Affine Point Pattern Matching

Voss, Klaus; Suesse, Herbert

doi:10.1007/3-540-45404-7_21

Cited by 8 publications

(6 citation statements)

References 8 publications

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“…Broadly speaking, the existing algorithms can be categorized into three groups: invariant-based methods, e.g. [23][24][25][26], optimization-based methods, e.g. [5,27,10,6,12,21,28,11] and spectral matching methods, e.g.…”

Section: Related Workmentioning

confidence: 99%

On affine registration of planar point sets using complex numbers

Yang

2011

Computer Vision and Image Understanding

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a b s t r a c tWe propose a novel algorithm for affine registration of 2D point sets. The main idea is to treat the 2D points as complex numbers and from each point set, a polynomial with complex coefficients can be computed whose roots are the points in the given point set. The two-step algorithm first reduces the affine registration problem to a rigid registration problem, and the unknown rotation is then computed using the coefficients of these polynomials. The algorithm is entirely algebraic with clear underlying geometric motivation. The implementation is straightforward and it takes less than a second to compute the affine transformation for point sets containing hundreds of points. We validate the algorithm on a variety of synthetic 2D point sets as well as point sets extracted from real-world images.Published by Elsevier Inc.

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Section: Related Workmentioning

confidence: 99%

On affine registration of planar point sets using complex numbers

Yang

2011

Computer Vision and Image Understanding

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“…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. Recently, [25] proposed a set of affine moment descriptors that use complex moments in the definition, and the resulting descriptors can be converted to affine moment invariants.…”

Section: Previous Workmentioning

confidence: 99%

“…Given the point sets IP; Q Q, their respective normalized discrete linear moments m p ; m q are given as [50], [27] …”

Section: Orthogonal Reductionmentioning

confidence: 99%

“…In this paper, 1 we study the more classical problem of matching point sets related by affine transforms. The novel viewpoint taken here is the emphasis on affine registrations in IR m for 4 m 12, and this differs substantially from the past literature on this subject, which has been overwhelmingly devoted to registration problems in IR 2 and IR 3 , e.g., [28], [42], [43], [47], [50].…”

Section: Introductionmentioning

confidence: 98%

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Higher Dimensional Affine Registration and Vision Applications

Chi

Shahed

et al. 2008

Lecture Notes in Computer Science

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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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“…As discrimination can be increased by adding higher order even moment invariants, several four-order moment invariants were tested. However, only the so-called φ 11 (Voss et al, 2001) produces a good separation between clusters (see Flusser, 2000 for constructing moment invariants). The first three and the eleventh Hu's moments are independent and given by:…”

Section: Feature Extraction and Analysis Of Bacillimentioning

confidence: 99%

Automatic identification of Mycobacterium tuberculosis by Gaussian mixture models

Forero

Cristóbal²,

Desco

2006

Journal of Microscopy

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Summary Tuberculosis and other kinds of mycobacteriosis are serious illnesses for which early diagnosis is critical for disease control. Sputum sample analysis is a common manual technique employed for bacillus detection but current sample‐analysis techniques are time‐consuming, very tedious, subject to poor specificity and require highly trained personnel. Image‐processing and pattern‐recognition techniques are appropriate tools for improving the manual screening of samples. Here we present a new technique for sputum image analysis that combines invariant shape features and chromatic channel thresholding. Some feature descriptors were extracted from an edited bacillus data set to characterize their shape. They were statistically represented by using a Gaussian mixture model representation and a minimal error Bayesian classification procedure was employed for the last identification stage. This technique constitutes a step towards automating the process and providing a high specificity.

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Affine Point Pattern Matching

Cited by 8 publications

References 8 publications

On affine registration of planar point sets using complex numbers

On affine registration of planar point sets using complex numbers

Higher Dimensional Affine Registration and Vision Applications

Automatic identification of Mycobacterium tuberculosis by Gaussian mixture models

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