Vector fields are a special kind of multidimensional data, which are in a certain sense similar to digital color images, but are distinct from them in several aspects. In each pixel, the field is assigned to a vector that shows the direction and the magnitude of the quantity, which has been measured. To detect the patterns of interest in the field, special matching methods must be developed. In this paper, we propose a method for the description and matching of vector field patterns under an unknown affine transformation of the field. Unlike digital images, transformations of vector fields act not only on the spatial coordinates but also on the field values, which makes the detection different from the image case. To measure the similarity between the template and the field patch, we propose original invariants with respect to total affine transformation. They are designed from the vector field moments. It is demonstrated by experiments on real data from fluid mechanics that they perform significantly better than potential competitors.

Vector field (VF) is a special kind of multidimensional data. In each pixel, VF contains information about the direction and the magnitude of the measured quantity. To detect the patterns of interest in the field, special matching methods must be developed. We propose a method for the description and matching of VF patterns under an unknown affine transformation of the field. Unlike digital images, transformations of VFs act not only on the spatial coordinates but also on the field values, which makes the detection different. To measure the similarity between the template and the field patch, we propose original invariants with respect to affine transformation designed from moments. Their performance is demonstrated by experiments on real data from fluid mechanics.

We present new approach to study of behavior of the solar atmosphere. In actual fact it is processing of plasma parameters obtained from remote satellite observations. In this study we focused on physical data characterizing the so-called solar wind. Ever-present dynamic magnetic field affects other physical variables such as speed, temperature, density, etc. in the solar atmosphere. The turning points of the magnetic induction magnitude and direction time curves are computed. They serve as estimates of the beginning and end shockwave in solar wind and also as boundaries of segments for statistical analysis of magnetic field variables by Kendall rank correlation.

We propose a method for the recognition of vector field patterns under an unknown rotation. The rotation is modeled as a total transformation, which is applied on both spatial coordinates and field values. The invariants are constructed from orthogonal Gaussian-Hermite moments. Their numerical stability and recognition power are shown to be better than those of the invariants published so far.

We propose methodology for the analysis of active regions on the Sun. It is based on high-order statistical moments of image histogram, particularly on its skewness. The methodology includes a new technique to select regions with possible formation of the flare. We track these areas in the time video sequences to search for triggers - turning point(s), when the pre-flare phase changes to the full developed event. The frequency analysis in the flare formation areas is based on Fourier analysis, Morlet wavelets, and principal component analysis. Results have been evaluated to achieve the periods of oscillations stimulating the flare origin.

In this paper, we propose a new theory of invariants to Gaussian blur. We introduce a notion of a primordial image as a canonical form of all Gaussian blur-equivalent images. The primordial image is defined in spectral domain by means of projection operators. We prove that the moments of the primordial image are invariant to Gaussian blur and we derive recursive formulas for their direct computation without actually constructing the primordial image itself. We show how to extend their invariance also to image rotation. The application of these invariants is in blur-invariant image comparison and recognition. In the experimental part, we perform an exhaustive comparison with two main competitors: 1) the Zhang distance and 2) the local phase quantization.

In this paper we introduce a new theory of blur invariants. Blur invariants are image features which preserve their values if the image is convolved by a point-spread function (PSF) of a certain class. We present the invariants to convolution with an arbitrary N-fold symmetric PSF, both in Fourier and image domain. We introduce a notion of a primordial image as a canonical form of all blur-equivalent images. It is defined in spectral domain by means of projection operators. We prove that the moments of the primordial image are invariant to blur and we derive recursive formulae for their direct computation without actually constructing the primordial image. We further prove they form a complete set of invariants and show how to extent their invariance also to translation, rotation and scaling. We illustrate by simulated and real-data experiments their invariance and recognition power. Potential applications of this method are wherever one wants to recognize objects on blurred images.

Steerability is a useful and important property of "kernel" functions. It enables certain complicated operations involving orientation manipulation on images to be executed with high efficiency. Thus, we focus our attention on the steerability of Hermite polynomials and their versions modulated by the Gaussian function with different powers, defined as the Hermite kernel. Certain special cases of such kernel, Hermite polynomials, Hermite functions and Gaussian derivatives are discussed in detail. Correspondingly, these cases demonstrate that the Hermite kernel is a powerful and effective tool for image processing. Furthermore, the steerability of the Hermite kernel is proved with the help of a property of Hermite polynomials revealing the rule concerning the product of two Hermite polynomials after coordination rotation. Consequently, any order of the Hermite kernel inherits steerability. Moreover, a couple sets of an explicit interpolation function and basis function can be directly obtained. We provide some examples to verify steerability of the Hermite kernel. Experimental results show the effectiveness of steerability and its potential applications in the fields of image processing and computer vision.

