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.
Recently, thanks to algebraic geometry concepts, theoretical foundations have been laid to extend the HT technique to the detection of algebraic objects of codimension greater than one (for instance algebraic space curves) taking advantage of various families of algebraic plane curves (see @cite_8 and @cite_54 ). Being so general, such a method allows to deal with different shapes, possibly compound, and to get the most suitable approximating profile among a large vocabulary of curves.
@cite_54 @cite_8
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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. 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. This paper presents a 3-D object recognition method and its implementation on a robotic navigation aid to allow real-time detection of indoor structural objects for the navigation of a blind person. The method segments a point cloud into numerous planar patches and extracts their inter-plane relationships (IPRs).Based on the existing IPRs of the object models, the method defines six high level features (HLFs) and determines the HLFs for each patch. A Gaussian-mixture-model-based plane classifier is then devised to classify each planar patch into one belonging to a particular object model. Finally, a recursive plane clustering procedure is used to cluster the classified planes into the model objects. As the proposed method uses geometric context to detect an object, it is robust to the object’s visual appearance change. As a result, it is ideal for detecting structural objects (e.g., stairways, doorways, and so on). In addition, it has high scalability and parallelism. The method is also capable of detecting some indoor non-structural objects. Experimental results demonstrate that the proposed method has a high success rate in object recognition. Abstract The Hough transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve. The initial work showed how to detect both analytic curves (1,2) and non-analytic curves, (3) but these methods were restricted to binary edge images. This work was generalized to the detection of some analytic curves in grey level images, specifically lines, (4) circles (5) and parabolas. (6) The line detection case is the best known of these and has been ingeniously exploited in several applications. (7,8,9) We show how the boundaries of an arbitrary non-analytic shape can be used to construct a mapping between image space and Hough transform space. Such a mapping can be exploited to detect instances of that particular shape in an image. Furthermore, variations in the shape such as rotations, scale changes or figure ground reversals correspond to straightforward transformations of this mapping. However, the most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler component shapes. This makes the generalized Hough transform a kind of universal transform which can be used to find arbitrarily complex shapes.