Problem Of Shape Recovery Research Articles

Perception of 3D Symmetrical and Nearly Symmetrical Shapes

The human visual system uses priors to convert an ill-posed inverse problem of 3D shape recovery into a well-posed one. In previous studies, we have demonstrated the use of priors like symmetry, compactness and minimal surface in the perception of 3D symmetric shapes. We also showed that binocular perception of symmetric shapes can be well modeled by the above-mentioned priors and binocular depth order information. In this study, which used a shape-matching task, we show that these priors can also be used to model perception of near-symmetrical shapes. Our near-symmetrical shapes are asymmetrical shapes obtained from affine distortions of symmetrical shapes. We found that the perception of symmetrical shapes is closer to veridical than the perception of asymmetrical shapes. We introduce a metric to measure asymmetry of abstract polyhedral shapes, and a similar metric to measure shape dissimilarity between two polyhedral shapes. We report some key observations obtained by analyzing the data from the experiment. A website was developed with all the shapes used in the experiment, along with the shapes recovered by the subject and the shapes recovered by the model. This website provides a qualitative analysis of the effectiveness of the model and also helps demonstrate the goodness of the shape metric.

Wing aerodynamic optimization using efficient mathematically-extracted modal design variables

Aerodynamic shape optimization of a transonic wing using mathematically-extracted modal design variables is presented. A novel approach is used for deriving design variables using a singular value decomposition of a set of training aerofoils to obtain an efficient, reduced set of orthogonal ‘modes’ that represent typical aerodynamic design parameters. These design parameters have previously been tested on geometric shape recovery problems and aerodynamic shape optimization in two dimensions, and shown to be efficient at covering a large portion of the design space; the work is extended here to consider their use in three dimensions. Wing shape optimization in transonic flow is performed using an upwind flow-solver and parallel gradient-based optimizer, and a small number of global deformation modes are compared to a section-based local application of these modes and to a previously-used section-based domain element approach to deformations. An effective geometric deformation localization method is also presented, to ensure global modes can be reconstructed exactly by superposition of local modes. The modal approach is shown to be particularly efficient, with improved convergence over the domain element method, and only 10 modal design variables result in a 28% drag reduction.

Surface inspection system for industrial components based on shape from shading minimization approach

An inspection system using estimated three-dimensional (3-D) surface characteristics information to detect and classify the faults to increase the quality control on the frequently used industrial components is proposed. Shape from shading (SFS) is one of the basic and classic 3-D shape recovery problems in computer vision. In our application, we developed a system using Frankot and Chellappa SFS method based on the minimization of the selected basis function. First, the specialized image acquisition system captured the images of the component. To eliminate noise, wavelet transform is applied to the taken images. Then, estimated gradients were used to obtain depth and surface profiles. Depth information was used to determine and classify the surface defects. Also, a comparison made with some linearization-based SFS algorithms was discussed. The developed system was applied to real products and the results indicated that using SFS approaches is useful and various types of defects can easily be detected in a short period of time.

High-fidelity aerodynamic shape optimization using efficient orthogonal modal design variables with a constrained global optimizer

Abstract Aerodynamic shape optimization of aerofoils using efficient orthogonal design variables is considered using a global search algorithm. A novel approach is presented for deriving shape design variables, using a proper orthogonal decomposition of a set of training aerofoils to obtain an optimally efficient set of aerofoil deformation modes that represent typical design parameters such as thickness and camber. A major advantage of this extraction method is the production of orthogonal design variables, and this is particularly important in aerodynamic shape optimization. These design parameters have previously been tested on geometric shape recovery problems and been shown to be efficient at covering a large portion of the design space, hence the work is extended here to consider their use in aerodynamic shape optimization. A global search algorithm with an efficient constraint handling method has been developed and used here to optimize a suite of inviscid and viscous compressible aerofoil test cases using varying numbers of modal parameters. Often, an artefact of inviscid optimizations is an oscillatory pressure distribution, so to alleviate this drag minimization with a modulus of curvature penalty is also considered for the inviscid optimizations, where the penalty is used to force smoother pressure distributions; this is not necessary in the viscous optimizations. Results indicate that often fewer than 10 design parameters are required to obtain shock free solutions even from highly-loaded aerofoils with significant shocks.

