# Mtar: a Robust 2d Shape Representation

@article{Rube2006MtarAR, title={Mtar: a Robust 2d Shape Representation}, author={Ibrahim El Rube and Naif A. Alajlan and Mohamed S. Kamel and Maher Ahmed and George H. Freeman}, journal={Int. J. Image Graph.}, year={2006}, volume={6}, pages={421-444} }

In this paper, a new 2D shape Multiscale Triangle-Area Representation (MTAR) method is proposed. This representation utilizes a simple geometric principle, that is, the area of the triangles formed by the shape boundary points. The wavelet transform is used for smoothing and decomposing the shape boundaries into multiscale levels. At each scale level, a TAR image and the corresponding Maxima-Minima lines are obtained. The resulting MTAR is more robust to noise, less complex, and more selective…

## Figures and Tables from this paper

## 12 Citations

THE PROPOSED HIRRARCHICAL STRIP CUTS MECHANISM FOR BRISK SHAPE RETRIEVAL

- Psychology
- 2017

Chuang et al. (2011) [117] proposed ghostly change based shape descriptor that was utilized 1D ceaseless wavelet change to make a multi-scale shape representation. Yang et al. [44] proposed a…

Similarity measurement with mesh distance fourier transform in 2D binary image

- Computer ScienceRACS
- 2015

A novel shape feature named Mesh Distance Fourier Descriptor (MDFD) which takes into account the contour information of each of the boundary points with respect to other contour points in the images such that the relationship of one boundary point is evaluated withrespect to all other boundary points in 2D space.

Extraction of filled in strokes from cheque image using pseudo 2D wavelet with adjustable support

- Computer ScienceIEEE International Conference on Image Processing 2005
- 2005

This paper presents a method for processing complicated grey images in two steps, based on the construction of a pseudo 2D wavelet with adjustable rectangular supports, which is also effective for slightly skewed cheque image.

Hierarchical String Cuts: A Translation, Rotation, Scale, and Mirror Invariant Descriptor for Fast Shape Retrieval

- Computer ScienceIEEE Transactions on Image Processing
- 2014

A novel approach to partition a shape into multiple level curve segments of different lengths from a point moving around the contour to describe the shape gradually and completely from the global information to the finest details is proposed.

Farthest point distance: A new shape signature for Fourier descriptors

- Computer ScienceSignal Process. Image Commun.
- 2009

Shape Representation and Retrieval Using Radial Basis Probabilistic Neural Networks

- Computer Science
- 2008

This paper uses radial basis probabilistic neural networks to recognize the object shapes based on moment invariants features extracted from the shape contour to solve the 2D shape retrieval problem.

The distance between shape centroids is less than a quarter of the shape perimeter

- MathematicsPattern Recognit.
- 2011

ADR shape descriptor - Distance between shape centroids versus shape diameter

- Computer ScienceComput. Vis. Image Underst.
- 2012

Distance between Shape Centroids versus Shape Diameter

- Computer Science
- 2012

It is shown that ρ(S) ranges over the interval [0, 1) and the established upper bound 1 is the best possible by constructing shapes whose ρ (S) values are arbitrary close to 1.

Analysis of a shape descriptor: Distance between two shape centroids versus shape diameter

- Computer Science2012 International Conference on Informatics, Electronics & Vision (ICIEV)
- 2012

A shape descriptor ρ(S) that is defined as the ratio of the squared distance between centroids and the squared diameter of shape S is studied, meaning in particular that value 1 is not taken, that 1 is the best possible upper bound, and and examples of shapes whose ρ (S) values are arbitrarily close to 1 are given.

## References

SHOWING 1-10 OF 41 REFERENCES

Recognition of 2D Standalone and Occluded Objects Using Wavelet Transform

- Computer ScienceInt. J. Pattern Recognit. Artif. Intell.
- 2001

A planar curve descriptor which is invariant to translation, size, rotation and starting point in tracing the boundary is developed based on the periodized wavelet transform for recognition of two-dimensional closed boundary curves and is extended for the recognition of occluded objects.

Coarse-to-fine multiscale affine invariant shape matching and classification

- Computer ScienceProceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004.
- 2004

A multiscale algorithm for matching and classifying 2-D shapes is developed that is invariant to the affine transformation and to the boundary starting point variation and is not sensitive to small boundary deformations.

Affine-similar shape retrieval: application to multiview 3-D object recognition

- Computer ScienceIEEE Trans. Image Process.
- 2001

Results indicate that robust and efficient 3-D free-form object recognition through multiview representation can be achieved using the CSS representation.

Multiresolution moment-Fourier-wavelet descriptor for 2D pattern recognition

- Computer ScienceDefense, Security, and Sensing
- 1997

Experimental results show that the descriptor proposed in this paper is a reliable tool for recognizing Chinese characters and is invariant to shift, rotation, and scaling of the original image.

2-D Shape Representation and Averaging Using Normalized Wavelet Descriptors

- Computer ScienceSimul.
- 1996

Results from the method as applied to shape representation and averaging for biological objects are presented, along with its applications to contour data compression.

Silhouette-Based Isolated Object Recognition through Curvature Scale Space

- Computer ScienceIEEE Trans. Pattern Anal. Mach. Intell.
- 1995

A complete, fast and practical isolated object recognition system has been developed which is very robust with respect to scale, position and orientation changes of the objects as well as noise and…

Multiscale curvature-based shape representation using B-spline wavelets

- Computer ScienceIEEE Trans. Image Process.
- 1999

This paper presents a new multiscale curvature-based shape representation technique with application to curve data compression using B-spline wavelets and introduces a coarse-to-fine matching algorithm which automatically detects the dominant points and uses them as knots for curve interpolation.

Classification of Similar 2-D Objects by Wavelet-Sparse-Matrix (WSM) Method

- Computer ScienceInt. J. Pattern Recognit. Artif. Intell.
- 2001

Wavelet-Sparse-Matrix method is proposed to extract the spatial features of 2-D objects for classifying objects that have subtle differences, which can considerably improve the distinction of slightly dissimilar objects.

A Dyadic Wavelet Affine Invariant Function for 2D Shape Recognition

- Mathematics, Computer ScienceIEEE Trans. Pattern Anal. Mach. Intell.
- 2001

The wavelet based conic equation is introduced and the invariant function is based on analyzing the object boundary using the dyadic wavelet transform and the stability under large perspective transformation is tested.

Scale-based description and recognition of planar curves

- Mathematics, Environmental Science
- 1984

A method of finding points of inflection on a planar curve at varying levels of detail and combining them to obtain a representation of the curve invariant under rotation, uniform scaling and…