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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Hough transform (HT) is a well-known technique for extracting lines. However, it is difficult for most existing HT methods to extract line segments robustly from complicated images, mainly because the influence from various objects other than line segments are not taken into account. This paper proposes an accurate and robust evaluator that dynamically removes contributions of backgrounds and analyzes voting patterns around peaks in the accumulator space. In the experiments, four peak detection algorithms are tested against seven images completely automatically. Results show that our method is superior to existing methods in terms of accuracy and robustness while there are no clear differences in execution time. The proposed evaluator detects peaks after the HT and hence it can be applied to any HT that keeps the basic characteristics of the voting process. 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. Abstract The Hough transform (HT) is commonly used in machine vision applications for detecting discontinuous patterns in noisy images. The process of using the HT to detect lines in an image involves the computation of the HT for the entire image, accumulating votes in an accumulator array and searching the array for peaks which hold information of potential lines present in the input image. The peaks provide only the length of the normal to the line and the angle that the normal makes with the x -axis. They do not provide any information regarding the length, position or end points of the line segments. However, the butterfly shaped [1] spread of votes in the accumulator array, generated by the process of peak formation, holds vital information like the length and position of the input line segment. Some authors [2] have used this property to develop an algorithm to determine the coordinates of the end points, the length, and the normal parameters of straight lines. A limitation of this method, making it unsuitable for application to a real machine vision problem, is that it would yield erroneous results if applied to an image consisting of anything more than a single line segment. Moreover, the precision of this algorithm is dependent on the sharpness of the peak. In this paper, new techniques which address the above mentioned shortcomings have been described. This paper details the method developed to provide complete line segment description for an image consisting of multiple line segments. In addition, the developed techniques are more robust and accurate than the previously proposed methods as they do not depend upon the sharpness of the peak. The Hough transform is a standard pattern recognition technique introduced between the 1960s and the 1970s for the detection of straight lines, circles, and ellipses. Here we offer a mathematical foundation, based on algebraic-geometry arguments, of an extension of this approach to the automated recognition of rational cubic, quartic, and elliptic curves. The accuracy of this approach is tested against synthetic data and in the case of experimental observations provided by the NASA Solar Dynamics Observatory mission.