Two-dimensional shape recognition using oriented-polar representation

1997 ◽  
Vol 36 (10) ◽  
pp. 2828 ◽  
Author(s):  
Neng-Chung Hu
Keyword(s):  
Shape Recognition ◽  
Two Dimensional ◽  
Polar Representation ◽  
Dimensional Shape

A TWO-DIMENSIONAL SHAPE RECOGNITION SCHEME BASED ON PRINCIPAL COMPONENT ANALYSIS

1994 ◽  
Vol 08 (04) ◽  
pp. 859-875 ◽  
Author(s):  
CHIN-CHEN CHANG ◽  
YAW-WEN CHEN ◽  
DANIEL JAMES BUEHRER
Keyword(s):  
Shape Matching ◽  
Shape Recognition ◽  
Computation Time ◽  
Principal Component ◽  
Two Dimensional ◽  
Shape Features ◽  
Matching Algorithm ◽  
Boundary Points ◽  
Dimensional Shape ◽  
The Difference

In this paper, we propose a simple, but efficient method to recognize two-dimensional shapes without regard to their translation, rotation, and scaling factors. In our scheme, we use all of the boundary points to calculate the first principal component, which is the first shape feature. Next, by dividing the boundary points into groups by projecting them onto the first principal component, each shape is partitioned into several blocks. These blocks are processed separately to produce the remaining shape features. In shape matching, we compare two shapes by calculating the difference between the two sets of features to see whether the two shapes are similar or not. The amount of storage used to represent a shape in our method is fixed, unlike most other shape recognition schemes. The time complexity of our shape matching algorithm is also O(n), where n is the number of blocks. Therefore, the matching algorithm takes little computation time, and is independent of translation, rotation, and scaling of shapes.

Perceptual Frames of Reference and Two-Dimensional Shape Recognition: Further Examination of Internal Axes

Perception ◽  
1993 ◽  
Vol 22 (11) ◽  
pp. 1343-1364 ◽  
Author(s):  
Philip T Quinlan ◽  
Glyn W Humphreys
Keyword(s):  
Shape Recognition ◽  
Shape Perception ◽  
The Other ◽  
Frames Of Reference ◽  
Classification Task ◽  
Structural Description ◽  
Two Dimensional ◽  
Dimensional Shape ◽  
Axis Of Symmetry ◽  
Speeded Classification

Three experiments on the perception of simple four-sided two-dimensional shapes are reported. In the first experiment subjects were given a paper-and-pencil test in which they had to consider each of a set of shapes in turn. They were instructed to draw in what they considered to be the most salient axis of each of the shapes ie a line that they felt most naturally went with the shape. The results showed a significant tendency to draw an axis of symmetry if one was present. However, when presented with instances of a shape that was elongated but possessed no symmetries they failed to consistently draw any particular axis. A further, speeded classification, task revealed that for this shape explicit axis information appeared not to influence performance. In contrast, such information clearly affected performance with a shape that did possess a salient axis of symmetry and elongation. Indeed this axis was shown to be integral with the contour of the shape when a final classification experiment was carried out. The axis of elongation of the other shape acted as a characteristic which was separable from the contour. The results are discussed in relation to accounts of shape perception which assume that a necessary stage in the perception of shape is the derivation of an axis-based structural description.

scholarly journals Surface energies emerging in a microscopic, two-dimensional two-well problem

2017 ◽  
Vol 147 (5) ◽  
pp. 1041-1089 ◽  
Author(s):  
Georgy Kitavtsev ◽  
Stephan Luckhaus ◽  
Angkana Rüland
Keyword(s):  
Surface Energy ◽  
Two Dimensional ◽  
Direct Control ◽  
First Order ◽  
Surface Energies ◽  
Energy Scaling ◽  
Continuous Analogue ◽  
Dimensional Shape ◽  
Set Up ◽  
Microscopic Modelling

In this paper we are interested in the microscopic modelling of a two-dimensional two-well problem that arises from the square-to-rectangular transformation in (two-dimensional) shape-memory materials. In this discrete set-up, we focus on the surface energy scaling regime and further analyse the Hamiltonian that was introduced by Kitavtsev et al. in 2015. It turns out that this class of Hamiltonians allows for a direct control of the discrete second-order gradients and for a one-sided comparison with a two-dimensional spin system. Using this and relying on the ideas of Conti and Schweizer, which were developed for a continuous analogue of the model under consideration, we derive a (first-order) continuum limit. This shows the emergence of surface energy in the form of a sharp-interface limiting model as well the explicit structure of the minimizers to the latter.

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