One-sided Radial-Fundamental Matrix Estimation

For modern consumer cameras often approximate calibration data is available, making applications such as 3D reconstruction or photo registration easier as compared to the pure uncalibrated setting. In this paper we address the setting with calibrateduncalibrated image pairs: for one image intrinsic parameters are assumed to be known, whereas the second view has unknown distortion and calibration parameters. This situation arises e.g. when one would like to register archive imagery to recently taken photos. A commonly adopted strategy for determining epipolar geometry is based on feature matching and minimal solvers inside a RANSAC framework. However, only very few existing solutions apply to the calibrated-uncalibrated setting. We propose a simple and numerically stable two-step scheme to first estimate radial distortion parameters and subsequently the focal length using novel solvers. We demonstrate the performance on synthetic and real datasets.

Error bounds for low-rank approximations of the first exponential integral kernel

A hierarchical matrix is an efficient data-sparse representation of a matrix, especially useful for large dimensional problems. It consists of low-rank subblocks leading to low memory requirements as well as inexpensive computational costs. In this work, we discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. The operator is of convolution type, it is defined through the first exponential-integral function and, hence, it is weakly singular. We develop analytical expressions for the approximate degenerate kernels and deduce error upper bounds for these approximations. Some computational results illustrating the efficiency and robustness of the approach are presented.

Automated image analysis of lung branching morphogenesis from microscopic images of fetal rat explants

Background: Regulating mechanisms of branching morphogenesis of fetal lung rat explants have been an essential tool for molecular research. This work presents a new methodology to accurately quantify the epithelial, outer contour and peripheral airway buds of lung explants during cellular development from microscopic images. Methods: The outer contour was defined using an adaptive and multi-scale threshold algorithm whose level was automatically calculated based on an entropy maximization criterion. The inner lung epithelial was defined by a clustering procedure that groups small image regions according to the minimum description length principle and local statistical properties. Finally, the number of peripheral buds were counted as the skeleton branched ends from a skeletonized image of the lung inner epithelial. Results: The time for lung branching morphometric analysis was reduced in 98% in contrast to the manual method. Best results were obtained in the first two days of cellular development, with lesser standard deviations. Non-significant differences were found between the automatic and manual results in all culture days. Conclusions: The proposed method introduces a series of advantages related to its intuitive use and accuracy, making the technique suitable to images with different lightning characteristics and allowing a reliable comparison between different researchers.

Automated image analysis of lung branching morphogenesis

Regulating mechanisms of branchingmorphogenesis of fetal lung rat explants have been an essential tool formolecular research.This work presents a new methodology to accurately quantify the epithelial, outer contour, and peripheral airway buds of lung explants during cellular development frommicroscopic images. Methods.Theouter contour was defined using an adaptive and multiscale threshold algorithm whose level was automatically calculated based on an entropy maximization criterion. The inner lung epithelium was defined by a clustering procedure that groups small image regions according to the minimum description length principle and local statistical properties. Finally, the number of peripheral buds was counted as the skeleton branched ends from a skeletonized image of the lung inner epithelia. Results. The time for lung branching morphometric analysis was reduced in 98% in contrast to themanualmethod. Best results were obtained in the first two days of cellular development, with lesser standard deviations. Nonsignificant differences were found between the automatic and manual results in all culture days. Conclusions. The proposed method introduces a series of advantages related to its intuitive use and accuracy, making the technique suitable to images with different lighting characteristics and allowing a reliable comparison between different researchers.