encoding the pixel immediately following the encoding of an event in the first special context using a Golomb parameter obtained from values A and N for the second special context; and updating the values A and N for the second special context.

The method of claim 19 wherein the constant values are constant pixel values; and a pixel occurring in the second special context is the first pixel following a run of constant pixel values.

The method of claim 17 wherein the context is computed from values of pixels previously encoded and adjacent to the pixel being processed, and wherein a pixel occurs in said special context when gradients between pairs of the adjacent pixels are all zero 0.

The method of claim 22 wherein biases in prediction are cancelled, further comprising the steps of: for each context centering the distribution of prediction residuals occurring in that context by: for each context, computing a correction value C as a function of an accumulation of prediction residuals B encountered in the context and a count N of occurences of the context; and for each pixel, prior to encoding the pixel, correcting the predicted value of the pixel by adding the correction value C to the predicted value for the pixel.

The method of claim 23 wherein: the accumulation of prediction residuals B is the accumulation of prediction residuals prior to correction of the predicted value; and the correction value C is computed by dividing B by N.

The method of claim 23 further comprising the step of: adjusting the value C as a function of the values B and N. The method of claim 10 further comprising the step of: if the value N for a particular context exceeds a predetermined threshold value N0, resetting the values for N and A. The method of claim 26 wherein N and A are reset to half their values prior to being reset, respectively.

The method of claim 23 wherein: the accumulation of prediction residuals B is the accumulation of prediction residuals after correction of the predicted value; and further comprising the step of computing C and B by: if B is a large negative number, decrementing C and adding N to B; and if B is a large positive number, incrementing C and subtracting N from B. The method of claim 28, wherein the large negative number is a number less than or equal to the negative of N divided by 2, and wherein the large positive number is a number greater than N divided by 2.

The method of claim 23 further comprising the steps of: if B is less than or equal to the negative of N, decrementing C and adding N to B; and if B is greater than 0, incrementing C and subtracting N from B. The method of claim 11 the step of quantizing the context further comprises the step of: quantizing each gradient into one of a small number of regions defined by at least one integer valued threshold parameter.

The method of claim 31 wherein the context of a pixel being encoded is determined from a causal template of neighboring pixels, including a first pixel immediately north of the pixel being encoded, a second pixel west of the pixel being encoded, a third pixel northwest of the pixel being encoded, and a fourth pixel northeast of the pixel being encoded, each having a value, and the step of determining the context further comprises the steps of: determining a first gradient between the values of the fourth and the first pixels; determining a second gradient between the values of the first and the third pixels; and determining a third gradient between the values of the third and the second pixels.

The method of claim 32 wherein the causal template further includes a fifth pixel immediately west of said second pixel, and the step of determining the context further comprises the step of: determining a fourth gradient between the values of the second and fifth pixels.

An image compression encoder system wherein for each pixel in an image there is a context based on the pixels that have been encoded prior to the each pixel, having an encoder comprising: a. The image compression encoder system of claim 40 further comprising: a second multiplexer connected to the second storage unit for selectively adding the value N for the context to the value B for the context, subtracting the value N for the context from the value B for the context, or adding the residual value to the value B for the context.

An image decoder system wherein for each pixel in a compressed image there is a context based on the pixels that have been decoded prior to the each pixel, the decoder comprising: a.

The image compression encoder system of claim 48 further comprising: a second multiplexer connected to the second storage unit for selectively adding the value N for the context to the value B for the context, subtracting the value N for the context from the value B for the context, or adding the residual value to the value B for the context.

A method of operating a computer to decompress encoded digitized images comprising the steps of: a. The method of claim 51 wherein the alphabet extension is a length of consecutive constant values. The method of claim 52 wherein the consequtive constant values are consecutive constant prediction residuals, the method further comprising: the step of ranking the lengths of consecutive constant prediction residuals by occurrence counts; and for an occurrence of a length r of consecutive constant prediction residuals, decoding the length as a Golomb code for the rank of the length, i r.

The method of claim 52 further comprising the steps of: definining a second special context; when decoding a pixel immediately following the decoding of an event in the first special context: decoding the pixel immediately following the decoding of an event in the first special context using a Golomb parameter obtained from values A and N for the second special context; and updating the values A and N for the second special context.

The method of claim 55 wherein the constant values are constant pixel values; and a pixel occurring in the second special context is the first pixel following the decoding of a run of constant pixel values. A computer storage media having computer executable instructions for controlling the operation of a computer to compress digitized images, comprising: instructions for causing said computer to, for each pixel in the image: i.

A computer storage media having computer executable instructions for controlling the operation of a computer to decompress compressed digitized images, comprising: instructions for causing said computer to, for each encoded pixel in the compressed digitized image: i. Provisional Application No. The present application is related to U. Technical Field of the Invention The invention relates generally to image compression, and, more particularly, to low complexity lossless and near-lossless adaptive compression having context-specific Huffman codes.

Background Art The use of compression algorithms for efficient data storage and communication has become a key component in most digital imaging systems. In many applications a reduction in the amount of resources required to store or transmit data is crucial, so that compression can be viewed as an enabling technology. Image compression algorithms are broadly classified into lossy irreversible schemes, for which the original pixel intensities cannot be perfectly recovered from the encoded bit stream, and lossless reversible schemes, for which the coding algorithms yield decompressed images identical to the original digitized images.

