This paper focuses on the optimal weighting of the components of a rotation invariant feature vector. This feature descriptor is not expected to be outstanding in performance, it is published here to illustrate the mathematics of the tuning problem. Theoretical tools are used to find proper distance functions. It is assumed, that the resulting error is properly expressed as the sum of squared p...

Large Deformation Diffeomorphic Metric Mapping (LDDMM) is a widely used deformable registration algorithm for computing smooth invertible maps between various types of anatomical shapes such as landmarks, curves, surfaces or images. In this work, we specifically focus on the case of images and adopt an optimal control point of view so as to extend the original LDDMM with Sum of Squared Differen...

In a masterfully written (in german language) thirty pages long paper (and published in 1828 in Crelle’s Journal ) A. F. Möbius studied some properties of the polynomial equations for the circumradius of arbitrary cyclic polygons (convex and nonconvex) and produced a polynomial of degree δn = n2 ( n−1 b(n−1)/2c )− 2n−2 that relates the square of a circumradius (r) of a cyclic polygon to the squ...

We show that the sum of squared differences, commonly used as a dissimilarity measure in variational methods is biased towards high gradients and large intensity differences, and that it can affect drastically the quality of motion estimation techniques such as deformable registration. We propose a method which solves that problem by recalling that the Euler-Lagrange equation of the dissimilari...

Registration of longitudinally acquired 3D ultrasound (US) images plays an important role in monitoring and quantifying progression/regression of carotid atherosclerosis. We introduce an image-based non-rigid registration algorithm to align the baseline 3D carotid US with longitudinal images acquired over several follow-up time points. This algorithm minimizes the sum of absolute intensity diff...

We derive new bounds on the total squared correlation (TSC) of quaternary (quadriphase) signature/sequence sets for all lengths L and set sizes K. Then, for all K,L, we design minimum-TSC optimal sets that meet the new bounds with equality. Direct numerical comparison with the TSC value of the recently obtained optimal binary sets shows under what K,L realizations gains are materialized by movi...

We report an experimental study of diffusion in a quasi-one-dimensional (q1D) colloid suspension which behaves like a Tonks gas. The mean squared displacement as a function of time is described well with an ansatz encompassing a time regime that is both shorter and longer than the mean time between collisions. The ansatz asserts that the inverse mean squared displacement is the sum of the inver...

A model-based windowed chi-squared procedure is proposed for identifying falsified sensor measurements. We employ the widely-used static chi-squared and the dynamic cumulative sum (CUSUM) fault/attack detection procedures as benchmarks to compare the performance of the windowed chisquared detector. In particular, we characterize the state degradation that a class of attacks can induce to the sy...

This paper aims at evaluating multi-camera configurations as a function of the descriptive parameters of complex biological objects. Multi-baseline Stereo has potential to handle projective distortion at large baselines. Being close to the observed object and the orientation of object surfaces pointing toward the camera increase the projection distortion. An example is 3D reconstruction of plan...