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.
Feature curves are often identified as ridges and valleys, thus representing the extrema of principal curvatures @cite_62 @cite_43 @cite_79 or sharp features @cite_31 . Other types of lines used for feature curve representation are parabolic ones. They partition the surface into hyperbolic and elliptic regions, and zero-mean curvature curves, which classify sub-surfaces into concave and convex shapes @cite_47 . Parabolic lines correspond to the zeros of the Gaussian and mean curvature, respectively. Finally, demarcating curves are the zero-crossings of the curvature in its gradient direction @cite_60 @cite_73 . In general, all these curves, defined as the zero set of a scalar function, do not consider curve with knots, fact that an algebraic curve like the (see @cite_75 ) could arrange.
@cite_31 @cite_62 @cite_60 @cite_43 @cite_79 @cite_47 @cite_73 @cite_75
2063409146 2169231734 2149887512 2112696958
For smooth curved surfaces the dominant image feature is the apparent contour, or outline. This is the projection of the contour generator, the locus of points on the surface which separate visible and occluded parts. The contour generator is dependent of the local surface geometry and the viewpoint. Each viewpoint will generate a different contour generator. This paper addresses the problem of recovering the three–dimensional shape and motion of curves and surfaces from image sequences of apparent contours. @PARASPLIT For known viewer motion the visible surfaces can then be reconstructed by exploiting a spatio–temporal parametrization of the apparent contours and contour generators under viewer motion. A natural parametrization exploits the contour generators and the epipolar geometry between successive viewpoints. The epipolar parametrization leads to simplified expressions for the recovery of depth and surface curvatures from image velocities and accelerations and known viewer motion. @PARASPLIT The parametrization is, however, degenerate when the apparent contour is singular since the ray is tangent to the contour generator and at frontier points when the epipolar plane is a tangent plane to the surface. At these isolated points the epipolar parametrization can no longer be used to recover the local surface geometry. This paper reviews the epipolar parametrization and shows how the degenerate cases can be used to recover surface geometry and unknown viewer motion from apparent contours of curved surfaces. Practical implementations are outlined. Sharp edges, ridges, valleys, and prongs are critical for the appearance and an accurate representation of a 3D model. In this paper, we propose a novel approach that deals with the global shape of features in a robust way. Based on a remeshing algorithm which delivers an isotropic mesh in a feature-sensitive metric, features are recognized on multiple scales via integral invariants of local neighborhoods. Morphological and smoothing operations are then used for feature region extraction and classification into basic types such as ridges, valleys, and prongs. The resulting representation of feature regions is further used for feature-specific editing operations 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. In this paper, we introduce a feature-preserving denoising algorithm. It is built on the premise that the underlying surface of a noisy mesh is piecewise smooth, and a sharp feature lies on the intersection of multiple smooth surface regions. A vertex close to a sharp feature is likely to have a neighborhood that includes distinct smooth segments. By defining the consistent subneighborhood as the segment whose geometry and normal orientation most consistent with those of the vertex, we can completely remove the influence from neighbors lying on other segments during denoising. Our method identifies piecewise smooth subneighborhoods using a robust density-based clustering algorithm based on shared nearest neighbors. In our method, we obtain an initial estimate of vertex normals and curvature tensors by robustly fitting a local quadric model. An anisotropic filter based on optimal estimation theory is further applied to smooth the normal field and the curvature tensor field. This is followed by second-order bilateral filtering, which better preserves curvature details and alleviates volume shrinkage during denoising. The support of these filters is defined by the consistent subneighborhood of a vertex. We have applied this algorithm to both generic and CAD models, and sharp features, such as edges and corners, are very well preserved.