Affine-invariant, elastic shape analysis of planar contours

Bryner, Darshan; Srivastava, Anuj; Klassen, Eric

doi:10.1109/cvpr.2012.6247700

Cited by 16 publications

(25 citation statements)

References 11 publications

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“…After reviewing the current literature, we find that (i) while item (1) was introduced in both [8] and [4], these papers did not have items (2) and (3); (ii) item (2) -elastic, affine-invariant shape analysis -was introduced in [3] and developed further in [2], but those papers did not have items (1) or (3); (iii) item (3) was proposed in [17] but without either (1) or (2). To reiterate, there is no paper currently in the literature that performs even two of the three items together, which underlines the novelty of our approach.…”

Section: Our Approach and Contributionsmentioning

confidence: 98%

“…The work of Bryner et al [4] incorporates recent simplifications for elastic shape analysis provided in [15] for a computational speed-up. The works of [8] and [4] only formulate an intrinsic similarityinvariant shape prior rather than allowing for an affineinvariant, elastic shape model, which has been developed in [3] and [2].…”

Section: Past Work On Prior-driven Active Contoursmentioning

confidence: 99%

“…Section 2 reviews the affine-invariant, elastic shape analysis method from [3], and then develops the algorithmic tools to build intrinsic statistical shape models on the affine shape space. Section 3 describes the Bayesian active contour model, focusing on computation of the shape prior energy gradient with respect to the L 2 metric.…”

Section: Our Approach and Contributionsmentioning

confidence: 99%

“…Using the mathematical representation presented in [3] on affine-invariant elastic shape, we develop an intrinsic statistical model on the space of canonical, or affinestandardized, closed curves that will serve as a shape prior for the segmentation. Due to elastic matching of curves, this shape model captures the underlying shape variation of a shape class more accurately and leads to a more parsimonious shape model than its extrinsic counterparts often used in previous geometric Bayesian contour models.…”

Section: Our Approach and Contributionsmentioning

confidence: 99%

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Bayesian Active Contours with Affine-Invariant, Elastic Shape Prior

Bryner

Srivastava

2014

2014 IEEE Conference on Computer Vision and Pattern Recognition

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Active contour, especially in conjunction with priorshape models, has become an important tool in image segmentation. However, most contour methods use shape priors based on similarity-shape analysis, i.e. analysis that is invariant to rotation, translation, and scale. In practice, the training shapes used for prior-shape models may be collected from viewing angles different from those for the test images and require invariance to a larger class of transformation. Using an elastic, affine-invariant shape modeling of planar curves, we propose an active contour algorithm in which the training and test shapes can be at arbitrary affine transformations, and the resulting segmentation is robust to perspective skews. We construct a shape space of affinestandardized curves and derive a statistical model for capturing class-specific shape variability. The active contour is then driven by the true gradient of a total energy composed of a data term, a smoothing term, and an affine-invariant shape-prior term. This framework is demonstrated using a number of examples involving the segmentation of occluded or noisy images of targets subject to perspective skew.

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Section: Our Approach and Contributionsmentioning

confidence: 98%

Section: Past Work On Prior-driven Active Contoursmentioning

confidence: 99%

Section: Our Approach and Contributionsmentioning

confidence: 99%

Section: Our Approach and Contributionsmentioning

confidence: 99%

See 2 more Smart Citations

Bayesian Active Contours with Affine-Invariant, Elastic Shape Prior

Bryner

Srivastava

2014

2014 IEEE Conference on Computer Vision and Pattern Recognition

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“…First of all the choice of the invariants could be examined theoretically or even by an exhaustive series of experimental tests, to find the most robust set, On the other hand, different kind of affine invariant features could also be considered (e.g., [21]). At the same time, other affine registration methods (e.g., [29]) could be tested as second step of the method.…”

Section: Discussionmentioning

confidence: 99%

Geometric and Visual Reconstruction of Binary Shapes

Németh¹

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Best approach direction for spherical random variables

Jha

2021

Can J Statistics

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The quantiles of projections are discussed for spherical random variables. The concept of best approach direction is defined for any quantile based on the ordering of projections in different directions. The usefulness of the concept is discussed when the preferred direction for a specified proportion of observations is of interest. The variation of best approach directions with quantiles is studied for different families of distributions on the sphere, which helps in gaining insights into the symmetry, uniformity, and multimodality of the distributions. Exact polynomial-time algorithms are provided for the computation of its estimate on circle and spheres. The connected highest sample-density regions for spherical observations can be directly derived from these estimates. Inferential properties of the estimator are studied. Simulations and analyses of real data are performed to illustrate the results.

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Affine-invariant, elastic shape analysis of planar contours

Cited by 16 publications

References 11 publications

Bayesian Active Contours with Affine-Invariant, Elastic Shape Prior

Bayesian Active Contours with Affine-Invariant, Elastic Shape Prior

Geometric and Visual Reconstruction of Binary Shapes

Best approach direction for spherical random variables

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