Jan Flusser

Image registration methods: a survey

This paper aims to present a review of recent as well as classic image registration methods. Image registration is the process of overlaying images (two or more) of the same scene taken at different times, from different viewpoints, and/or by different sensors. The registration geometrically align two images (the reference and sensed images). The reviewed approaches are classified according to their nature (areabased and feature-based) and according to four basic steps of image registration procedure: feature detection, feature matching, mapping function design, and image transformation and resampling. Main contributions, advantages, and drawbacks of the methods are mentioned in the paper. Problematic issues of image registration and outlook for the future research are discussed too. The major goal of the paper is to provide a comprehensive reference source for the researchers involved in image registration, regardless of particular application areas. q 2003 Elsevier B.V. All rights reserved.

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.

On the independence of rotation moment invariants

Abstract The problem of the independence and completeness of rotation moment invariants is addressed in this paper. First, a general method for constructing invariants of arbitrary orders by means of complex moments is described. As a major contribution of the paper, it is shown that for any set of invariants there exists a relatively small basis by means of which all other invariants can be generated. The method how to construct such a basis and how to prove its independence and completeness is presented. Some practical impacts of the new results are mentioned at the end of the paper.

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.

Multichannel blind iterative image restoration

Blind image deconvolution is required in many applications of microscopy imaging, remote sensing, and astronomical imaging. Unfortunately in a single-channel framework, serious conceptual and numerical problems are often encountered. Very recently, an eigenvector-based method (EVAM) was proposed for a multichannel framework which determines perfectly convolution masks in a noise-free environment if channel disparity, called co-primeness, is satisfied. We propose a novel iterative algorithm based on recent anisotropic denoising techniques of total variation and a Mumford-Shah functional with the EVAM restoration condition included. A linearization scheme of half-quadratic regularization together with a cell-centered finite difference discretization scheme is used in the algorithm and provides a unified approach to the solution of total variation or Mumford-Shah. The algorithm performs well even on very noisy images and does not require an exact estimation of mask orders. We demonstrate capabilities of the algorithm on synthetic data. Finally, the algorithm is applied to defocused images taken with a digital camera and to data from astronomical ground-based observations of the Sun.

Image representation via a finite Radon transform

A model of finite Radon transforms composed of Radon projections is presented. The model generalizes to finite group projections in the classical Radon transform theory. The Radon projector averages a function on a group over cosets of a subgroup. Reconstruction formulae that were formally similar to the convolved backprojection ones are derived, and an iterative reconstruction technique is found to converge after a finite number of steps. Applying these results to the group Z/sub 2//sup P/, new computationally favorable image representations have been obtained. A numerical study of the transform coding aspects is attached. >

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

A new wavelet-based measure of image focus

We present a new measure of image focus. It is based on wavelet transform of the image and is defined as a ratio of high-pass band and low-pass band norms. We show this measure is monotonic with respect to the degree of defocusation and sufficiently robust. We experimentally illustrate its performance on simulated as well as real data and compare it with existing focus measures (gray-level variance and energy of Laplacian). Finally, an application of the new measure in astronomical imaging is shown.

Multichannel blind deconvolution of spatially misaligned images

Existing multichannel blind restoration techniques assume perfect spatial alignment of channels, correct estimation of blur size, and are prone to noise. We developed an alternating minimization scheme based on a maximum a posteriori estimation with a priori distribution of blurs derived from the multichannel framework and a priori distribution of original images defined by the variational integral. This stochastic approach enables us to recover the blurs and the original image from channels severely corrupted by noise. We observe that the exact knowledge of the blur size is not necessary, and we prove that translation misregistration up to a certain extent can be automatically removed in the restoration process.

Moment forms invariant to rotation and blur in arbitrary number of dimensions

We present the construction of combined blur and rotation moment invariants in arbitrary number of dimensions. Moment invariants to convolution with an arbitrary centrosymmetric filter are derived first, and then their rotationally invariant forms are found by means of group representation theory to achieve the desired combined invariance. Several examples of the invariants are calculated explicitly to illustrate the proposed procedure. Their invariance, robustness, and capability of using in template matching and in image registration are demonstrated on 3D MRI data and 2D indoor images.