A new method of moment computation based on decomposition of the object into rectangular blocks is presented. The decomposition is accomplished by means of distance transform. The method is compared with earlier morphological methods, namely with erosion decomposition to squares. All the methods are also compared with direct computation by definition.

Pattern recognition of objects on affinely distorted images based on moments is important task researched for many years. Affinemoment invariants are significant tool for it. They can be generated by a few methods. Automated direct solution of the Cayley - Aronhold differential equation has not been referred yet. It makes possible to generate invariants with much higher weights than other methods, but we must pay more attention to the numerical stability of the computation. The method is demonstrated on examples.

In this paper, a new set of moment invariants with respect to rotation, translation, and scaling suitable for recognition of objects having N-fold rotation symmetry are presented. Moment invariants described earlier cannot be used for this purpose because most moments of symmetric objects vanish. The invariants proposed here are based on complex moments. Their independence and completeness are proven theoretically and their performance is demonstrated by experiments.

The paper is devoted to the moment invariants with respect to projective transform. It has been a common belief that such invariants do not exist. We show that projective moment invariants exist in a form of infinite series containing moments with positive as well as negative indices.

We present a multichannel blind deconvolution method based on so-called subspace technique that was originally proposed by Harikumar and Bresler (1996, 1999). When at least two differently degraded images (channels) of the original scene are provided, the method is better conditioned than classical single channel ones. In comparison with earlier multichannel blind deconvolution techniques the subspace method is not iterative and this possibly implies an implementation that can be computationally more efficient. An application of the proposed method to the restoration of the images of sunspots is presented.

Analysis and interpretation of an image which was acquired by a nonideal imaging system is the key problem in many application areas. The observed image is usually corrupted by blurring, spatial degradations, and random noise. Classical methods like blind deconvolution try to estimate the blur parameters and to restore the image. We propose an alternative approach. We derive the features for image representation which are invariant with respect to blur regardless of the degradation PSF provided that it is centrally symmetric. As we prove in the paper, there exist two classes of such features: the first one in the spatial domain and the second one in the frequency domain. We also derive so-called combined invariants, which are invariant to composite geometric and blur degradations. Knowing these features, we can recognize objects in the degraded scene without any restoration.

The paper is devoted to the feature-based recognition of degraded signals acquired by a linear time-invariant system The proposed approach consists of describing signals by features which are invariant with respect to the degradation and recognizing signals in the feature space. Neither impulse response identification nor signal restoration are required. Thanks to this, the new approach is in many applications much more effective than the classical one based on blind deconvolution. Two sets of appropriate blur-invariant features (the first one in time domain, the other one in spectral domain) are introduced in this paper. The proof of their invariance is given and their performance is illustrated by numerical experiments.

The article is devoted to the feature-based recognition of blurred images acquired by a linear shift-invariant imaging system against an image database. The proposed approach consists of describing images by features that are invariant with respect to blur and recognizing images in the feature space. The PSF identification and image restoration are not required. A set of symmetric blur invariants based on image moments is introduced. A numerical experiment is presented to illustrate the utilization of the invariants for blurred image recognition. Robustness of the features is also briefly discussed.

The paper deals with features of a point set which are invariant with respect to the projective transform. First, some properties of the area of a triangle under a projective transform and the cross-ratio are discussed. Two types of projective triangular invariants of point sets are derived. One of them is a quotient of two different products of the areas of triangles formed by the vertices of the polygon. It is invariant to the labeling of the vertices. The number of the features is discussed and a method for its reduction is presented. The other type of features is expressed as functions of a five-point cross-ratios and it is invariant to the choice of labeling of the points. The possibility of the normalization of these invariants is shown. The performance of the features is demonstrated by numerical experiments.

A new method is described for automatic control point selection and matching. First, reference and sensed images are segmented and closed-boundary regions are extracted. Each region is represented by a set of affine-invariant moment-based features. Correspondence between the regions is then established by a two-stage matching algorithm that works both in the feature space and in the image space. Centers of gravity of corresponding regions are used as control points. A practical use of the proposed method is demonstrated by registration of SPOT and Landsat TM images. It is shown that the authors' method can produce subpixel registration accuracy.>