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Representation and Recognition of FreeForm Surfaces
, 1992
"... We introduce a new surface representation for recognizing curved objects. Our approach begins by representing an object by a discrete mesh of points built from range data or from a geometric model of the object. The mesh is computed from the data by deforming a standard shaped mesh, for example, an ..."
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We introduce a new surface representation for recognizing curved objects. Our approach begins by representing an object by a discrete mesh of points built from range data or from a geometric model of the object. The mesh is computed from the data by deforming a standard shaped mesh, for example, an ellipsoid, until it fits the surface of the object. We define local regularity constraints that the mesh must satisfy. We then define a canonical mapping between the mesh describing the object and a standard spherical mesh. A surface curvature index that is poseinvariant is stored at every node of the mesh. We use this object representation for recognition by comparing the spherical model of a reference object with the model extracted from a new observed scene. We show how the similarity between reference model and observed data can be evaluated and we show how the pose of the reference object in the observed scene can be easily computed using this representation. We present results on real range images which show that this approach to modelling and recognizing threedimensional objects has three main advantages: First, it is applicable to complex curved surfaces that cannot be handled by conventional techniques. Second, it reduces the recognition problem to the computation of similarity between spherical distributions; in particular, the recognition algorithm does not require any combinatorial search. Finally, even though it is based on a spherical mapping, the approach can handle occlusions and partial views.
TexturePreserving Shadow Removal in Color Images Containing Curved Surfaces
"... Several approaches to shadow removal in color images have been introduced in recent years. Yet these methods fail in removing shadows that are cast on curved surfaces, as well as retaining the original texture of the image in shadow boundaries, known as penumbra regions. In this paper, we propose a ..."
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Several approaches to shadow removal in color images have been introduced in recent years. Yet these methods fail in removing shadows that are cast on curved surfaces, as well as retaining the original texture of the image in shadow boundaries, known as penumbra regions. In this paper, we propose a novel approach which effectively removes shadows from curved surfaces while retaining the textural information in the penumbra, yielding high quality shadowfree images. Our approach aims at finding scale factors to cancel the effect of shadows, including penumbra regions where illumination changes gradually. Due to the fact that surface geometry is also taken into account when computing the scale factors, our method can handle a wider range of shadow images than current stateoftheart methods, as demonstrated by several examples. 1.
SurfacefromGradients with Incomplete Data for Single View Modeling ∗
"... Surface gradients are useful to surface reconstruction in single view modeling, shapefromshading, and photometric stereo. Previous algorithms minimize a complex, nonlinear energy functional, or require dense surface gradients to perform integration to generate 3D locations, or require userinput h ..."
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Surface gradients are useful to surface reconstruction in single view modeling, shapefromshading, and photometric stereo. Previous algorithms minimize a complex, nonlinear energy functional, or require dense surface gradients to perform integration to generate 3D locations, or require userinput heights to constrain the solution space, or produce severe distortion and smooth out surface details. Most singleview algorithms output a Monge patch (heightfield), which may introduce further surface distortion along object silhouettes and surface orientation discontinuities. Our proposed algorithm operates on a single view of complete or incomplete data. The data can be gradients without 3D locations, or 3D locations without gradients. The output surface, which is not necessarily a heightfield, preserves salient depth and orientation discontinuities. Experimental comparisons on both simple and complex data show that our method produces better surfaces with significantly less distortion and more details preserved. The implementation of our closedform solution is very straightforward.
Playing with Puffball: Simple scale invariant inflation for use in vision and graphics
"... We describe how inflation, the act of mapping a 2D silhouette to a 3D region, can be applied in two disparate problems to offer insight and improvement: silhouette part segmentation and imagebased material transfer. To demonstrate this, we introduce Puffball, a novel inflation technique, which achie ..."
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We describe how inflation, the act of mapping a 2D silhouette to a 3D region, can be applied in two disparate problems to offer insight and improvement: silhouette part segmentation and imagebased material transfer. To demonstrate this, we introduce Puffball, a novel inflation technique, which achieves similar results to existing inflation approaches – including smoothness, robustness, and scale and shiftinvariance – through an exceedingly simple and accessible formulation. The part segmentation algorithm avoids many of the pitfalls of previous approaches by finding part boundaries on a canonical 3D shape rather than in the contour of the 2D shape; the algorithm gives reliable and intuitive boundaries, even in cases where traditional approaches like the Minima rule are misled. To demonstrate it’s effectiveness, we present data in which subjects prefer Puffball’s segmentations to more traditional Minimarulebased segmentations across several categories of silhouettes. The texture transfer algorithm utilizes Puffball’s estimated shape information to produce visually pleasing and realistically synthesized surface textures with no explicit knowledge of either underlying shape.
1SurfaceFromGradients Without Discrete Integrability Enforcement: a Gaussian Kernel Approach
"... Abstract—Representative surface reconstruction algorithms taking a gradient field as input enforces the integrability constraint in a discrete manner. While enforcing integrability allows the subsequent integration to produce surface heights, existing algorithms have one or more of the following di ..."
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Abstract—Representative surface reconstruction algorithms taking a gradient field as input enforces the integrability constraint in a discrete manner. While enforcing integrability allows the subsequent integration to produce surface heights, existing algorithms have one or more of the following disadvantages: they can only handle dense perpixel gradient fields, smooth out sharp features in a partially integrable field, or produce severe surface distortion in the results. In this paper, we present a method which does not enforce discrete integrability, and reconstructs a 3D continuous surface from a gradient or a height field, or a combination of both, which can be dense or sparse. The key of our approach is the use of kernel basis functions, which transfers the continuous surface reconstruction problem into high dimensional space where a closedform solution exists. By using the Gaussian kernel, we can derive a straightforward implementation which is able produce results better than traditional techniques. In general, an important advantage of our kernel based method is that the method does not suffer discretization and finite approximation, both of which leads to surface distortion, which is typical of Fourier or wavelet bases widely adopted by previous representative approaches. We perform comparison with classical and recent methods, on benchmark as well as challenging data sets, to demonstrate that our method produces accurate surface reconstruction that preserves salient and sharp features. The source code and executable of the system is available for downloading. Index Terms—Surface from gradients, integrability, kernel methods, basis functions. I.