Improved Distortion Measures for Image Vector Quantization

The role played b y the distortion measure in a vector quant izat ion image encoder is very imporsuch distortion function as long as d ( X , C ) and the centroid of a set of vectors using this distortion function exists. tant. In the following paper we suggest a general class of distor t ion function, the input-dependent weighted square e r r o r distortion, which is computationally simple and can b e used t o incorporate some psychovisual characteristics. T w o techniques of using th i s distorThe centroid for a cluster or a set of input vectors is defined to be the vector (not necessarily unique) having a minimum average distortion between it and any other member of the set. Thus, for such a set B , the centroid C is given by t ion funct ion have been discussed. Incorporat ing various classes depending on image act ivi ty in t h e distort ion measure, b e t t e r subjective quality can b e achieved wi thout added complexity, as o u r simulation s tudies have shown. This s t ra tegy of classified codebook is opt imal and more general t h a n the conventional subcodebook method. We also show that incorporat ing dimensional emphasis, blockiness can be reduced in lieu of marginally m o r e computat ion. Each member of a codebook is a centroid, which is whv the same has been used to denote both. 11. Input-Dependent Weighted Square Error D i s t o r t , The distortion measure almost universally used in image coding is the mean square error (MSE) distortion, 1 d(X, C) = -[X K CIt . [ X C], (2) I. Introductioii where t indicates transpose, and vectors are column vectors. In Vector Quantiza.tion (VQ) has evolved as an efficient computation technique specially for low rate speech and image coding. From a pre-computed set of typical vectors/blocks called codebook, the VQ encoder finds the one b&t matching the input vector, and transmits the index of this best match. The VQ decoder simply looks up the codebook for the vector. Refer to [l] for the basics of VQ and to [2] for a review on VQ image encoder. case of MSE the distortion value is proportional to the square of the Euclidean distance between the two vectors, and the centroid happens to be the mean of the set. Since the primary objective of an image coder is human viewing, the mathematical function used for computing the distortion is nothing but an attempted quantification of human visual discomfort towards quantization errors in the decoded picture. It has been recognized quite early that the MSE distortion is far from a true measure of the psychovisual distortion. This fact 'motivated the search for a computationally simple, yet more humanlike, distortion measure. For a given training sequence and N1 cardinality of the codebook, the LBG algorithm [3] designs the optimum vector quantizer, i.e., the quantizer which encodes the training sequence with minimum average distortion. A distortion function is used to measure this quantization distortion. If X be a K-dimensional input vector, and C, also li-dimensional, be a member of the codebook, then d ( X , C) is the distortion function (a scalar) associated with the VQ coder. The LBG algorithm works for any work done at the Uept. of EE, California Institute of Technology, Pasadena, with the financial support of Pacific Bell The MSE distortion is a special case of a class of distortion measures meeting the LBG requirement, namely the weighted mean square error (WMSE) distortion, 1 Ii d ( X , C) = -[X cy . w. [ X C ] , (3) where W is the weight matrix of size Ii x Ii. We suggest a general class .of distortion measure by extending the WMSE func-