The Gradient Product Transform: An Image Filter for Symmetry Detection
Christoph Dalitz, Jens Wilberg
⚠ This is a preprint. It may change before it is accepted for publication.

Abstract

The Gradient Product Transform (GPT) is an image filter that converts a gray scale image into a float image, such that points representing a point reflection symmetry center obtain a high score. Beside the symmetry score, it also yields an estimator for the size of the symmetry region around each point. Apart from describing the GPT, the article also explains its application for two use cases: detection of objects with a point reflection or C2m rotational symmetry, and the extraction of blood vessel skeletons from medical images. For the detection of symmetric objects, a score normalization procedure is suggested that allows to choose a fixed threshold for score values representing actual symmetries.

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