The revised fundamental theorem of moment invariants

This paper presents a novel technique to determine image distortion properties, such as translation, scale, rotation and skew properties, by only using its moments. The properties are retrieved by solving the algebraic relationships between moment functions of original and geometrically distorted images. These properties, to the best of our knowledge, have yet to be presented in any papers. The derived distortion properties are experimentally validated using randomly scaled, rotated and skewed images. Promising results are produced from these experiments.

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“…(1) into Eq. (4), and taking into consideration the Jacobian constant for substuting f (x , y ) [4], the equation now becomes…”

Section: Relationship Of Distorted Moments and Original Momentsmentioning

confidence: 99%

Retrieving geometric distortion properties from image moments

Ann

Besar

Abas

et al. 2009

IEICE Electron. Express

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“…In particular, the invariant-based approach uses moment invariants that are invariant under affine transforms [27]. For example, affine moment invariants for images have been proposed in [35], [16], and in [55], cross-weighted moment invariants are used for alignment and recognition. Seusse et al [47], [50] introduce the idea of discrete affine moments, and the normalization technique used in these papers, although in a different context, is the same as our orthogonal reduction step.…”

Section: Previous Workmentioning

confidence: 99%

Higher-Dimensional Affine Registration and Vision Applications

Nejhum

Chi

et al. 2011

IEEE Trans. Pattern Anal. Mach. Intell.

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Abstract-Affine registration has a long and venerable history in computer vision literature, and in particular, extensive work has been done for affine registration in IR 2 and IR 3 . This paper studies affine registration in IR m with m typically ranging from 4 to 12. To justify breaking of this dimension barrier, the first part of the paper describes three novel matching problems that can be formulated and solved as affine point-set registration problems in dimensions greater than three: stereo correspondence under motion, image set matching, and covariant point-set matching, problems that are not only interesting in their own right but also have potential for important vision applications. Unfortunately, most of the existing affine registration algorithms do not generalize easily to higher dimensions due to their inefficiency. Therefore, the second part of this paper develops a novel algorithm for estimating the affine transform between two point sets in IR m . Specifically, the algorithm follows the common approach of iteratively solving the correspondences and transform. The initial correspondences are determined using the novel notion of local spectral features, features constructed from local distance matrices. Unlike many correspondence-based methods, the proposed algorithm is capable of registering point sets of different size, and the use of local features provides some degree of robustness against noise and outliers. The proposed algorithm is validated on a variety of synthetic point sets in different dimensions with varying degrees of deformation and noise, and the paper also shows experimentally that several instances of the aforementioned three matching problems can indeed be solved satisfactorily using the proposed affine registration algorithm.

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“…The geometric moment invariants were first proposed by Hu [6] and revised by Reiss [7]. Several other types of moment invariants have been proposed [8].…”

Section: Introductionmentioning

confidence: 99%

Hidden Markov models with spectral features for 2D shape recognition

Cai

Liu

2001

IEEE Trans. Pattern Anal. Machine Intell.

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AbstractÐIn this paper, we present a technique using Markov models with spectral features for recognizing 2D shapes. We will analyze the properties of Fourier spectral features derived from closed contours of 2D shapes and use these features for 2D pattern recognition. We develop algorithms for reestimating parameters of hidden Markov models. To demonstrate the effectiveness of our models, we have tested our methods on two image databases: hand-tools and unconstrained handwritten numerals. We are able to achieve high recognition rates of 99.4 percent and 96.7 percent without rejection on these two sets of image data, respectively.

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The revised fundamental theorem of moment invariants

Cited by 215 publications

References 18 publications

Retrieving geometric distortion properties from image moments

Retrieving geometric distortion properties from image moments

Higher-Dimensional Affine Registration and Vision Applications

Hidden Markov models with spectral features for 2D shape recognition

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