Tomáš Suk

Pattern recognition by affine moment invariants

Abstract The paper deals with moment invariants, which are invariant under general affine transformation and may be used for recognition of affine-deformed objects. Our approach is based on the theory of algebraic invariants. The invariants from second- and third-order moments are derived and shown to be complete. The paper is a significant extension and generalization of recent works. Several numerical experiments dealing with pattern recognition by means of the affine moment invariants as the features are described.

Degraded image analysis: an invariant approach

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.

Rotation Moment Invariants for Recognition of Symmetric Objects

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

Affine moment invariants: a new tool for character recognition

Abstract Affine moment invariants (AMIs) have been derived recently by Flusser and Suk (1992). In this paper, the AMIs are used as the features for recognition of handwritten characters independent of their size, slant and other variations. A comparison with classical moment invariants is also given.

Recognition of blurred images by the method of moments

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.

Combined blur and affine moment invariants and their use in pattern recognition

Abstract The paper is devoted to the recognition of objects and patterns deformed by imaging geometry as well as by unknown blurring. We introduce a new class of features invariant simultaneously to blurring with a centrosymmetric PSF and to affine transformation. As we prove in the paper, they can be constructed by combining affine moment invariants and blur invariants derived earlier. Combined invariants allow to recognize objects in the degraded scene without any restoration.

Image features invariant with respect to blur

Abstract The paper is devoted to the feature-based description of blurred images acquired by a linear shift-invariant imaging system. The proposed features are invariant with respect to blur (this means with respect to the system point spread function), are based on image moments and are calculated directly from the blurred image. This way, we are able to describe the original image without the PSF identification and image restoration. In many applications (such as in image recognition from a database) our approach is much more effective than the traditional “blind-restoration” one. The derivation of the blur invariants is the major theoretical result of the paper. Several experiments are presented to illustrate the efficiency of the invariants for blurred image description. Stability of the invariants with respect to additive random noise and boundary effect is also discussed and is shown to be sufficiently high.

Graph method for generating affine moment invariants

A general method of systematic derivation of affine moment invariants of any weights and orders is introduced. Each invariant is expressed by its generating graph. Techniques for elimination of reducible invariants and dependent invariants are discussed. This approach is illustrated on the set of all affine moment invariants up to the weight ten.

Affine moment invariants generated by graph method

The paper presents a general method of an automatic deriving affine moment invariants of any weights and orders. The method is based on representation of the invariants by graphs. We propose an algorithm for eliminating reducible and dependent invariants. This method represents a systematic approach to the generation of all relevant moment features for recognition of affinely distorted objects. We also show the difference between pseudoinvariants and true invariants.

Invariant-based registration of rotated and blurred images

Image registration is a classical problem in remotely sensed image analysis. In this paper, attention is paid to control point matching for the case when the images are blurred and rotated compared to one another. The matching is performed by means of a new class of moment invariants, which are calculated over the neighborhood of each candidate. The proposed invariants are invariant not only to rotation and translation but also to image blurring by any symmetric point spread function. Thanks to this, the authors can register blurred images directly without any de-blurring.