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.
* Hough transform We devote this section to a brief introduction to the HT technique, while we refer to recent surveys (for instance @cite_49 @cite_20 ) for a detailed overview.
@cite_20 @cite_49
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The generalised Hough transform (GHT) is useful for detecting or locating translated two-dimensional objects. However, a weakness of the GHT is its storage requirements and hence the increased computational complexity resulting from the four-dimensional parameter space. In this paper, we present the results of our work which involves investigation of the performance of several efficient GHT techniques including an extension of Thomas's rotation-invariant algorithm. It is shown that our extension of Thomas's algorithm has very low memory requirements and computational complexity, and produces the best results in various tests. In 1962 Hough earned the patent for a method 1], popularly called Hough Transform (HT) that efficiently identifies lines in images. It is an important tool even after the golden jubilee year of existence, as evidenced by more than 2500 research papers dealing with its variants, generalizations, properties and applications in diverse fields. The current paper is a survey of HT and its variants, their limitations and the modifications made to overcome them, the implementation issues in software and hardware, and applications in various fields. Our survey, along with more than 200 references, will help the researchers and students to get a comprehensive view on HT and guide them in applying it properly to their problems of interest. HighlightsA survey of Hough Transform (HT) has been done.The main variants of HT and its formulations have been described.The hardware and software implementations of HT have been described.HT has many applications in diverse fields. Out of them some applications in some selected fields have been mentioned.