Integral Invariants and Shape Matching

Manay, Siddharth; Cremers, Daniel; Hong, Byung-Woo; Yezzi, Anthony; Soatto, Stefano

doi:10.1007/0-8176-4481-4_6

Cited by 73 publications

(106 citation statements)

References 61 publications

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“…These method are simple and robust, but less ability to distinguish, and can't be used for precise matching. The more ability of description methods are Fourier method, wavelet description method, measuring distance [1], shape context [2] [3], integral invariants [4], Heat Kernel [5].…”

Section: A Component-stroke Detectionmentioning

confidence: 99%

Component-stroke Corresponding System for Chinese Characters of Different Styles

Che¹,

Liang²,

Yue³

2015

Proceedings of the 2015 International Conference on Computer Science and Intelligent Communication

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Abstract-Stroke and shape of the Chinese character with different script has changed hugely among different style. To present the correspondence between Chinese characters component-strokes, this paper designs a component-stroke corresponding system for Chinese characters based on sematic knowledge. Firstly, we acquire the correspondence between components by the way of semi-automatic. Then we get the feature points from the intersection of skeleton and contour by skeleton algorithm, finally we finish the Chinese character component-stroke correspondence process. Our system can present a robust and fast component-strokes correspondence results.

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Section: A Component-stroke Detectionmentioning

confidence: 99%

Component-stroke Corresponding System for Chinese Characters of Different Styles

Che¹,

Liang²,

Yue³

2015

Proceedings of the 2015 International Conference on Computer Science and Intelligent Communication

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“…We employed the MCFs for the 10-DS, SC, and mixture of vMDs to calculate the dissimilarity in (3). In addition, for reference purposes, we compared all the above descriptors and the integral invariant (INI) descriptor [11]. This comparison examines the differences between matching methods for ordered and unordered shapes.…”

Section: Drawing Data Setmentioning

confidence: 99%

Matching Handwritten Line Drawings with Von Mises Distributions

Ueaoki

Iwata

Saito

et al. 2011

IEICE Trans. Inf. & Syst.

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SUMMARYA two-dimensional shape is generally represented with line drawings or object contours in a digital image. Shapes can be divided into two types, namely ordered and unordered shapes. An ordered shape is an ordered set of points, while an unordered shape is an unordered set. As a result, each type typically uses different attributes to define the local descriptors involved in representing the local distributions of points sampled from the shape. Throughout this paper, we focus on unordered shapes. Since most local descriptors of unordered shapes are not scale-invariant, we usually make the shapes in an image data set the same size through scale normalization, before applying shape matching procedures. Shapes obtained through scale normalization are suitable for such descriptors if the original whole shapes are similar. However, they are not suitable if parts of each original shape are drawn using different scales. Thus, in this paper, we present a scale-invariant descriptor constructed by von Mises distributions to deal with such shapes. Since this descriptor has the merits of being both scale-invariant and a probability distribution, it does not require scale normalization and can employ an arbitrary measure of probability distributions in matching shape points. In experiments on shape matching and retrieval, we show the effectiveness of our descriptor, compared to several conventional descriptors.

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“…image retrieval, object classification, object recognition, object identification, etc). Different mathematical tools have been used to define the shape descriptors: algebraic invariants [14], Fourier analysis [6], morphological operations [26], integral transformations [23], statistical methods [17], fractal techniques [15], logic [27], combinatorial methods [1], multiscale approaches [9], integral invariants [16], multi-scale integral geometry [3,4,18], etc. Generally speaking, shape descriptors can be classified into two groups: area based descriptors and boundary based ones.…”

Section: Introductionmentioning

confidence: 99%

“…In the literature so far, more attention has been paid to the area based descriptors, not only because of their robustness but also because they are easier to be efficiently estimated when working with discrete data. Due to the recent proliferation of image verification, identification and recognition systems there is a strong demand for shape properties that can be derived from their boundaries [16,19,30]. It is worth mentioning that some objects, like human signatures for example, are open curves by their nature and area based descriptors cannot be used for their analysis.…”

Section: Introductionmentioning

confidence: 99%

Measuring linearity of curves in 2D and 3D

Rosin

Pantović

Žunić

2016

Pattern Recognition

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In this paper we define a new linearity measure for open curve segments in 2D and 3D. The measure considers the distance of the curve end points to the curve centroid. It is simple to compute and has the basic properties that should be satisfied by any linearity measure. The new measure ranges over the interval (0, 1], and produces the value 1 if and only if the measured curve is a perfect straight line segment. Also, the new linearity measure is invariant with respect to translations, rotations and scaling transformations. The new measure is theoretically well founded and, because of this, its behaviour can be well understood and predicted to some extent. This is always beneficial because it indicates the suitability of the new measure to the desired application.Several experiments are provided to illustrate the behaviour and to demonstrate the efficiency and applicability of the new linearity measure.

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Integral Invariants and Shape Matching

Cited by 73 publications

References 61 publications

Component-stroke Corresponding System for Chinese Characters of Different Styles

Component-stroke Corresponding System for Chinese Characters of Different Styles

Matching Handwritten Line Drawings with Von Mises Distributions

Measuring linearity of curves in 2D and 3D

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