图像识别中英文对照外文翻译文献.doc

中英文对照外文翻译文献 Elastic image matching Abstract One fundamental problem in image recognition is to establish the resemblance of two images. This can be done by searching the best pixel to pixel mapping taking into account monotonicity and continuity constraints. We show that this problem is NP-complete by reduction from 3-SAT, thus giving evidence that the known exponential time algorithms are justified, but approximation algorithms or simplifications are necessary. Keywords: Elastic image matching; Two-dimensional warping; NP-completeness 1. Introduction In image recognition, a common problem is to match two given images, e.g. when comparing an observed image to given references. In that pro-cess, elastic image matching, two-dimensional (2D-)warping (Uchida and Sakoe, 1998) or similar types of invariant methods (Keysers et al., 2000) can be used. For this purpose, we can define cost functions depending on the distortion introduced in the matching and search for the best matching with respect to a given cost function. In this paper, we show that it is an algorithmically hard problem to decide whether a matching between two images exists with costs below a given threshold. We show that the problem image matching is NP-complete by means of a reduction from 3-SAT, which is a common method of demonstrating a problem to be intrinsically hard (Garey and Johnson, 1979). This result shows the inherent computational difficulties in this type of image comparison, while interestingly the same problem is solvable for 1D sequences in polynomial time, e.g. the dynamic time warping problem in speech recognition (see e.g. Ney et al., 1992). This has the following implications: researchers who are interested in an exact solution to this problem cannot hope to find a polynomial time algorithm, unless P=NP. Furthermore, one can conclude that exponential time algorithms as presented and extended by Uchida and Sakoe (1998, 1999a,b, 2000a,b) may be justified for some image matching applica