The Hough transform is a voting scheme for locating geometric objects in point clouds. This paper describes its application for detecting lines in three dimensional point clouds. For parameter quantization, a recently proposed method for Hough parameter space regularization is used. The voting process is done in an iterative way by selecting the line with the most votes and removing the corresponding points in each step. To overcome the inherent inaccuracies of the parameter space discretization, each line is estimated with an orthogonal least squares fit among the candidate points returned from the Hough transform. Source CodeThe reviewed C++ source code for this algorithm is available from the web page of this article 1 . Compilation and usage instruction are included in the README.txt file of the archive. Supplementary MaterialSix reference data sets are provided with the article. The data sets contain both synthetic data and experimental data of radioactive beams recorded in an active target time projection chamber (AT-TPC).

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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 C 2m 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. Source Code The reviewed C++ source code for this algorithm is available from the web page of this article 1. Compilation and usage instructions are included in the README.txt file of the archive.