A parallel windowing approach to the Hough transform for line segment detection

In the wide range of image processing and computer vision problems, line segment detection has always been among the most critical headlines. Detection of primitives such as linear features and straight edges has diverse applications in many image understanding and perception tasks. The research presented in this dissertation is a contribution to the detection of straight-line segments by identifying the location of their endpoints within a two-dimensional digital image. The proposed method is based on a unique domain-crossing approach that takes both image and parameter domain information into consideration. First, the straight-line parameters, i.e. location and orientation, have been identified using an advanced Fourier-based Hough transform. As well as producing more accurate and robust detection of straight-lines, this method has been proven to have better efficiency in terms of computational time in comparison with the standard Hough transform. Second, for each straight-line a window-of-interest is designed in the image domain and the disturbance caused by the other neighbouring segments is removed to capture the Hough transform buttery of the target segment. In this way, for each straight-line a separate buttery is constructed. The boundary of the buttery wings are further smoothed and approximated by a curve fitting approach. Finally, segments endpoints were identified using buttery boundary points and the Hough transform peak. Experimental results on synthetic and real images have shown that the proposed method enjoys a superior performance compared with the existing similar representative works

Polygonal Chains Cannot Lock in 4D

We prove that, in all dimensions d>=4, every simple open polygonal chain and every tree may be straightened, and every simple closed polygonal chain may be convexified. These reconfigurations can be achieved by algorithms that use polynomial time in the number of vertices, and result in a polynomial number of ``moves.'' These results contrast to those known for d=2, where trees can ``lock,'' and for d=3, where open and closed chains can lock.Comment: Major revision of the Aug. 1999 version, including: Proof extended to show trees cannot lock in 4D; new example of the implementation straightening a chain of n=100 vertices; improved time complexity for chain to O(n^2); fixed several minor technical errors. (Thanks to three referees.) 29 pages; 15 figures. v3: Reference update