George A. Papakostas

A new class of Zernike moments for computer vision applications

A Modified Direct Method for the computation of the Zernike moments is presented in this paper. The presence of many factorial terms, in the direct method for computing the Zernike moments, makes their computation process a very time consuming task. Although the computational power of the modern computers is impressively increasing, the calculation of the factorial of a big number is still an inaccurate numerical procedure. The main concept of the present paper is that, by using Stirlings Approximation formula for the factorial and by applying some suitable mathematical properties, a novel, factorial-free direct method can be developed. The resulted moments are not equal to those computed by the original direct method, but they are a sufficiently accurate approximation of them. Besides, their variability does not affect their ability to describe uniquely and distinguish the objects they represent. This is verified by pattern recognition simulation examples.

Fuzzy Cognitive Maps for Pattern Recognition Applications

A first attempt to incorporate Fuzzy Cognitive Maps (FCMs), in pattern classification applications is performed in this paper. Fuzzy Cognitive Maps, as an illustrative causative representation of modeling and manipulation of complex systems, can be used to model the behavior of any system. By transforming a pattern classification problem into a problem of discovering the way the sets of patterns interact with each other and with the classes that they belong to, we could describe the problem in terms of Fuzzy Cognitive Maps. More precisely, some FCM architectures are introduced and studied with respect to their pattern recognition abilities. An efficient novel hybrid classifier is proposed as an alternative classification structure, which exploits both neural networks and FCMs to ensure improved classification capabilities. Appropriate experiments with four well-known benchmark classification problems and a typical computer vision application establish the usefulness of the Fuzzy Cognitive Maps, in a pattern recognition research field. Moreover, the present paper introduces the use of more flexible FCMs by incorporating nodes with adaptively adjusted activation functions. This advanced feature gives more degrees of freedom in the FCM structure to learn and store knowledge, as needed in pattern recognition tasks.

Novel moment invariants for improved classification performance in computer vision applications

A novel set of moment invariants based on the Krawtchouk moments are introduced in this paper. These moment invariants are computed over a finite number of image intensity slices, extracted by applying an innovative image representation scheme, the image slice representation (ISR) method. Based on this technique an image is decomposed to a several non-overlapped intensity slices, which can be considered as binary slices of certain intensity. This image representation gives the advantage to accelerate the computation of images moments since the image can be described in a number of homogenous rectangular blocks, which permits the simplification of the computation formulas. The moments computed over the extracted slices seem to be more efficient than the corresponding moments of the same order that describe the whole image, in recognizing the pattern under processing. The proposed moment invariants are exhaustively tested in several well known computer vision datasets, regarding their rotation, scaling and translation (RST) invariant recognition performance, by resulting to remarkable outcomes.

Moment-based local binary patterns: A novel descriptor for invariant pattern recognition applications

A novel descriptor able to improve the classification capabilities of a typical pattern recognition system is proposed in this paper. The introduced descriptor is derived by incorporating two efficient region descriptors, namely image moments and local binary patterns (LBP), commonly used in pattern recognition applications, in the last decades. The main idea behind this novel feature extraction methodology is the need of improved recognition capabilities, a goal achieved by the combinative use of these descriptors. This collaboration aims to make use of the major advantages each one presents, by simultaneously complementing each other, in order to elevate their weak points. In this way, the useful properties of the moments and moment invariants regarding their robustness to the noise presence, their global information coding mechanism and their invariant behaviour under scaling, translation and rotation conditions, along with the local nature of the LBP, are combined in a single concrete methodology. As a result a novel descriptor invariant to common geometric transformations of the described object, capable to encode its local characteristics, is formed and its classification capabilities are investigated through massive experimental scenarios. The experiments have shown the superiority of the introduced descriptor over the moment invariants, the LBP operator and other well-known from the literature descriptors such as HOG, HOG-LBP and LBP-HF.

A unified methodology for the efficient computation of discrete orthogonal image moments

A novel methodology is proposed in this paper to accelerate the computation of discrete orthogonal image moments. The computation scheme is mainly based on a new image representation method, the image slice representation (ISR) method, according to which an image can be expressed as the outcome of an appropriate combination of several non-overlapped intensity slices. This image representation decomposes an image into a number of binary slices of the same size whose pixels come in two intensities, black or any other gray-level value. Therefore the image block representation can be effectively applied to describe the image in a more compact way. Once the image is partitioned into intensity blocks, the computation of the image moments can be accelerated, as the moments can be computed by using decoupled computation forms. The proposed algorithm constitutes a unified methodology that can be applied to any discrete moment family in the same way and produces similar promising results, as has been concluded through a detailed experimental investigation.

