Color Image Analysis by Quaternion-Type Moments

International audienceIn this paper, by using the quaternion algebra, the conventional complex-type moments (CTMs) for gray-scale images are generalized to color images as quaternion-type moments (QTMs) in a holistic manner. We first provide a general formula of QTMs from which we derive a set of quaternion-valued QTM invariants (QTMIs) to image rotation, scale and translation transformations by eliminating the influence of transformation parameters. An efficient computation algorithm is also proposed so as to reduce computational complexity. The performance of the proposed QTMs and QTMIs are evaluated considering several application frameworks ranging from color image reconstruction, face recognition to image registration. We show they achieve better performance than CTMs and CTM invariants (CTMIs). We also discuss the choice of the unit pure quaternion influence with the help of experiments. appears to be an optimal choice

Image analysis using visual saliency with applications in hazmat sign detection and recognition

Visual saliency is the perceptual process that makes attractive objects stand out from their surroundings in the low-level human visual system. Visual saliency has been modeled as a preprocessing step of the human visual system for selecting the important visual information from a scene. We investigate bottom-up visual saliency using spectral analysis approaches. We present separate and composite model families that generalize existing frequency domain visual saliency models. We propose several frequency domain visual saliency models to generate saliency maps using new spectrum processing methods and an entropy-based saliency map selection approach. A group of saliency map candidates are then obtained by inverse transform. A final saliency map is selected among the candidates by minimizing the entropy of the saliency map candidates. The proposed models based on the separate and composite model families are also extended to various color spaces. We develop an evaluation tool for benchmarking visual saliency models. Experimental results show that the proposed models are more accurate and efficient than most state-of-the-art visual saliency models in predicting eye fixation.^ We use the above visual saliency models to detect the location of hazardous material (hazmat) signs in complex scenes. We develop a hazmat sign location detection and content recognition system using visual saliency. Saliency maps are employed to extract salient regions that are likely to contain hazmat sign candidates and then use a Fourier descriptor based contour matching method to locate the border of hazmat signs in these regions. This visual saliency based approach is able to increase the accuracy of sign location detection, reduce the number of false positive objects, and speed up the overall image analysis process. We also propose a color recognition method to interpret the color inside the detected hazmat sign. Experimental results show that our proposed hazmat sign location detection method is capable of detecting and recognizing projective distorted, blurred, and shaded hazmat signs at various distances.^ In other work we investigate error concealment for scalable video coding (SVC). When video compressed with SVC is transmitted over loss-prone networks, the decompressed video can suffer severe visual degradation across multiple frames. In order to enhance the visual quality, we propose an inter-layer error concealment method using motion vector averaging and slice interleaving to deal with burst packet losses and error propagation. Experimental results show that the proposed error concealment methods outperform two existing methods

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-like Transforms

We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions--the B-spline factorization theorem. In particular, starting from well-localized scaling functions, we construct HT pairs of biorthogonal wavelet bases of L^2(R) by relating the corresponding wavelet filters via a discrete form of the continuous HT filter. As a concrete application of this methodology, we identify HT pairs of spline wavelets of a specific flavor, which are then combined to realize a family of complex wavelets that resemble the optimally-localized Gabor function for sufficiently large orders. Analytic wavelets, derived from the complexification of HT wavelet pairs, exhibit a one-sided spectrum. Based on the tensor-product of such analytic wavelets, and, in effect, by appropriately combining four separable biorthogonal wavelet bases of L^2(R^2), we then discuss a methodology for constructing 2D directional-selective complex wavelets. In particular, analogous to the HT correspondence between the components of the 1D counterpart, we relate the real and imaginary components of these complex wavelets using a multi-dimensional extension of the HT--the directional HT. Next, we construct a family of complex spline wavelets that resemble the directional Gabor functions proposed by Daugman. Finally, we present an efficient FFT-based filterbank algorithm for implementing the associated complex wavelet transform.Comment: 36 pages, 8 figure

Quaternion Matrices : Statistical Properties and Applications to Signal Processing and Wavelets

Similarly to how complex numbers provide a possible framework for extending scalar signal processing techniques to 2-channel signals, the 4-dimensional hypercomplex algebra of quaternions can be used to represent signals with 3 or 4 components. For a quaternion random vector to be suited for quaternion linear processing, it must be (second-order) proper. We consider the likelihood ratio test (LRT) for propriety, and compute the exact distribution for statistics of Box type, which include this LRT. Various approximate distributions are compared. The Wishart distribution of a quaternion sample covariance matrix is derived from first principles. Quaternions are isomorphic to an algebra of structured 4x4 real matrices. This mapping is our main tool, and suggests considering more general real matrix problems as a way of investigating quaternion linear algorithms. A quaternion vector autoregressive (VAR) time-series model is equivalent to a structured real VAR model. We show that generalised least squares (and Gaussian maximum likelihood) estimation of the parameters reduces to ordinary least squares, but only if the innovations are proper. A LRT is suggested to simultaneously test for quaternion structure in the regression coefficients and innovation covariance. Matrix-valued wavelets (MVWs) are generalised (multi)wavelets for vector-valued signals. Quaternion wavelets are equivalent to structured MVWs. Taking into account orthogonal similarity, all MVWs can be constructed from non-trivial MVWs. We show that there are no non-scalar non-trivial MVWs with short support [0,3]. Through symbolic computation we construct the families of shortest non-trivial 2x2 Daubechies MVWs and quaternion Daubechies wavelets.Open Acces