Image Registration

The problem of image registration is described and steps involved in registering various types of images are given. The chapter also covers the history of image registration and its evolution during the past century.

The topics of similarity and dissimilarity measures are discussed in detail. The chapter starts with definitions of similarity and dissimilarity measures and lists the requirements for them to be metrics. In addition to the existing similarity and dissimilarity measures, 3 new similarity measures and 1 new dissimilarity measure are introduced. The performances of 16 similarity measures and 10 dissimilarity measures in image matching are determined and compared, and their sensitivities to noise and blurring as well as to intensity and geometric changes are also determined and compared. The similarity measures tested are Pearson correlation, Tanimoto measure, stochastic sign change, deterministic sign change, minimum ratio, Spearman’s ρ, Kendall’s τ, greatest deviation, ordinal measure, correlation ratio, energy of joint probability density, material similarity, Shannon mutual information, Rényi mutual information, Tsallis mutual information, and I _α information. The dissimilarity measures tested are L ₁ norm, median of absolute differences, square L ₂ norm, median of square differences, normalized square L ₂ norm, incremental sign distance, intensity-ratio variance, intensity-mapping-ratio variance, rank distance, joint entropy, and exclusive F-information.

The principles behind various point detectors are discussed, steps to implement them are given, and the repeatability, positional accuracy, and speed of a number of popular point detectors are determined and compared. In addition, their sensitivities to noise, blurring, and intensity and geometric changes are measured and compared. Correlation-based, edge-based, model-based, uniqueness-based, curvature-based, Laplacian-based, gradient-based, Hough transform-based, symmetry-based, intensity-based, filtering-based, transform domain-based, pattern recognition-based, moments-based, and entropy-based detectors are discussed. Also discussed are new point detectors formulated in terms of invariant moments, filter responses, image intensities, and other image properties.

This chapter discusses various image features used in image matching. The features measure statistical, geometric, algebraic, spatial, differential, color, fractal, information-theoretic, and other image properties. Overall, 122 image features are described and 47 of them are compared for accuracy and speed, as well as for sensitivity to noise, blurring, and intensity and geometric changes. In addition, dependency of the features on template or image size are examined and compared.

Image descriptors represent homogeneous features in an image or sub-image. The principles behind histogram-based, spin image-based, filtering-based, and moment-based descriptors are reviewed, and strategies to efficiently compute them are given. In addition, means to combine homogeneous descriptors to composite descriptors are described, and methods to determine the similarity or dissimilarity between the descriptors are outlined. Also discussed in this chapter are determination of global scale and rotational differences between two images by the scale-invariant feature transform (SIFT) and log-polar mapping.

While the focus in Chap. 5 was on descriptors that were made up of homogeneous features, the focus in this chapter is on descriptors that are composed of features of different types. Heterogeneous descriptors are created from a combination of various types of features as described in Chap. 4. The features are selected in such a way that the combined feature set delivers the most information about an image or sub-image. Also discussed in this chapter are various feature-selection methods that choose the optimal or suboptimal feature set from a large number of features. Both filter and wrapper feature selection algorithms are discussed, including max-min, sequential forward selection, sequential backward selection, plus l take away r, and branch and bound algorithms.

Various point pattern matching algorithms are reviewed and compared. Among the matching algorithms discussed are random sample and consensus (RANSAC), graph-based, feature-based, clustering-based, invariance-based, axis of minimum inertia-based, relaxation-based, and spectral graph theory-based algorithms. To speed up the matching process, the coarse-to-fine search strategy is also discussed and its use in matching of point patterns with nonlinear geometric differences is demonstrated. Also included in this chapter are detailed matching algorithms and methods to determine their performances.

The problem of robust parameter estimation in image registration is discussed and various robust methods for estimating registration parameters under outliers and inaccurate correspondences are reviewed and compared. After reviewing ordinary least-squares and weighted least-squares estimation, robust estimators such as maximum likelihood (M), repeated median (RM), scale (S), least median of squares (LMS), least trimmed square (LTS), and rank (R) estimators are described and compared.

The problem of image warping or image transformation for the purpose of aligning/overlaying images is discussed. First, global transformations, such as rigid, similarity, affine, projective, cylindrical, and spherical mapping are reviewed. Then, adaptive transformations including explicit, implicit, and parametric functions are reviewed. Properties of various transformations are explored and a guide to their selection is provided. Finally, performances of ten popular adaptive transformation functions in the registration of various types of images are determined and compared. The transformations tested are multiquadric, thin-plate (surface) spline, compactly supported radial basis functions, local weighted mean, moving least squares, piecewise linear, Loop’s subdivision, parametric Shepard, weighted linear, and interpolating implicit methods.

Image resampling, image compositing, and image mosaicking are discussed. Among the discussed resampling methods are nearest-neighbor, bilinear interpolation, cubic convolution, cubic spline, and compactly supported methods. After describing the principle behind each method, the computational complexities of the methods are determined and compared. Also included in this chapter are topics of image compositing and mosaicking. A new intensity blending method to produce seamless image composites from images with intensity differences is introduced.

While Chaps. 2–10 discussed tools used in the design of various components of an image registration system, this chapter discusses methods to design complete image registration systems for various applications. Among the image registration methods discussed are principal-axis, multi-resolution, optimization-based, boundary-based, model-based, and adaptive methods. While evaluation of various components of an image registration system were discussed in Chaps. 2–10, methods to evaluate full image registration systems are discussed in this chapter.