Efficient Rotation-Scaling-Translation Parameters Estimation Based on Fractal Image Model

TL;DR

This paper introduces a fractal image model-based maximum likelihood estimator for rotation, scaling, and translation parameters in subpixel image registration, outperforming existing methods especially with textures fitting the model assumptions.

Contribution

The paper proposes the MLfBm estimator leveraging fractal modeling for improved accuracy in geometric transformation estimation in image registration.

Findings

Reduces estimation errors by a factor of 1.75 to 2

Decreases false match probability up to 5 times

Provides confidence intervals based on Cramer-Rao bounds

Abstract

This paper deals with area-based subpixel image registration under rotation-isometric scaling-translation transformation hypothesis. Our approach is based on a parametrical modeling of geometrically transformed textural image fragments and maximum likelihood estimation of transformation vector between them. Due to the parametrical approach based on the fractional Brownian motion modeling of the local fragments texture, the proposed estimator MLfBm (ML stands for "Maximum Likelihood" and fBm for "Fractal Brownian motion") has the ability to better adapt to real image texture content compared to other methods relying on universal similarity measures like mutual information or normalized correlation. The main benefits are observed when assumptions underlying the fBm model are fully satisfied, e.g. for isotropic normally distributed textures with stationary increments. Experiments on both simulated and real images and for high and weak correlation between registered images show that the MLfBm estimator offers significant improvement compared to other state-of-the-art methods. It reduces translation vector, rotation angle and scaling factor estimation errors by a factor of about 1.75...2 and it decreases probability of false match by up to 5 times. Besides, an accurate confidence interval for MLfBm estimates can be obtained from the Cramer-Rao lower bound on rotation-scaling-translation parameters estimation error. This bound depends on texture roughness, noise level in reference and template images, correlation between these images and geometrical transformation parameters.