This thesis investigates shape adaptative coding of arbitrarily shaped segments. The texture and contour coding efficiency is discussed and solutions to tackle the associated problems are proposed. The presented methods are evaluated using standard image sequences. A mathematical approach for shape-adaptative transforms using linear operators is developed, followed by a metric that theoretically evaluates the transform performances. Experimental results show that the proposed metric is an efficient tool for such purposes. The proper way for grouping the 1-D transform coefficients of two image segments of different sizes is analyzed. Based on this analysis, a new low complexity method for grouping the coefficients is proposed. A better performance than other reported methods in the literature is attested by the experimental results. A mathematical analysis of the performance limitations of shape-adaptative transforms due to coefficients quantization is presented. The drawbacks discussed are the mean weighting distortion and the signal error correlation produced by the quantization process. An efficient method to simultaneously overcome both problems is proposed. The differential chain coder is an efficient and frequently employed structure for lossless encoding of object boundaries. Many modifications in the differential chain coders are investigated and evaluated, resulting in a method that reduces the bit rate to encode the object shape. Finally, a generic scheme for sub-band decomposition using shape-adaptative discrete wavelet transform is proposed. The experimental results show that such a scheme is able to provide a performance gain over the shape-adptative discrete cosine transform at low bit rates. The preliminary results suggest that this scheme could be a promising new approach for shape adaptative video coding.