Bivariate Gamma Distributions for Image Registration and Change Detection

This paper evaluates the potential interest of using bivariate gamma distributions for image registration and change detection. The first part of this paper studies estimators for the parameters of bivariate gamma distributions based on the maximum likelihood principle and the method of moments. The performance of both methods are compared in terms of estimated mean square errors and theoretical asymptotic variances. The mutual information is a classical similarity measure which can be used for image registration or change detection. The second part of the paper studies some properties of the mutual information for bivariate Gamma distributions. Image registration and change detection techniques based on bivariate gamma distributions are finally investigated. Simulation results conducted on synthetic and real data are very encouraging. Bivariate gamma distributions are good candidates allowing us to develop new image registration algorithms and new change detectors

An Appearance-Based Method for Parametric Video Registration

In this paper we address the problem of multi frame video registration using the combination of an appearance-based technique and a parametric model of the transformations. This technique uses an image that is selected as reference frame, and therefore, estimates the transformation that occurred to each frame in the sequence respect to this absolute referenced one. Both global and local information are employed to the estimation of these registered images. Global information is applied in terms of linear appearance subspace constraints, under the subspace constancy assumption [4], where variabilities of each frame respect to the reference frame are encoded. Local information is used by means of a polynomial parametric model that estimates the velocities field evoluton in each frame. The objective function to be minimized considers both issues at the same time, i.e., the appearance representation and the time evolution across the sequence. This function is the connection between the global coordinates in the subspace representation and the time evolution and the parametric optical flow estimates. Thus, the appearance constraints result to take into account al the images in a sequence in order to estimate the transformation parameters

Estimation under group actions: recovering orbits from invariants

Motivated by geometric problems in signal processing, computer vision, and structural biology, we study a class of orbit recovery problems where we observe very noisy copies of an unknown signal, each acted upon by a random element of some group (such as Z/p or SO(3)). The goal is to recover the orbit of the signal under the group action in the high-noise regime. This generalizes problems of interest such as multi-reference alignment (MRA) and the reconstruction problem in cryo-electron microscopy (cryo-EM). We obtain matching lower and upper bounds on the sample complexity of these problems in high generality, showing that the statistical difficulty is intricately determined by the invariant theory of the underlying symmetry group. In particular, we determine that for cryo-EM with noise variance $\sigma^2$ and uniform viewing directions, the number of samples required scales as $\sigma^6$. We match this bound with a novel algorithm for ab initio reconstruction in cryo-EM, based on invariant features of degree at most 3. We further discuss how to recover multiple molecular structures from heterogeneous cryo-EM samples.Comment: 54 pages. This version contains a number of new result

Image registration and visualization of in situ gene expression images.

In the age of high-throughput molecular biology techniques, scientists have incorporated the methodology of in-situ hybridization to map spatial patterns of gene expression. In order to compare expression patterns within a common tissue structure, these images need to be registered or organized into a common coordinate system for alignment to a reference or atlas images. We use three different image registration methodologies (manual; correlation based; mutual information based) to determine the common coordinate system for the reference and in-situ hybridization images. All three methodologies are incorporated into a Matlab tool to visualize the results in a user friendly way and save them for future work. Our results suggest that the user-defined landmark method is best when considering images from different modalities; automated landmark detection is best when the images are expected to have a high degree of consistency; and the mutual information methodology is useful when the images are from the same modality

Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates

The study of cerebral anatomy in developing neonates is of great importance for the understanding of brain development during the early period of life. This dissertation therefore focuses on three challenges in the modelling of cerebral anatomy in neonates during brain development. The methods that have been developed all use Magnetic Resonance Images (MRI) as source data. To facilitate study of vascular development in the neonatal period, a set of image analysis algorithms are developed to automatically extract and model cerebral vessel trees. The whole process consists of cerebral vessel tracking from automatically placed seed points, vessel tree generation, and vasculature registration and matching. These algorithms have been tested on clinical Time-of- Flight (TOF) MR angiographic datasets. To facilitate study of the neonatal cortex a complete cerebral cortex segmentation and reconstruction pipeline has been developed. Segmentation of the neonatal cortex is not effectively done by existing algorithms designed for the adult brain because the contrast between grey and white matter is reversed. This causes pixels containing tissue mixtures to be incorrectly labelled by conventional methods. The neonatal cortical segmentation method that has been developed is based on a novel expectation-maximization (EM) method with explicit correction for mislabelled partial volume voxels. Based on the resulting cortical segmentation, an implicit surface evolution technique is adopted for the reconstruction of the cortex in neonates. The performance of the method is investigated by performing a detailed landmark study. To facilitate study of cortical development, a cortical surface registration algorithm for aligning the cortical surface is developed. The method first inflates extracted cortical surfaces and then performs a non-rigid surface registration using free-form deformations (FFDs) to remove residual alignment. Validation experiments using data labelled by an expert observer demonstrate that the method can capture local changes and follow the growth of specific sulcus

Superresolution Enhancement of Hyperspectral CHRIS/Proba Images With a Thin-Plate Spline Nonrigid Transform Model

Given the hyperspectral-oriented waveband configuration of multiangular CHRIS/Proba imagery, the scope of its application could widen if the present 18-m resolution would be improved. The multiangular images of CHRIS could be used as input for superresolution (SR) image reconstruction. A critical procedure in SR is an accurate registration of the low-resolution images. Conventional methods based on affine transformation may not be effective given the local geometric distortion in high off-nadir angular images. This paper examines the use of a non-rigid transform to improve the result of a nonuniform interpolation and deconvolution SR method. A scale-invariant feature transform is used to collect control points (CPs). To ensure the quality of CPs, a rigorous screening procedure is designed: 1) an ambiguity test; 2) the m-estimator sample consensus method; and 3) an iterative method using statistical characteristics of the distribution of random errors. A thin-plate spline (TPS) nonrigid transform is then used for the registration. The proposed registration method is examined with a Delaunay triangulation-based nonuniform interpolation and reconstruction SR method. Our results show that the TPS nonrigid transform allows accurate registration of angular images. SR results obtained from simulated LR images are evaluated using three quantitative measures, namely, relative mean-square error, structural similarity, and edge stability. Compared to the SR methods that use an affine transform, our proposed method performs better with all three evaluation measures. With a higher level of spatial detail, SR-enhanced CHRIS images might be more effective than the original data in various applications.JRC.H.7-Climate Risk Managemen