The Gradient Product Transform: An Image Filter for Symmetry Detection
Christoph Dalitz, Jens Wilberg, Manuel Jeltsch
Christoph Dalitz, Jens Wilberg, and Manuel Jeltsch, The Gradient Product Transform: An Image Filter for Symmetry Detection, Image Processing On Line, 9 (2019), pp. 413–431.

Communicated by Julie Delon
Demo edited by Mariano Rodríguez


The Gradient Product Transform (GPT) is an image filter that converts a grayscale 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.