Recovery Of Superquadrics From 3-D Information

Boult, Terrance E.; Gross, Ari D.

doi:10.1117/12.942759

Cited by 19 publications

(19 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The input is a set of 3D points from range images. Boult and Gross [6] used a gradient descent minimization method for superquadric recovery, but had problems with convergence for cylindrically shaped objects. Solina and Bajcsy [26] employed a modified error-of-fit function and obtained better results.…”

Section: Fig 1 3d Shape Modelsmentioning

confidence: 99%

“…They can model a diverse set of objects, and are intrinsically symmetric about the coordinate axes. Several researchers have used superquadrics for object modeling, motion analysis, and object recognition [1,2,6,7,10,12,[23][24][25][26]. Barr [1,2] applied simple deformations such as tapering, bending, and twisting to superquadrics and Zhang et al [28][29][30] proposed nonlinear deformable superquadric models to model a wider range of shapes.…”

Section: Fig 1 3d Shape Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Extending Superquadrics with Exponent Functions: Modeling and Reconstruction

Zhou

Kambhamettu

2001

Graphical Models

View full text Add to dashboard Cite

Section: Fig 1 3d Shape Modelsmentioning

confidence: 99%

Section: Fig 1 3d Shape Modelsmentioning

confidence: 99%

Extending Superquadrics with Exponent Functions: Modeling and Reconstruction

Zhou

Kambhamettu

2001

Graphical Models

View full text Add to dashboard Cite

“…Perhaps the simplest method of fitting these models to range data is to use a standard gradient descent technique to adjust the deformations t~ for each part [12,13,15]. Letting u~/be the value of the ith deformation mode at time k, and ~ be the distance between data point j and the part surface at time k, then the update rule is simply fik+l = fik _ je k [13] As the elements of the Jacobian matrix 0/~ i are expensive to calculate analytically, I have instead calculated the values of the vector Je ~ numerically. I have also found it useful to add Poission-distributed noise to the vector Je ~ in order to avoid shallow local minima.…”

Section: Fitting 3d Modelsmentioning

confidence: 99%

“…Although equation [~5] is much more efficient than equation [13], it cannot easily be used to adjust parameters other than the modal deformation parameters. Thus, for instance, it cannot be used to adjust the superquadric shape parameters.…”

Section: Fitting 3d Modelsmentioning

confidence: 99%

Automatic extraction of deformable part models

Pentland

1990

Int J Comput Vision

201

View full text Add to dashboard Cite

I describe a system that first segments an image into parts, and then fits deformable models to range data associated with the image. Models are represented by using modal dynamics applied to volumetric primitives, which significantly improves the computational complexity of both model recovery and subsequent processing. The segmentation procedure uses two simple mechanisms: a filtering operation to produce a large set of potential object parts, followed by a quadratic integer optimization that searches among these part hypotheses to produce a maximum-likelihood estimate of the image's part structure. Once a segmentation has been produced, a volumetric description is obtained by a fitting procedure that minimizes squared error between the range measurements an the model's visible surface. For simple part shapes, it is possible to compute the deformable model's parameters using only the shape of its symmetry axes.

show abstract

“…Here, a complex surface is represented by patches of primitive surfaces. Superquadrics [4,2,7,17], an extension of quadric surfaces, fall in the same category. An example of a superquadric is an ellipsoid that can smoothly deform into various exotic shapes.…”

Section: Some Existing Boundary Representationsmentioning

confidence: 99%

Representing and comparing shapes using shape polynomials

Taubin

Bolle²,

Cooper³

Proceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition

View full text Add to dashboard Cite

We address the problem of multiresolution 2D and 3D shape representation. Shape is defined as a probability measure with compact support. Both object representations, typically sets of curves and/or surface patches, and observations, sets of scattered data, can be represented in this way. Global properties of shapes are defined as expectations (statistical averages) of certain functions. In particular, the moments of the shapes are global properties. For any shape Ë and every integer ¼ we associate a shape polynomial of degree ¾ whose coefficients are functions of the moments of Ë. These polynomials are related to the shape Ë in an affine invariant way. They yield small values near Ë and large values far away and their level sets approximate Ë. With the shape polynomials we define two distances between shapes. An asymmetric distance measures how well one shape fits as a subset of another one; a symmetric version indicates how equal two shapes are. The evaluation of these distance measures is determined via a sequence of computationally very fast matrix operations. The distance measures are used for recognition and positioning of objects in occluded environments.

show abstract

Recovery Of Superquadrics From 3-D Information

Cited by 19 publications

References 8 publications

Extending Superquadrics with Exponent Functions: Modeling and Reconstruction

Extending Superquadrics with Exponent Functions: Modeling and Reconstruction

Automatic extraction of deformable part models

Representing and comparing shapes using shape polynomials

Contact Info

Product

Resources

About