The Information Available to a Moving Observer on Shape with Unknown, Isotropic BRDFs.

Psychophysical studies show motion cues inform about shape even with unknown reflectance. Recent works in computer vision have considered shape recovery for an object of unknown BRDF using light source or object motions. This paper proposes a theory that addresses the remaining problem of determining shape from the (small or differential) motion of the camera, for unknown isotropic BRDFs. Our theory derives a differential stereo relation that relates camera motion to surface depth, which generalizes traditional Lambertian assumptions. Under orthographic projection, we show differential stereo may not determine shape for general BRDFs, but suffices to yield an invariant for several restricted (still unknown) BRDFs exhibited by common materials. For the perspective case, we show that differential stereo yields the surface depth for unknown isotropic BRDF and unknown directional lighting, while additional constraints are obtained with restrictions on the BRDF or lighting. The limits imposed by our theory are intrinsic to the shape recovery problem and independent of choice of reconstruction method. We also illustrate trends shared by theories on shape from differential motion of light source, object or camera, to relate the hardness of surface reconstruction to the complexity of imaging setup.

Metric-Based Mathematical Derivation of Efficient Airfoil Design Variables

Within an aerodynamic shape optimization framework, an efficient shape parameterization and deformation scheme is critical to allow flexible deformation of the surface with the maximum possible design space coverage. Numerous approaches have been developed for the geometric representation of airfoils. A fundamental approach is considered here from the geometric perspective; and a method is presented to allow the derivation of efficient, generic, and orthogonal airfoil geometric design variables. This is achieved by the mathematical decomposition of a training library. The resulting geometric modes are independent of a parameterization scheme, surface and volume mesh, and flow solver; thus, they are generally applicable. However, these modes are dependent on the training library, and so a benchmark performance measure, called the airfoil technology factor, has also been incorporated into the scheme to allow intelligent metric-based filtering, or design space reduction, of the training library to ensure efficient airfoil deformation modes are extracted. Results are presented for several geometric shape recovery problems, using two optimization approaches, and it is shown that these mathematically extracted degrees of freedom perform particularly well in all cases, showing excellent design space coverage. These design variables are also shown to outperform those based on other widely used approaches; the Hicks–Henne “bump” functions and a linear (deformative) approximation to Sobieczky's parametric section parameterization are considered.

Electromagnetic treatment for the inverse reflectance-based shape recovery problem

Electromagnetic treatment for the inverse reflectance-based shape recovery problem

Any Pair of 2D Curves Is Consistent with a 3D Symmetric Interpretation

Symmetry has been shown to be a very effective a priori constraint in solving a 3D shape recovery problem. Symmetry is useful in 3D recovery because it is a form of redundancy. There are, however, some fundamental limits to the effectiveness of symmetry. Specifically, given two arbitrary curves in a single 2D image, one can always find a 3D mirror-symmetric interpretation of these curves under quite general assumptions. The symmetric interpretation is unique under a perspective projection and there is a one parameter family of symmetric interpretations under an orthographic projection. We formally state and prove this observation for the case of one-to-one and many-to-many point correspondences. We conclude by discussing the role of degenerate views, higher-order features in determining the point correspondences, as well as the role of the planarity constraint. When the correspondence of features is known and/or curves can be assumed to be planar, 3D symmetry becomes non-accidental in the sense that a 2D image of a 3D asymmetric shape obtained from a random viewing direction will not allow for 3D symmetric interpretations.

An iterative algorithm based on level set method for the shape recovery problem

In this paper, we propose an iterative algorithm based on the level set method for the shape recovery problem. We use a suitable preconditioner for the artificial time-dependent system for the level set formulation and propose an iterative algorithm of the level set function. We prove the convergence of our algorithm under some hypothesis. Numerical experiments show the efficiency of the algorithm.

