Abstract Feature curves are largely adopted to highlight shape features, such as sharp lines, or to divide surfaces into meaningful segments, like convex or concave regions. Extracting these curves is not sufficient to convey prominent and meaningful information about a shape. We have first to separate the curves belonging to features from those caused by noise and then to select the lines, which describe non-trivial portions of a surface. The automatic detection of such features is crucial for the identification and or annotation of relevant parts of a given shape. To do this, the Hough transform (HT) is a feature extraction technique widely used in image analysis, computer vision and digital image processing, while, for 3D shapes, the extraction of salient feature curves is still an open problem. Thanks to algebraic geometry concepts, the HT technique has been recently extended to include a vast class of algebraic curves, thus proving to be a competitive tool for yielding an explicit representation of the diverse feature lines equations. In the paper, for the first time we apply this novel extension of the HT technique to the realm of 3D shapes in order to identify and localize semantic features like patterns, decorations or anatomical details on 3D objects (both complete and fragments), even in the case of features partially damaged or incomplete. The method recognizes various features, possibly compound, and it selects the most suitable feature profiles among families of algebraic curves.
In this paper, we present a novel method for detecting partial symmetries in very large point clouds of 3D city scans. Unlike previous work, which has only been demonstrated on data sets of a few hundred megabytes maximum, our method scales to very large scenes: We map the detection problem to a nearest-neighbour problem in a low-dimensional feature space, and follow this with a cascade of tests for geometric clustering of potential matches. Our algorithm robustly handles noisy real-world scanner data, obtaining a recognition performance comparable to that of state-of-the-art methods. In practice, it scales linearly with scene size and achieves a high absolute throughput, processing half a terabyte of scanner data overnight on a dual socket commodity PC. This paper addresses approximate partial symmetry detection in 3D point clouds, a classical and foundational tool for analyzing geometry. We present a novel, fully unsupervised method that detects partial symmetry under significant geometric variability, and without constraints on the number and arrangement of instances. The core idea is a matching scheme that finds consistent co-occurrence patterns in a frame-invariant way. We obtain a canonical partition of the input shape into building blocks and can handle ambiguous data by aggregating co-occurrence information across both all building block instances and the area they cover. We evaluate our method on several benchmark data sets and demonstrate its significant improvements in handling geometric variability, including scanning noise, irregular patterns, appearance variation and shape deformation. Feature detection in geometric datasets is a fundamental tool for solving shape matching problems such as partial symmetry detection. Traditional techniques usually employ a priori models such as crease lines that are unspecific to the actual application. Our paper examines the idea of learning geometric features. We introduce a formal model for a class of linear feature constellations based on a Markov chain model and propose a novel, efficient algorithm for detecting a large number of features simultaneously. After a short user-guided training stage, in which one or a few example lines are sketched directly onto the input data, our algorithm automatically finds all pieces of geometry similar to the marked areas. In particular, the algorithm is able recognize larger classes of semantically similar but geometrically varying features, which is very difficult using unsupervised techniques. In a number of experiments, we apply our technique to point cloud data from 3D scanners. The algorithm is able to detect features with very low rates of false positives and negatives and to recognize broader classes of similar geometry (such as “windows” in a building scan) even from few training examples, thereby significantly improving over previous unsupervised techniques.