A Hybrid Method for Computing Apparent Ridges

Abstract

Abstract-We propose a hybrid method for computing apparent ridges. Our method combines object-space and image-space computations and runs partially in the GPU, taking advantage of modern graphic cards processing power and producing faster results in real time.Expressive line drawing of 3D models is a classic artistic technique and remains an important problem in NonPhotorealistic Rendering [1]. A good line drawing can convey the shape geometry without using other cues like shading, color, and texture. Frequently, a few good lines are enough to convey the main geometric features [2]. There are several techniques for depicting shapes with lines, but no single method has proved to be the best for an arbitrary model or viewing position.Object contours or silhouettes are perhaps the most basic type of view-dependent line. Although they may not capture all relevant geometric features in an object, any line drawing should contain the visible boundaries of the object [4]. Ridges and valleys [5] are found by computing principal curvatures and principal directions, and their derivatives. They are second-order curves that complement contour information. Since their definition only takes into account the geometry of the model, ridges and valleys are viewindependent features. This can cause animation artifacts as these features appear to be rigid, independent of the viewing point. Suggestive contours [6] are view-dependent lines that naturally extend contours at the joints. They also depend on second-order information, being based on the radial curvature in the view direction and its derivative. However, suggestive contours do not appear at elliptic regions (where the Gaussian curvature is positive). Thus, convex features cannot be depicted with suggestive contours. Moreover, they do not include silhouettes, which must be computed separately. Apparent ridges [3] is a recent technique that seems to produce good results. With a single mathematical definition of what a good line is, apparent ridges depict most features that are captured by other definitions and some additional features not captured before, and its lines are view-dependent. Apparent ridges combine both second-order information and view-dependency: they are based on a viewdependent curvature that plays an analogue role for apparent ridges as the curvature does for ridges and valleys. Another advantage is that contours are a special case of apparent ridges and so do not require an additional rendering step.Unlike the original method [3], which works entirely over the mesh in object space, our method computes the curvature data needed to find apparent ridges in an object-space phase and an image-space phase. This split allows us to use vertex shaders and pixel shaders to compute each part in the GPU, exploiting GPU processing power and parallelism.To compute apparent ridges, one must first compute the view-dependent curvature q 1 and its derivative D t1 q 1 in the maximum view-dependent principal direction t 1 . Apparent ridges are the maxima of q 1 in the t 1 dire...

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“…Several methods directly devoted or potentially applicable to the representation of 3D archaeological artifacts using NPR techniques have been discussed during the last decades. See (Jardim & De Figueiredo, 2010;Roussou & Drettakis, 2003;Tao et al, 2009) and (Judd et al, 2007) for a very interesting open source approach of NPR applied to a 3D model build with mesh and a fine implementation called Suggestive contour software (DeCarlo & Rusinkiewicz, 2007).…”