This study presents two sets of translation invariant wavelet transforms for coding an arbitrarily shaped image. Each set can be viewed as a shape-adaptive discrete wavelet transform (SA-DWT) with the property of translation invariance. The proposed transform schemes have the following merits: (1) they are translation invariant, (2) no sharp transition appears at the edges of the image, (3) the number of pixels is maintained constant after transformation, (4) the correlation of pixels is fully exploited, and (5) the property of self-similarity across scales is preserved.
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