The latter, in general, are required in applications where the pictures are subjected to further processing, e. Most lossy compression techniques are designed for the human visual system and may destroy some of the information required during processing.

Thus, images from digital radiology in medicine or from satellites in space are usually compressed by reversible methods. Lossless compression is generally the choice also for images obtained at great cost, for which it may be unwise to discard any information that later may be found to be necessary, or in applications where the desired quality of the rendered image is unknown at the time of acquisition, as may be the case in digital photography.

Gray-scale images are considered as two-dimensional arrays of intensity values, digitized to some number of bits. In most applications 8 bits are used, although 12 bits is customary in digital radiology. Color images, in turn, are usually represented in some color space e. Thus, the tools employed in the compression of color images are derived from those developed for gray-scale images and the discussion herein will generally focus on the latter, but should be considered also applicable to color images.

It should be noted though that the combination of these tools in the case of color may take into account the possible correlation between color planes e. Lossless image compression techniques often consist of two distinct and independent components: modeling and coding. The modeling part can be formulated as an inductive inference problem, in which an image is observed pixel by pixel in some pre-defined order e. Notice that pixel values are indexed with only one subscript, despite corresponding to a two-dimensional array.

This subscript denotes the "time" index in the pre-defined order. In the coding part of the scheme, this probability assignment could be used sequentially by an arithmetic coder to obtain a total code length of.

Arithmetic coding is described in J. Rissanen and G. Langdon, Jr. Theory, vol. IT, pp. Alternatively, in a two-pass scheme the conditional distribution can be learned from the whole image in a first pass and and some description of it must be sent to the decoder as header information.

In this case, the total code length includes the length of the header. Yet, both the second encoding pass and the single-pass decoding are subject to the same sequential formulation. In state-of-the-art lossless image compression schemes, the probability assignment is generally broken into the following components: a. Again, this context is a function of a past subsequence xi1 xi2. An image is input to a modeler Inside the modeler , the image is input to a predictor The errors are then modeled in an error modeler The probability distribution of the error values and the error values for individual pixels are fed to a coder to produce an output compressed bitstream Some of the best available published compression ratios correspond to the scheme discussed in M.

Weinberger, J. Rissanen, and R. Image Processing, Vol. The degree of quantization is determined dynamically with a complex calculation based on an intricate database of symbol occurrence counts. The variable sizes of the conditioning contexts are optimized based on the concept of stochastic complexity in order to prevent "overfitting" the model. In principle, larger contexts better capture the inherent "structure" of the data, as they imply more skewed distributions for the prediction residuals, which results in a better fit.

However, choosing a model whose complexity is unnecessarily large i. These redundant parameters imply a "model cost," which in a sequential scheme can be interpreted as capturing the penalties of "context dilution" occurring when count statistics must be spread over too many contexts, thus affecting the accuracy of the corresponding estimates.

In non-sequential two-pass schemes the model cost represents the code length required to encode the model parameters estimated in the first pass, which must be transmitted to the decoder. The prediction step in Weinberger et al. The resulting code length is provably asymptotically optimal in a certain broad class of processes used to model the data.

Both the modeling and coding part of the scheme of Weinberger et al. Some alternatives exist which use a fixed predictor and a non-optimized context model for the prediction residuals, with only moderate deterioration in the compression ratios obtained for some types of images especially natural landscapes and portraits; the deterioration is more significant for medical and satellite images. Digital compression and coding of continuous tone still images--Requirements and guidelines, September This technique is also described in U.

Other alternatives have been designed with simplicity in mind and propose minor variations of traditional DPCM techniques a discussion of the DPCM technique may be found in A. Netravali and J. Limb, "Picture coding: A review," Proc. IEEE, vol. Thus, these techniques are fundamentally limited in their compression performance by the first order entropy of the prediction residuals.

Their ability to "decorrelate" the data is reduced to the prediction step, which in general cannot achieve total decorrelation. However, such adaptive learning is exceedingly complex. Nevertheless, a low-complexity edge detector is desirable in order to approach the best possible predictors.

Digital compression and coding of continuous tone still images--Requirements and guidelines, September , not only discards edge information that might be available in the causal template, but produces very different compression results depending on the selected predictor. Moreover, the best predictor depends heavily on the image. Accordingly, it is desirable to have an image compressor that uses low-complexity predictors with some degree of edge detection.

The term "low-complexity" herein connotes an image compression system which uses predictors based on additions and shift operations, which avoids floating point arithmetics and general multiplications, and which does not use arithmetic coding.

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## CALIC IMAGE COMPRESSION PDF

Variability gtdh, dv Influence Error distribution Group pixels Previous prediction error gt Each group has its new prediction why? How to adapt — past? Comparative study of various still image coding techniques. PowerPoint PPT presentation free to view. It measures the amount of noise introduced through a lossy compression of the image, however, the subjective judgment of the viewer also is regarded as an important measure, perhaps, being the most important measure. Algorithms may take advantage of visual perception and the statistical properties of image data to provide superior results compared with generic compression methods.

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## CALIC – A lossless image compression

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