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.
To overcome some of these limitations, other variants have been proposed, one of the most popular being the Generalized Hough Transform (GHT) by Ballard @cite_5 . Since its conception, it proved to be very useful for detecting and locating translated two-dimensional objects, without requiring a parametric analytic expression. Thus, GHT is more general than SHT, as it is able to detect a larger class of rigid objects, still retaining the robustness of SHT. Nevertheless, GHT often requires brute force to enumerate all the possible orientations and scales of the input shape, thus the number of parameters needs to be increased in its process. Further, GHT cannot adequately handle shapes that are more flexible, as in the case of different instances of the same shape, which are similar but not identical, e.g. pet als and leaves.
@cite_5
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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. 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. Hough transform based methods for object detection work by allowing image features to vote for the location of the object. While this representation allows for parts observed in different training instances to support a single object hypothesis, it also produces false positives by accumulating votes that are consistent in location but inconsistent in other properties like pose, color, shape or type. In this work, we propose to augment the Hough transform with latent variables in order to enforce consistency among votes. To this end, only votes that agree on the assignment of the latent variable are allowed to support a single hypothesis. For training a Latent Hough Transform (LHT) model, we propose a learning scheme that exploits the linearity of the Hough transform based methods. Our experiments on two datasets including the challenging PASCAL VOC 2007 benchmark show that our method outperforms traditional Hough transform based methods leading to state-of-the-art performance on some categories. Hough transform-based methods for detecting multiple objects use nonmaxima suppression or mode seeking to locate and distinguish peaks in Hough images. Such postprocessing requires the tuning of many parameters and is often fragile, especially when objects are located spatially close to each other. In this paper, we develop a new probabilistic framework for object detection which is related to the Hough transform. It shares the simplicity and wide applicability of the Hough transform but, at the same time, bypasses the problem of multiple peak identification in Hough images and permits detection of multiple objects without invoking nonmaximum suppression heuristics. Our experiments demonstrate that this method results in a significant improvement in detection accuracy both for the classical task of straight line detection and for a more modern category-level (pedestrian) detection problem.