545 research outputs found
Curvature estimation for meshes via algebraic quadric fitting
We introduce the novel method for estimation of mean and Gaussian curvature
and several related quantities for polygonal meshes. The algebraic quadric
fitting curvature (AQFC) is based on local approximation of the mesh vertices
and associated normals by a quadratic surface. The quadric is computed as an
implicit surface, so it minimizes algebraic distances and normal deviations
from the approximated point-normal neighbourhood of the processed vertex. Its
mean and Gaussian curvature estimate is then obtained as the respective
curvature of its orthogonal projection onto the fitted quadratic surface.
Experimental results for both sampled parametric surfaces and arbitrary meshes
are provided. The proposed method AQFC approaches the true curvatures of the
reference smooth surfaces with increasing density of sampling, regardless of
its regularity. It is resilient to irregular sampling of the mesh, compared to
the contemporary curvature estimators. In the case of arbitrary meshes,
obtained from scanning, AQFC provides robust curvature estimation.Comment: 14 page
Surface and Volumetric Segmentation of Complex 3-D Objects Using Parametric Shape Models
The problem of part definition, description, and decomposition is central to the shape recognition systems. In this dissertation, we develop an integrated framework for segmenting dense range data of complex 3-D scenes into their constituent parts in terms of surface and volumetric primitives. Unlike previous approaches, we use geometric properties derived from surface, as well as volumetric models, to recover structured descriptions of complex objects without a priori domain knowledge or stored models.
To recover shape descriptions, we use bi-quadric models for surface representation and superquadric models for object-centered volumetric representation. The surface segmentation uses a novel approach of searching for the best piecewise description of the image in terms of bi-quadric (z = f(x,y)) models. It is used to generate the region adjacency graphs, to localize surface discontinuities, and to derive global shape properties of the surfaces. A superquadric model is recovered for the entire data set and residuals are computed to evaluate the fit. The goodness-of-fit value based on the inside-outside function, and the mean-squared distance of data from the model provide quantitative evaluation of the model. The qualitative evaluation criteria check the local consistency of the model in the form of residual maps of overestimated and underestimated data regions.
The control structure invokes the models in a systematic manner, evaluates the intermediate descriptions, and integrates them to achieve final segmentation. Superquadric and bi-quadric models are recovered in parallel to incorporate the best of the coarse-to-fine and fine-to-coarse segmentation strategies. The model evaluation criteria determine the dimensionality of the scene, and decide whether to terminate the procedure, or selectively refine the segmentation by following a global-to-local part segmentation approach. The control module generates hypotheses about superquadric models at clusters of underestimated data and performs controlled extrapolation of the part-model by shrinking the global model. As the global model shrinks and the local models grow, they are evaluated and tested for termination or further segmentation.
We present results on real range images of scenes of varying complexity, including objects with occluding parts, and scenes where surface segmentation is not sufficient to guide the volumetric segmentation. We analyze the issue of segmentation of complex scenes thoroughly by studying the effect of missing data on volumetric model recovery, generating object-centered descriptions, and presenting a complete set of criteria for the evaluation of the superquadric models. We conclude by discussing the applications of our approach in data reduction, 3-D object recognition, geometric modeling, automatic model generation. object manipulation, and active vision
Active rough shape estimation of unknown objects
International audienceThis paper presents a method to determine the rough shape of an object. This is a step in the development of a One Click Grasping Tool, a grasping tool of everyday-life objects for an assistant robot dedicated to elderly or disabled. The goal is to determine the quadric that approximates at best the shape of an unknown object using multi-view measurements. Non-linear optimization techniques are considered to achieve this goal. Since multiple views are necessary, an active vision process is considered in order to minimize the uncertainty on the estimated parameters and determine the next best view. Finally, results that show the validity of the approach are presented
Generic Primitive Detection in Point Clouds Using Novel Minimal Quadric Fits
We present a novel and effective method for detecting 3D primitives in
cluttered, unorganized point clouds, without axillary segmentation or type
specification. We consider the quadric surfaces for encapsulating the basic
building blocks of our environments - planes, spheres, ellipsoids, cones or
cylinders, in a unified fashion. Moreover, quadrics allow us to model higher
degree of freedom shapes, such as hyperboloids or paraboloids that could be
used in non-rigid settings.
We begin by contributing two novel quadric fits targeting 3D point sets that
are endowed with tangent space information. Based upon the idea of aligning the
quadric gradients with the surface normals, our first formulation is exact and
requires as low as four oriented points. The second fit approximates the first,
and reduces the computational effort. We theoretically analyze these fits with
rigor, and give algebraic and geometric arguments. Next, by re-parameterizing
the solution, we devise a new local Hough voting scheme on the null-space
coefficients that is combined with RANSAC, reducing the complexity from
to (three points). To the best of our knowledge, this is the
first method capable of performing a generic cross-type multi-object primitive
detection in difficult scenes without segmentation. Our extensive qualitative
and quantitative results show that our method is efficient and flexible, as
well as being accurate.Comment: Submitted to IEEE Transactions on Pattern Analysis and Machine
Intelligence (T-PAMI). arXiv admin note: substantial text overlap with
arXiv:1803.0719
A graph-spectral approach to shape-from-shading
In this paper, we explore how graph-spectral methods can be used to develop a new shape-from-shading algorithm. We characterize the field of surface normals using a weight matrix whose elements are computed from the sectional curvature between different image locations and penalize large changes in surface normal direction. Modeling the blocks of the weight matrix as distinct surface patches, we use a graph seriation method to find a surface integration path that maximizes the sum of curvature-dependent weights and that can be used for the purposes of height reconstruction. To smooth the reconstructed surface, we fit quadrics to the height data for each patch. The smoothed surface normal directions are updated ensuring compliance with Lambert's law. The processes of height recovery and surface normal adjustment are interleaved and iterated until a stable surface is obtained. We provide results on synthetic and real-world imagery
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