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.
A popular choice to locate features is to estimate the curvature, either on meshes @cite_60 @cite_43 or point clouds @cite_13 @cite_63 ). When dealing with curvature estimation, parameters have to be tuned according to the target feature scale and the underlying noise. The Moving Least Square method @cite_50 and its variations are robust to scale variations @cite_63 @cite_32 and does not incorporate smoothness effects in the estimation. Alternative approaches to locate curvature extrema use discrete differential operators @cite_34 or probabilistic methods, such as random walks @cite_45 . For details on the comparison of methods for curvature estimation, we refer to a recent benchmark @cite_64 .
@cite_64 @cite_60 @cite_32 @cite_43 @cite_45 @cite_50 @cite_63 @cite_34 @cite_13
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While it is usually not difficult to compute principal curvatures of a smooth surface of sufficient differentiability, it is a rather difficult task when only a polygonal approximation of the surface is available, because of the inherent ambiguity of such representation. A number of different approaches has been proposed in the past that tackle this problem using various techniques. Most papers tend to focus on a particular method, while an comprehensive comparison of the different approaches is usually missing. We present results of a large experiment, involving both common and recently proposed curvature estimation techniques, applied to triangle meshes of varying properties. It turns out that none of the approaches provides reliable results under all circumstances. Motivated by this observation, we investigate mesh statistics, which can be computed from vertex positions and mesh connectivity information only, and which can help in deciding which estimator will work best for a particular case. Finally, we propose a meta-estimator, which makes a choice between existing algorithms based on the value of the mesh statistics, and we demonstrate that such meta-estimator, despite its simplicity, provides considerably more robust results than any existing approach. Curves on objects can convey the inherent features of the shape. This paper defines a new class of view-independent curves, denoted demarcating curves. In a nutshell, demarcating curves are the loci of the "strongest" inflections on the surface. Due to their appealing capabilities to extract and emphasize 3D textures, they are applied to artifact illustration in archaeology, where they can serve as a worthy alternative to the expensive, time-consuming, and biased manual depiction currently used. The crest lines, salient subsets of the extrema of the principal curvatures over their corresponding curvature lines, are powerful shape descriptors which are widely used for shape matching, interrogation, and visualization purposes. In this paper, we develop fast, accurate, and reliable methods for detecting the crest lines on surfaces approximated by dense triangle meshes. The methods exploit intrinsic geometric properties of the curvature extrema and provide with an inherent level-of-detail control of the detected crest lines. As an immediate application, we use of the crest lines for adaptive mesh simplification purposes. Archaeological line drawing is an essential component of an archaeological report. In this paper, we propose a multi-scale approach to generating 3D line drawing on a triangular mesh model for archaeological illustration. The discrete multi-scale representation of a given model is first constructed based on random walks. Then, we propose a probabilistic method for local scale selection based on the minimum description length (MDL) principle. Finally, the ridges or valleys are detected with the selected scales. Experimental results show that the multi-scale 3D line drawings can well depict the shapes of cultural heritage objects. Compared with the traditional manual method, our method is more accurate and convenient. Furthermore, the time cost of archaeological mapping is decreased to a large extent and the detected lines can be rendered with specific scales and view directions. The computer-generated line drawing can be used to assist the archaeologists to draw archaeological line drawing. We present a new technique for extracting line-type features on point-sampled geometry. Given an unstructured point cloud as input, our method first applies principal component analysis on local neighborhoods to classify points according to the likelihood that they belong to a feature. Using hysteresis thresholding, we then compute a minimum spanning graph as an initial approximation of the feature lines. To smooth out the features while maintaining a close connection to the underlying surface, we use an adaptation of active contour models. Central to our method is a multi-scale classification operator that allows feature analysis at multiple scales, using the size of the local neighborhoods as a discrete scale parameter. This significantly improves the reliability of the detection phase and makes our method more robust in the presence of noise. To illustrate the usefulness of our method, we have implemented a non-photorealistic point renderer to visualize point-sampled surfaces as line drawings of their extracted feature curves. Defining sharp features in a 3D model facilitates a better understanding of the surface and aids geometric processing and graphics applications, such as reconstruction, filtering, simplification, reverse engineering, visualization, and non-photo realism. We present a robust method that identifies sharp features in a point-based model by returning a set of smooth spline curves aligned along the edges. Our feature extraction leverages the concepts of robust moving least squares to locally project points to potential features. The algorithm processes these points to construct arc-length parameterized spline curves fit using an iterative refinement method, aligning smooth and continuous curves through the feature points. We demonstrate the benefits of our method with three applications: surface segmentation, surface meshing and point-based compression. Feature lines are salient surface characteristics. Their definition involves third and fourth order surface derivatives. This often yields to unpleasantly rough and squiggly feature lines since third order derivatives are highly sensitive against unwanted surface noise. The present work proposes two novel concepts for a more stable algorithm producing visually more pleasing feature lines: First, a new computation scheme based on discrete differential geometry is presented, avoiding costly computations of higher order approximating surfaces. Secondly, this scheme is augmented by a filtering method for higher order surface derivatives to improve both the stability of the extraction of feature lines and the smoothness of their appearance.