# The Curvature Primal Sketch

@article{Asada1986TheCP, title={The Curvature Primal Sketch}, author={Haruo Asada and Michael Brady}, journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, year={1986}, volume={PAMI-8}, pages={2-14} }

In this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape. We call the representation the Curvature Primal Sketch because of the close analogy to the primal sketch representation advocated by Marr for describing significant intensity changes. We define a set of primitive parameterized curvature discontinuities, and derive expressions for their convolutions with the first and second derivatives of a Gaussian. We describe…

## 820 Citations

### Toward a surface primal sketch

- 1985

Mathematics

Proceedings. 1985 IEEE International Conference on Robotics and Automation

This paper reports progress toward the development of a representation of significant surface changes in dense depth maps by analogy with representations of intensity changes, image structure, and changes in curvature of planar curves.

### Using Curvature Information in the Decomposition and Representation of Planar Curves

- 1992

Computer Science

This paper describes a new symbolic representation for planar curves based on a segmentation of the curve based on regions of uniform curvature that decomposes the curve at multiple scales and the parts produced appear to correspond to a natural decomposition of the curves.

### On planar curve representation

- 1994

Mathematics

Proceedings of 1st International Conference on Image Processing

A new scheme, based on the concept of stressed curves, is developed for extracting significant curvature points on a planar curve that offers efficient and accurate extraction of significant curvatures points with a smaller computational complexity.

### Shape Features Using Curvature Morphology

- 1989

Computer Science

Other Conferences

A scheme for obtaining the discrete curvature function of planar contours based on the chain-code representation of a boundary and a new scale-space representation for curvature named the Morphological Curvature Scale-Space are presented.

### Curvature Morphology

- 2007

Computer Science

A scheme for obtaining the discrete curvature function of planar contours based on the chain-code representation of a boundary is presented and a new scale-space representation for curvature named the Morphological Curvature Scale-Space is suggested.

### A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves

- 1992

Physics

IEEE Trans. Pattern Anal. Mach. Intell.

A shape representation technique suitable for tasks that call for recognition of a noisy curve of arbitrary shape at an arbitrary scale or orientation is presented and several evolution and arc length evolution properties of planar curves are discussed.

### Multiscale segmentation and approximation for significant description of 2D contours

- 1997

Computer Science

Proceedings of International Conference on Image Processing

This paper proposes a new approach for the multiscale segmentation and approximation of 2D contours, strictly based on discrete geometry principles, and the resulting algorithm named MuscaGrip computes, at multiple scales, two grouping processes.

### A Unified Curvature Definition for Regular, Polygonal, and Digital Planar Curves

- 2008

Mathematics

International Journal of Computer Vision

The proposed definition of visual curvature is the first ever that applies to regular curves as defined in differential geometry as well as to turn angles of polygonal curves and it yields stable curvature estimates of curves in digital images even under sever distortions.

### A Shape Representation with Elastic Quadratic Polynomials—Preservation of High Curvature Points under Noisy Conditions

- 2008

Mathematics

International Journal of Computer Vision

The results show that the proposed technique is highly effective in preserving salient high curvature points with a relatively small Hausdorff distance and a computational cost.

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Mathematics

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It is argued that "non-attentive" vision is in practice implemented by these grouping operations and first order discriminations acting on the primal sketch, and implies that such knowledge should influence the control of, rather than interfering with, the actual data-processing that is taking place lower down.

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A family of symbols is defined by which much of the useful information in an image may be represented, and it is shown that these descriptors may readily be computed from measurements similar to those made by simple cells in the visual cortex of the cat.