IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL I, NO. 2. APRIL 1992 The LBG algorithm smooths high frequencies(loss aumont? Sub codebook There is a trade-off between low distortion and high compression rate(computational cost) It is not easy to take into account the properties of the human visual system [28], [33] diagonal Diagonal The use of the wavelet transform (i. e, multiresolution) s is one way of becoming these different problems The wavelet decomposition of an image enables the Fig. 12, Multiresolution codebook generation of a codebook containing two-dimensiona vectors for each resolution level and preferential direc- for all coefficients x belonging to the subimage, g(r)being tion(horizontal, vertical, and diagonal). Each of thes subcodebooks(see Fig. 12)is generated using the LBG quantization of x. algorithm Total distortion of the image for a total rate of R, bits The training set is comprised of vectors belonging to per pixel is then given by different images corresponding to the resolution and ori- D,(R)=3M DS(RS)+232m 2 Dm. d(R,wd) entation under consideration The initial codebook is generated by splitting centroid(center of gravity) of this training set [211 A multiresolution codebook can thus be obtained by as- where DM(rM )corresponds to the distortion in the sub embling all of these resulting subcodebooks. Each sub age of lowest resolution M(texture subimage) codebook has a low distortion level and contains few The problem of finding an optimal bit assignment(in words, which clearly facilitates the search for the best bits per pixel)for each subimage vector quantizer is then coding vector; the coding computational load is reduced, formulated as because only the appropriate subcodebook(resolution di rection)of the multiresolution codebook is checked for each input vector. In addition, the quality of the coded R, mage is better. The multiresolution codebook is depicted +∑,∑Dnd(Rnd)×Bnd Global codebook design has drawbacks in that it results in edge smoothing while the proposed method preserves edges. In fact, each subcodebook contains the shape of subject R the wavelet coefficients which are most highly represen tative in terms of the mse criterion where RM corresponds to the bit allocation, in bits per Since the spatial and frequency aspects of the image are pixel, of lowest resolution M subimage sification and search during the encoding of a subimage human eye is not equally sensitive to sion th taken into account in the wavelet decomposition, the clas- Assignment of the weights is based on the fact that the least mean squares. This frees us lo.e criterion such as frequencies On the basis of contrast sensitivity data col ector can be achieved using a si om using distortion lected by Campbell and Robson [10], and to obtain a con measurements such as weighted least mean squares or trolled degree of noise shaping across the subimages, we other measurements involving perceptual factors. These consider a function Bm, d such that algorithms are indeed costly in computation time Bmd="log(oa:“) (19) C. Optimal Bit Allocation where om, d is the standard deviation corresponding to sub image(m, d) and the values of y and Bm, d are chosen Multiresolution exploits the eye's masking effects, and experimentally in order to match human visi therefore, enables us to refine and select the type of cod- DF(R,)is the total weighted encoding distortion func ng according to the resolution level and the contour ori- tion and M is the lowest resolution considered entation. Although a flat noise shape minimizes the MSe The expression of dm. (Rm.) is given by (191 criterion, it is generally not optimal for a subjective qual ity of image. To apply noise shaping across the vQ sub D (P,C) images, we define a total weighted MSE distortion DF(R,) with ((I7))for a total bit rate R((18)). Let us define Dm. (Rm. d )the average distortion in the m, d(P, c)=A(k,m, d, c) coding of the subimage(m, d)for Rm. d bits per pixel (c+km.d Dn.d(Rmd)=E(x-q(x)°)=d(x,qx)c≥