A Fast 2D Shape Recovery Approach by Fusing Features and Appearance

In this paper, we present a fusion approach to solve the nonrigid shape recovery problem, which takes advantage of both the appearance information and the local features. We have two major contributions. First, we propose a novel progressive finite Newton optimization scheme for the feature-based nonrigid surface detection problem, which is reduced to only solving a set of linear equations. The key is to formulate the nonrigid surface detection as an unconstrained quadratic optimization problem that has a closed-form solution for a given set of observations. Second, we propose a deformable Lucas-Kanade algorithm that triangulates the template image into small patches and constrains the deformation through the second-order derivatives of the mesh vertices. We formulate it into a sparse regularized least squares problem, which is able to reduce the computational cost and the memory requirement. The inverse compositional algorithm is applied to efficiently solve the optimization problem. We have conducted extensive experiments for performance evaluation on various environments, whose promising results show that the proposed algorithm is both efficient and effective.

On level set regularization for highly ill-posed distributed parameter estimation problems

The recovery of a distributed parameter function with discontinuities from inverse problems with elliptic forward PDEs is fraught with theoretical and practical difficulties. Better results are obtained for problems where the solution may take on at each point only one of two values, thus yielding a shape recovery problem. This article considers level set regularization for such problems. However, rather than explicitly integrating a time embedded PDE to steady state, which typically requires thousands of iterations, methods based on Gauss–Newton are applied more directly. One of these can be viewed as damped Gauss–Newton utilized to approximate the steady state equations which in turn are viewed as the necessary conditions of a Tikhonov-type regularization with a sharpening sub-step at each iteration. In practice this method is eclipsed, however, by a special “finite time” or Levenberg–Marquardt-type method which we call dynamic regularization applied to the output least squares formulation. Our stopping criterion for the iteration does not involve knowledge of the true solution. The regularization functional is applied to the (smooth) level set function rather than to the discontinuous function to be recovered, and the second focus of this article is on selecting this functional. Typical choices may lead to flat level sets that in turn cause ill-conditioning. We propose a new, quartic, non-local regularization term that penalizes flatness and produces a smooth level set evolution, and compare its performance to more usual choices. Two numerical test cases are considered: a potential problem and the classical EIT/DC resistivity problem.

A Closed-Form Solution to Non-Rigid Shape and Motion Recovery

Recovery of three dimensional (3D) shape and motion of non-static scenes from a monocular video sequence is important for applications like robot navigation and human computer interaction. If every point in the scene randomly moves, it is impossible to recover the non-rigid shapes. In practice, many non-rigid objects, e.g. the human face under various expressions, deform with certain structures. Their shapes can be regarded as a weighted combination of certain shape bases. Shape and motion recovery under such situations has attracted much interest. Previous work on this problem (Bregler, C., Hertzmann, A., and Biermann, H. 2000. In Proc. Int. Conf. Computer Vision and Pattern Recognition; Brand, M. 2001. In Proc. Int. Conf. Computer Vision and Pattern Recognition; Torresani, L., Yang, D., Alexander, G., and Bregler, C. 2001. In Proc. Int. Conf. Computer Vision and Pattern Recognition) utilized only orthonormality constraints on the camera rotations (rotation constraints). This paper proves that using only the rotation constraints results in ambiguous and invalid solutions. The ambiguity arises from the fact that the shape bases are not unique. An arbitrary linear transformation of the bases produces another set of eligible bases. To eliminate the ambiguity, we propose a set of novel constraints, basis constraints, which uniquely determine the shape bases. We prove that, under the weak-perspective projection model, enforcing both the basis and the rotation constraints leads to a closed-form solution to the problem of non-rigid shape and motion recovery. The accuracy and robustness of our closed-form solution is evaluated quantitatively on synthetic data and qualitatively on real video sequences.

