Learning landmark geodesics using the ensemble Kalman filter

<p style='text-indent:20px;'>We study the problem of diffeomorphometric geodesic landmark matching where the objective is to find a diffeomorphism that, via its group action, maps between two sets of landmarks. It is well-known that the motion of the landmarks, and thereby the diffeomorphism, can be encoded by an initial momentum leading to a formulation where the landmark matching problem can be solved as an optimisation problem over such momenta. The novelty of our work lies in the application of a derivative-free Bayesian inverse method for learning the optimal momentum encoding the diffeomorphic mapping between the template and the target. The method we apply is the ensemble Kalman filter, an extension of the Kalman filter to nonlinear operators. We describe an efficient implementation of the algorithm and show several numerical results for various target shapes.</p>

A LANDMARK MATCHING ALGORITHM FOR THE GEOSTATIONARY SATELLITE IMAGES BASED ON MULTI-LEVEL GRIDS

The resolution of geostationary satellite image is not high and the image is covered with clouds. At present, when the extracted feature points are unstable, there are some problems, such as low matching accuracy or even matching failure. In this paper, a landmark matching algorithm is proposed to directly establish the multi-level grids for the image coastline and the coastline template. Through the similarity measure of the multi-level grids, the landmark matching is realized layer by layer. First of all, we've finished cloud detection, establishment of landmark data set, and extraction of image coastline. Then we design and implement the landmark matching algorithm based on multi-level grids. Finally, through analysis from different levels of landmarks and different proportion of cloud cover, the advantages and applicable conditions of this algorithm are given. The experimental results show that: 1) with the increase of cloud cover, the correct rate of landmark matching decreases, but the decrease is small. It shows that the matching algorithm in this paper is stable. Correct matching rate could always be stable at about 75 percent in the fourth level. 2) when the proportion of cloud cover is less than 20 percent, the higher the matching level, the higher the matching accuracy. When the cloud cover is more than 20 percent, the matching accuracy in the fourth level is the highest. This algorithm provides a stable method for the landmark matching of geostationary satellite image.

Planar morphometrics using Teichmüller maps

Inspired by the question of quantifying wing shape, we propose a computational approach for analysing planar shapes. We first establish a correspondence between the boundaries of two planar shapes with boundary landmarks using geometric functional data analysis and then compute a landmark-matching curvature-guided Teichmüller mapping with uniform quasi-conformal distortion in the bulk. This allows us to analyse the pair-wise difference between the planar shapes and construct a similarity matrix on which we deploy methods from network analysis to cluster shapes. We deploy our method to study a variety of Drosophila wings across species to highlight the phenotypic variation between them, and Lepidoptera wings over time to study the developmental progression of wings. Our approach of combining complex analysis, computation and statistics to quantify, compare and classify planar shapes may be usefully deployed in other biological and physical systems.

Multimodal Image Alignment via Linear Mapping between Feature Modalities

We propose a novel landmark matching based method for aligning multimodal images, which is accomplished uniquely by resolving a linear mapping between different feature modalities. This linear mapping results in a new measurement on similarity of images captured from different modalities. In addition, our method simultaneously solves this linear mapping and the landmark correspondences by minimizing a convex quadratic function. Our method can estimate complex image relationship between different modalities and nonlinear nonrigid spatial transformations even in the presence of heavy noise, as shown in our experiments carried out by using a variety of image modalities.