Multi resolution texture segmentation and autoregressive synthesis for wavelet based image coding

A unique texture oriented wavelet image compression scheme which uses autoregressive texture segmentation and synthesis is presented It rst estimates the information that would be lost at the desired compression ratio Estimation minimization multi resolution segmentation is performed on the residual estimate to identify distinct texture regions and to compute the model parameters necessary for texture synthesis The model parameters are saved and the lost texture is synthesized and added back to the image during the reconstruction process Several variations of autoregressive texture models are demonstrated Introduction As the demand for digital imagery increases in today s society there is also an increasing need for e cient means of data storage and transmission High compression image coding is essential particularly considering current bandwidth limitations of the Internet In many current applications the need for perceptually high quality imagery outweighs the requirement of numerical delity Often it is more important for an image to look acceptable to a human observer than to maximize numerical quality measurements such as peak signal to noise ratio PSNR When we limit compression based upon distortion measurements which consider only such numerical criterion we do not capitalize on the aspects of human vision which enable numerically di erent imagery to be perceived as very similar Methods which consider issues related to human perceptual mechanisms such as processing edge contours and textural information separately are known as second generation coding methods Past approaches to the problem of high compression image coding have attempted to capitalize on the fact that texture data need not be preserved with numerical delity and that texture modeling can be used as an e cient means of describing textural regions of an image Wavelet based compression is particularly e cient in the compression of smoothly varying regions of image data It is the discontinuities located between the regions along with high contrast textured regions which cause large transform coe cients and erroneous artifacts such as blurring or starring at high compression ratios Region based techniques potentially facilitate image compression since a homogeneous region of pixels can theoretically be described with a more compact representation than a non homogeneous one This paper presents a unique region based wavelet image compression scheme which synthetically replaces texture data attenuated as a result of the compression process We perform texture segmentation on an estimated residual imagewhich approximates the information that would be lost at the requested compression ratio The segmentation process utilizes an estimation minimization EM multi resolution algorithm which is a modi ed version of the method proposed by Bouman and Liu It identi es image regions which are expected to su er a signi cant amount of texture loss and additionally computes the parameters for an autoregressive model for each region of distinct texture Region based wavelet compression is performed on the original image using the partitions which result from the segmentation process We compare the performance of the autoregressive texture model in terms of coding e ciency and texture quality to the use of standard wavelet compression methods Previous work which has used texture synthesis for image compression has been done in both the spa tial and wavelet domains Di erent di culties are associated with each approach If texture is identi ed analyzed and synthesized in the spatial domain the non stationarity of the texture process complicates the modeling procedure Low frequency uctuations in image intensity make the texture more di cult to model accurately An inadequate model may fail to capture the low frequency elements of the texture sample Texture which is synthesized in the spatial domain may blend poorly into surrounding areas within the image Di erent challenges arise when texture processing is performed in the wavelet domain Although the wavelet coe cients at each scale and orientation can be modeled the relationships between these scales and orientations are not captured by such approaches Thus while the synthesized wavelet co e cients appear to be well modeled when an inverse wavelet transform is performed to produce the spatial domain representation the quality of the resulting synthetic texture is reduced Processing the texture residual which results from wavelet compression o ers a compromise between the two Since the error is approximately zero mean it can be adequately modeled as a stationary process And since it has components from many scales and orientations the issue of agreement between wavelet coe cients is greatly reduced By adding the synthetic texture details to the low frequency characteristics of the texture which remain after compression instead of replacing them the synthetic texture blends more easily into the image and macrotextures are preserved Choosing to model the texture residual simpli es the choice of domain for texture segmentation At low compression ratios a negligible amount of texture may be lost making the synthesis of texture unnecessary during reconstruction Only those regions which demonstrate a signi cant loss of texture as a result of compression need to be identi ed Texture segmentation is performed on a residual image which is computed by subtracting a reconstruction estimate from the original image The EM multi resolution segmentation algorithm ts well into the overall compression scheme since the autoregressive coe cients needed for texture synthesis are produced and utilized by the segmentation process The remainder of this paper is organized as follows Section describes the model used for the synthesis of the residual image and documents its performance in terms of visual quality and numerical model error Section details the segmentation procedure and its generation of model parameters Section outlines the complete compression system as well as presenting experimental results and the nal section presents a summary of the work and o ers conclusive remarks on its performance along with ideas for future direction Residual Image Synthesis Image regions characterized by texture must be identi ed so that the texture data may be e ciently com pressed An estimate of the reconstructed image is computed based upon the desired compression rate then subtracted from the original image to create an estimate of the texture residual Texture segmentation is performed on the residual estimate since only the portion of the texture lost as a result of compression will be modeled for synthesis during reconstruction Model parameters which describe the variations between neighboring pixel intensities are computed and saved for texture synthesis during reconstruction It is appropriate to consider only models with a compact parameter space since the model parameters will be included in the contents of the compressed image le A discussion of implementation and results are presented for the autoregressive texture synthesis method Texture synthesis methods based on auto correlation and Markov models were also considered but were eliminated based upon the amount of storage overhead required by each Twelve reference textures are used to demonstrate the performance of the selected texture models The eight bit texture images are shown in Figure This collection of textures was selected because they exhibit a variety of statistical and structural characteristics Texture residual is estimated for an approximate compression ratio of Figure shows the texture images which result when the reference textures are wavelet compressed at using an embedded zero tree encoding scheme Figure shows the residual images which result at this compression ratio These images were created by subtracting the wavelet compressed textures from the original reference textures The texture residual images are analyzed and synthesized using an autoregressive method For the purpose of display a bias of was added to each pixel value in the residual images Autoregressive texture synthesis The autoregressive model expresses a sample value as a nite linear combination of previous samples and a noise term given by Equation i x y X u v NAR u vi u v n x y where i x y is the intensity at x y NAR is the neighborhood of pixel x y n x y is a two dimensional zero mean white Gaussian noise source and u v is a set of prediction coe cients In Delp et al summarize how to compute the set of prediction coe cients NAR and the variance of the noise terms which minimize the squared error between the modeled pixel value and the actual pixel value This error can be computed by summing the di erence between these two values over the image as X