Numerical error analysis in Zernike moments computation

Abstract An exact analysis of the numerical errors being generated during the computation of the Zernike moments, by using the well-known ‘q-recursive’ method, is attempted in this paper. Overflow is one kind of error, which may occur when one needs to calculate the Zernike moments up to a high order. Moreover, by applying a novel methodology it is shown that there are specific formulas, which generate and propagate ‘finite precision error’. This finite precision error is accumulated during execution of the algorithm, and it finally ‘destroys’ the algorithm, in the sense that eventually makes its results totally unreliable. The knowledge of the exact computation errors and the way that they are generated and propagated is a fundamental step for developing more robust error-free recursive algorithms, for the computation of Zernike moments.

Towards Hebbian learning of Fuzzy Cognitive Maps in pattern classification problems

A detailed comparative analysis of the Hebbian-like learning algorithms applied to train Fuzzy Cognitive Maps (FCMs) operating as pattern classifiers, is presented in this paper. These algorithms aim to find appropriate weights between the concepts of the FCM classifier so it equilibrates to a desired state (class mapping). For these purposes, six different types of Hebbian learning algorithms from the literature have been selected and studied in this work. Along with the theoretical description of these algorithms and the analysis of their performance in classifying known patterns, a sensitivity analysis of the applied classification scheme, regarding some configuration parameters have taken place. It is worth noting that the algorithms are studied in a comparative fashion, under common configurations for several benchmark pattern classification datasets, by resulting to useful conclusions about their training capabilities.

Pattern classification by using improved wavelet Compressed Zernike Moments

In this paper, an improved Feature Extraction Method (FEM), which selects discriminative feature sets able to lead to high classification rates in pattern recognition tasks, is presented. The resulted features are the wavelet coefficients of an improved compressed signal, consisting of the Zernike moments amplitudes. By applying a straightforward methodology, it is aimed to construct optimal feature vectors in the sense of vector dimensionality and information content for classification purposes. The resulting surrogate feature vector is of lower dimensionality than the original Zernike moment feature vector and thus more appropriate for pattern recognition tasks. Appropriate validation tests have been arranged, in order to investigate the performance of the proposed algorithm by measuring the discriminative power of the new feature vectors despite the information loss.

A Unified Methodology for Computing Accurate Quaternion Color Moments and Moment Invariants

In this paper, a general framework for computing accurate quaternion color moments and their corresponding invariants is proposed. The proposed unified scheme arose by studying the characteristics of different orthogonal polynomials. These polynomials are used as kernels in order to form moments, the invariants of which can easily be derived. The resulted scheme permits the usage of any polynomial-like kernel in a unified and consistent way. The resulted moments and moment invariants demonstrate robustness to noisy conditions and high discriminative power. Additionally, in the case of continuous moments, accurate computations take place to avoid approximation errors. Based on this general methodology, the quaternion Tchebichef, Krawtchouk, Dual Hahn, Legendre, orthogonal Fourier-Mellin, pseudo Zernike and Zernike color moments, and their corresponding invariants are introduced. A selected paradigm presents the reconstruction capability of each moment family, whereas proper classification scenarios evaluate the performance of color moment invariants.

Adaptive color image watermarking by the use of quaternion image moments

Abstract The first adaptive moment-based color image watermarking is presented in this work. The proposed method exploits rotation invariance, high reconstruction capability and computation accuracy of the quaternion radial moments’ (QRMs), subject to the tradeoff between robustness and imperceptibility. The current system manages to multi-embed binary logos to color images applying QRMs as information carriers. A novel adaptive system adjusts the watermark’s embedding strength (online) by taking into account image’s morphology, with respect to robustness and imperceptibility. The method manages to experimentally justify and further eliminate the attack-free phenomenon that state-of-the-art methods suffer. The simulation results justified that the proposed framework manages to highly secure its carrying information under common signal processing and geometric attacking conditions. Furthermore, the adoption of the novel adaptive process enhances the robustness and imperceptibility requirements by reducing the Bit Error Rate even by 49% and producing even 5db higher PSNR values, respectively.