Continuous Image Representations Avoid the Histogram Binning Problem in Mutual Information Based Image Registration

Abstract

Mutual information (MI) based image-registration methods that use histograms are known to suffer from the so-called binning problem, caused by the absence of a principled technique for choosing the "optimal" number of bins to calculate the joint or marginal distributions. In this paper, we show that foregoing the notion of an image as a set of discrete pixel locations, and adopting a continuous representation is the solution to this problem. A new technique to calculate joint image histograms is proposed, which makes use of such a continuous representation. We report results on affine registration of a pair of 2D medical images under high noise, and demonstrate the smoothness of various information-theoretic similarity measures such as joint entropy (JE) or MI w.r.t. the transformation, when our proposed technique (referred to as the "robust histogram") is adopted to compute the required probability distributions.

Probability Density Estimation Using Isocontours and Isosurfaces: Applications to Information-Theoretic Image Registration

“…For each combination of bin count and noise, a brute-force search was performed so as to optimally align the synthetically rotated noisy image with the original one, as determined by finding the maximum of MI or NMI between the two images. Six different techniques were used for MI estimation: simple histograms with bilinear interpolation for image warping (referred to as “Simple Hist”),our proposed method using isocontours (referred to as “Isocontours”),histogramming with PVI (referred to as “PVI”),histogramming with cubic spline interpolation (referred to as “Cubic”),the method 2DPointProb proposed in [23], andsimple histogramming with 10 6 samples taken from subpixel locations uniformly randomly followed by usual binning (referred to as “Hist Samples”). These experiments were repeated for 30 noise trials at each noise standard deviation. For each method, the mean and the variance of the error (absolute difference between the predicted alignment and the ground-truth alignment) was measured (Fig.…”

“…This method, which was presented by us earlier in [23], is a biased estimator that does not assume a uniform distribution on location. In this technique, the total number of cooccurrences of intensities α 1 and α 2 from the two images, respectively, is obtained by counting the total number of intersections of the corresponding level curves.…”

“…In our work, we have also presented a detailed derivation for the joint density between two or more images and also extended the work to the 3D case, besides testing it thoroughly on affine image registration for varying noise levels and quantization widths. Prior work on image registration using such image-based techniques includes [24], [23], [10], and [14]. The work in [10], however, reports results only on template matching with translations, whereas the main focus of [14] is on the estimation of densities in vanishingly small circular neighborhoods.…”

Improving accuracy and efficiency of mutual information for multi-modal retinal image registration using adaptive probability density estimation

“…This approach accounts for absent intensity variations between a pixel and its neighbour, as before, aiming to reduce the artefacts introduces by pixel discretization. Rajwade proposed a similar idea [38] that interpolates the image to an infinite resolution. This approach could be seen as histogram interpolation, whereby we could scale the histogram by a given factor and then scale back to the original size.…”

A Combined Technique for Detecting Objects in Multimodal Images of Paintings

“…A size of the neighborhood and a number of grayscale levels are chosen in order to: (a) satisfy conditions (4)-(5); (b) correctly estimate probability mass functions; (c) provide reasonable precision of difference localization. Probability mass functions are estimated using the joint histogram of the image pair (Rajwade, 2006).…”