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Reflection symmetry5/11/2023 ![]() Experimental studies implemented on “Butterflies” and “Flavia” datasets have shown that the proposed algorithm takes several minutes per image to find a symmetry axis. It allows us to process large image databases and obtain the desired axis of approximate symmetry for each shape in database. As a first step of our contribution we develop the parallel version of the brute-force algorithm. Brute-force search algorithm definitely finds the axis of approximate symmetry which could be considered as ground-truth, but it requires quite a lot of time to process each image. As a measure of symmetry, we use the set-theoretic Jaccard similarity applied to two subsets of pixels of the image which is divided by some axis. In this paper, we investigate the exact method of searching an axis of binary image symmetry, based on brute-force search among all potential symmetry axes. All proposed methods were experimentally tested on Flavia leaves dataset. Also, the exact brute-force symmetry evaluation algorithm and two its optimizations are suggested for finding ground truth of symmetry axis. The start and the end points of skeleton division into “left” and “right” parts will be the points belonging to a symmetry axis of a figure. So, the most similar parts of a skeleton among all possible ones correspond to the most similar parts of a figure which are considered as reflection symmetric parts. As a result, the “left” and the “right” primitive sub-chains are achieved they can be compared by the known shape matching procedure based on pair-wise alignment of primitive chains. The left part is traversed counterclockwise and the right one – in clockwise direction. We propose to divide a skeleton of a shape into two parts – the “left” and the “right” sub-skeletons. In this paper the novel fast approach to identify the reflection symmetry axis of binary images is proposed.
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