Shape and impedance recovery of obstacles from electromagnetic scattering data

The problem of shape and impedance recovery of an arbitrary cylindrical obstacle from scattering data for electromagnetic waves generated by a line source parallel to the cylindrical obstacle is considered. Using the method of lines (MoL), an inversion procedure is developed that recovers both shape and impedance from scattering data for all angles and two different frequencies of the incident waves. Several numerical examples with synthetic scattering data and added noise are presented. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 596–600, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21418

Polygonal space carving with geometric anti-aliasing

This paper proposes an algorithm that solves the shape recovery problem from N arbitrary images. By introducing a polygonal carving technique, the proposed algorithm can reconstruct the image-consistent polygonal shape that is patched by input images. This algorithm eliminates the invalid vertices and polygons from the initial polygonal grid space according to the color variance that represents their image consistency. The carved shape is refined by moving the outlier vertices on the boundary of each image. The final reconstructed shape faithfully accounts for the input images, and its textured appearance reflects the similar color property of the target object.

Articulated soft objects for multiview shape and motion capture

We develop a framework for 3D shape and motion recovery of articulated deformable objects. We propose a formalism that incorporates the use of implicit surfaces into earlier robotics approaches that were designed to handle articulated structures. We demonstrate its effectiveness for human body modeling from synchronized video sequences. Our method is both robust and generic. It could easily be applied to other shape and motion recovery problems.

Shape representation using extended hyperquadrics

AbstractFor the preprocessing of shape recognition in computer vision, it is necessary to reconstruct a shape from 3D range data or 2D edge image data. Efforts have been made to approximate a shape‐recovery problem by using a super second‐order function or a hyperquadric function (an expansion of the former). However, the latter cannot be applied to a shape with any concavity. This paper proposes another expansion of the hyperquadric function which has minor additional parameters and can be applied to a great variety of shapes. This paper also shows the effectiveness of the method experimentally. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 86(4): 42–51, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.10142

Riemannian Drums, Anisotropic Curve Evolution, and Segmentation

The method of curve evolution is a popular method for recovering shape boundaries. However, isotropic metrics have always been used to induce the flow of the curve and potential steady states tend to be difficult to determine numerically, especially in noisy or low-contrast situations. Initial curves shrink past the steady state and soon vanish. In this paper, anisotropic metrics are considered to remedy the situation by taking the orientation of the feature gradient into account. The problem of shape recovery or segmentation is formulated as the problem of finding minimum cuts of a Riemannian manifold. Approximate methods, namely anisotropic geodesic flows and the solution of an eigenvalue problem, are discussed.

Numerical solution of the problem of shape recovery for a system of impedance surfaces

We consider the problem of shape determination of a system of surfaces with impedance properties, using the scattering pattern specified at a finite number of points. We use the method of artificial “embedding” of the given problem in a more general problem in which the impedance distribution at variable parts of the surface is also a desired parameter. This allows us to move to the nonlinear operator equation that permits efficient numerical solution. Calculated results are given.

Accurate recovery of three-dimensional shape from image focus

A new shape-from-focus method is described which is based on a new concept, named focused image surface (FIS). FIS of an object is defined as the surface formed by the set of points at which the object points are focused by a camera lens. According to paraxial-geometric optics, there is a one-to-one correspondence between the shape of an object and the shape of its FIS. Therefore, the problem of shape recovery can be posed as the problem of determining the shape of the FIS. From the shape of FIS the shape of the object is easily obtained. In this paper the shape of the FIS is determined by searching for a shape which maximizes a focus measure. In contrast to previous literature where the focus measure is computed over the planar image detector of the camera, here the focus measure is computed over the FIS. This results in more accurate shape recovery than the traditional methods. Also, using FIS, a more accurate focused image can be reconstructed from a sequence of images than is possible with traditional methods. The new method has been implemented on an actual camera system, and the results of shape recovery and focused image reconstruction are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>