In this paper, by a novel morphological decomposition method, we propose an efﬁcient compression approach. Our presented decomposition arises from solving a minimum set cover problem (MSCP) obtained from the image skeleton data. We ﬁrst use the skeleton pixels to create a collection of blocks which cover the foreground. The given blocks are both overlapped and too many. Hence, in order to ﬁnd the minimum number of the blocks that cover the foreground, we form an MCSP. To solve this problem, we present a new algorithm of which accuracy is better than those of the known methods in the literatures. Also, its error analysis is studied to obtain an error bound. In the sequel, we present a fast algorithm which include an extra parameter by which the relation between the accuracy and CPU time can be controlled. Finally, several examples are given to conﬁrm the efﬁciency of our approach. Keywords Decomposition · Compression · Minimum set cover algorithm Mathematics Subject Classiﬁcation 68U10 · 94A08 1 Introduction The difference is substantial. While minimal decomposi- tion into non-overlapping blocks is polynomial, the one into It is well known that there are several methods for com- overlapping blocks is NP complete. The
Journal of Mathematical Imaging and Vision – Springer Journals
Published: May 29, 2018
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