Shape normalization through compacting

Leu, Jia-Guu

doi:10.1016/0167-8655(89)90095-0

Cited by 45 publications

(18 citation statements)

References 5 publications

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“…The first two steps, centering and reshaping, are together referred to as "compacting" or "shape normalization" in the pattern recognition community. Readers are referred to [6], [11], and [27] for details. As shown in [11], the "compacting" process results in a 2-D affine invariant that is continuous, easy to compute, and robust to digitization errors.…”

Section: Blaisermentioning

confidence: 99%

“…This invariant shape can then be used as template in detection or classification problems or in image database searches. Invariant features of 2-D shapes under affine transformations have been studied in image processing and computer vision applications such as pattern recognition [23], [27], [28]. Good 2-D affine invariants are complete, easy to compute, stable under small distortions, and continuous.…”

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confidence: 99%

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Affine-permutation invariance of 2-D shapes

Moura

2005

IEEE Trans. on Image Process.

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Abstract-Shapes provide a rich set of clues on the identity and topological properties of an object. In many imaging environments, however, the same object appears to have different shapes due to distortions such as translation, rotation, reflection, scaling, or skewing. Further, the order by which the object's feature points are scanned changes, i.e., the order of the pixels may be permuted. Relating two-dimensional shapes of the same object distorted by different affine and permutation transformations is a challenge. We introduce a shape invariant that we refer to as the intrinsic shape of an object and describe an algorithm, BLAISER, to recover it. The intrinsic shape is invariant to affine-permutation distortions. It is a uniquely defined representative of the equivalence class of all affine-permutation distortions of the same object. BLAISER computes the intrinsic shape from any arbitrarily affine-permutation distorted image of the object, without prior knowledge regarding the distortions or the undistorted shape of the object. The critical step of BLAISER is the determination of the shape orientation and we provide a detailed discussion on this topic. The operations of BLAISER are based on low-order moments of the input shape and, thus, robust to error and noise. Examples illustrate the performance of the algorithm.Index Terms-Affine-permutation invariance, blind algorithm for intrinsic shape recovery, fold number, intrinsic shape, orbits, orientation indicator index (OII), point-based reorientation algorithm (PRA), shape invariance, shape space.

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Section: Blaisermentioning

confidence: 99%

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confidence: 99%

Affine-permutation invariance of 2-D shapes

Moura

2005

IEEE Trans. on Image Process.

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“…Image Normalization can achieve scaling and translation invariance. Image normalization techniques have been used for invariant pattern recognition (Leu, 1989).…”

Section: Introductionmentioning

confidence: 99%

Invariant Image Watermarking Using Accurate Zernike Moments

Ismail¹,

Shouman²,

Hosny³

et al. 2010

Journal of Computer Science

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problem statement: Digital image watermarking is the most popular method for image authentication, copyright protection and content description. Zernike moments are the most widely used moments in image processing and pattern recognition. The magnitudes of Zernike moments are rotation invariant so they can be used just as a watermark signal or be further modified to carry embedded data. The computed Zernike moments in Cartesian coordinate are not accurate due to geometrical and numerical error. Approach: In this study, we employed a robust image-watermarking algorithm using accurate Zernike moments. These moments are computed in polar coordinate, where both approximation and geometric errors are removed. Accurate Zernike moments are used in image watermarking and proved to be robust against different kind of geometric attacks. The performance of the proposed algorithm is evaluated using standard images. Results: Experimental results show that, accurate Zernike moments achieve higher degree of robustness than those approximated ones against rotation, scaling, flipping, JPEG compression and affine transformation. Conclusion: By computing accurate Zernike moments, the embedded bits watermark can be extracted at low error rate.

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“…This is what we do with the X-OII that we introduce next. The X-OII provides additional degrees of freedom in choosing the moments and is very useful in resolving, for example, reflection-symmetric shapes: either an individual moment can be used to generate the corresponding X-OII plot, or a few related moments can be combined to create a new measure of orientation as has been done in (1) and (5).…”

Section: Extended Oiimentioning

confidence: 99%

“…For the normalized or compact shapes [5], the first and second order shape moments are normalized to m 10 = m 01 = 0, m 20 = m 02 = 1, and m 11 = 0. Hence, when computing the OII in (1) for these compact shapes, the lowest order moments we are left to work with are the third order moments: m 21 , m 12 , m 30 , and m 03 .…”

Section: Extended Oiimentioning

confidence: 99%

Robust Reorientation of 2D Shapes Using the Orientation Indicator Index

Moura²

Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005.

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Shape reorientation is a critical step in many image processing and computer vision applications such as registration, detection, identification, and classification. Shape reorientation is a needed step to restore the correct orientation of a shape when its image is subject to an arbitrary rotation and reflection. In this paper, we present a robust method to determine the standard "normalized" orientation of twodimensional (2D) shapes in a blind manner, i.e., without any other information other than the given input shape. We introduce a set of orientation indicator indices (OII) that use low order central moments of the shape to monitor the orientational characteristics of the shape. Because these OII's use only low (up to third) order moments, they are robust to noise and errors. We show with examples how we bring consistently a given shape with an unknown arbitrary orientation to its standard normalized orientation using the OII.

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Shape normalization through compacting

Cited by 45 publications

References 5 publications

Affine-permutation invariance of 2-D shapes

Affine-permutation invariance of 2-D shapes

Invariant Image Watermarking Using Accurate Zernike Moments

Robust Reorientation of 2D Shapes Using the Orientation Indicator Index

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