Self-Calibration of Cameras with Euclidean Image Plane in Case of Two Views and Known Relative Rotation Angle

The internal calibration of a pinhole camera is given by five parameters that are combined into an upper-triangular $3\times 3$ calibration matrix. If the skew parameter is zero and the aspect ratio is equal to one, then the camera is said to have Euclidean image plane. In this paper, we propose a non-iterative self-calibration algorithm for a camera with Euclidean image plane in case the remaining three internal parameters --- the focal length and the principal point coordinates --- are fixed but unknown. The algorithm requires a set of $N \geq 7$ point correspondences in two views and also the measured relative rotation angle between the views. We show that the problem generically has six solutions (including complex ones). The algorithm has been implemented and tested both on synthetic data and on publicly available real dataset. The experiments demonstrate that the method is correct, numerically stable and robust.Comment: 13 pages, 7 eps-figure

A pp-adic RanSaC algorithm for stereo vision using Hensel lifting

A $p$-adic variation of the Ran(dom) Sa(mple) C(onsensus) method for solving the relative pose problem in stereo vision is developped. From two 2-adically encoded images a random sample of five pairs of corresponding points is taken, and the equations for the essential matrix are solved by lifting solutions modulo 2 to the 2-adic integers. A recently devised $p$-adic hierarchical classification algorithm imitating the known LBG quantisation method classifies the solutions for all the samples after having determined the number of clusters using the known intra-inter validity of clusterings. In the successful case, a cluster ranking will determine the cluster containing a 2-adic approximation to the "true" solution of the problem.Comment: 15 pages; typos removed, abstract changed, computation error remove

A New Solution to the Relative Orientation Problem using only 3 Points and the Vertical Direction

This paper presents a new method to recover the relative pose between two images, using three points and the vertical direction information. The vertical direction can be determined in two ways: 1- using direct physical measurement like IMU (inertial measurement unit), 2- using vertical vanishing point. This knowledge of the vertical direction solves 2 unknowns among the 3 parameters of the relative rotation, so that only 3 homologous points are requested to position a couple of images. Rewriting the coplanarity equations leads to a simpler solution. The remaining unknowns resolution is performed by an algebraic method using Grobner bases. The elements necessary to build a specific algebraic solver are given in this paper, allowing for a real-time implementation. The results on real and synthetic data show the efficiency of this method

Binomial Mitotic Segregation of MYCN-Carrying Double Minutes in Neuroblastoma Illustrates the Role of Randomness in Oncogene Amplification

BACKGROUND: Amplification of the oncogene MYCN in double minutes (DMs) is a common finding in neuroblastoma (NB). Because DMs lack centromeric sequences it has been unclear how NB cells retain and amplify extrachromosomal MYCN copies during tumour development. PRINCIPAL FINDINGS: We show that MYCN-carrying DMs in NB cells translocate from the nuclear interior to the periphery of the condensing chromatin at transition from interphase to prophase and are preferentially located adjacent to the telomere repeat sequences of the chromosomes throughout cell division. However, DM segregation was not affected by disruption of the telosome nucleoprotein complex and DMs readily migrated from human to murine chromatin in human/mouse cell hybrids, indicating that they do not bind to specific positional elements in human chromosomes. Scoring DM copy-numbers in ana/telophase cells revealed that DM segregation could be closely approximated by a binomial random distribution. Colony-forming assay demonstrated a strong growth-advantage for NB cells with high DM (MYCN) copy-numbers, compared to NB cells with lower copy-numbers. In fact, the overall distribution of DMs in growing NB cell populations could be readily reproduced by a mathematical model assuming binomial segregation at cell division combined with a proliferative advantage for cells with high DM copy-numbers. CONCLUSION: Binomial segregation at cell division explains the high degree of MYCN copy-number variability in NB. Our findings also provide a proof-of-principle for oncogene amplification through creation of genetic diversity by random events followed by Darwinian selection

Cryptic terminal chromosome rearrangements in colorectal carcinoma cell lines detected by subtelomeric FISH analysis.

Epithelial tumour karyotypes are often difficult to study by standard cytogenetic methods because of poor chromosome preparation quality and the high complexity of their genomic rearrangements. Subtelomeric fluorescence in situ hybridisation (FISH) has proved to be a useful method for detecting cryptic constitutional chromosomal rearrangements but little is known about its usefulness for tumour cytogenetic analysis. Using a combination of chromosome banding, multicolour karyotyping and subtelomeric FISH, five colorectal cancer cell lines were characterised. The resulting data were compared to results from previous studies by comparative genomic hybridisation and spectral karyotyping or multicolour FISH. Subtelomeric FISH made it possible to resolve several highly complex chromosome rearrangements, many of which had not been detected or were incompletely characterised by the other methods. In particular, previously undetected terminal imbalances were found in the two cell lines not showing microsatellite instability. Copyright (c) 2006 S. Karger AG, Base

Exploiting Mutual Camera Visibility in Multi-camera Motion Estimation

This paper addresses the estimation of camera motion and 3D reconstruction from image sequences for multiple independently moving cameras. If multiple moving cameras record the same scene, a camera is often visible in another camera's field of view. This poses a constraint on the position of the observed camera, which can be included into the conjoined optimization process. The paper contains the following contributions: Firstly, a fully automatic detection and tracking algorithm for the position of a moving camera in the image sequence of another moving camera is presented. Secondly, a sparse bundle adjustment algorithm is introduced, which includes this additional constraint on the position of the tracked camera. Since the additional constraints minimize the geometric error at the boundary of the reconstructed volume, the total reconstruction accuracy can be improved significantly. Experiments with synthetic and challenging real world scenes show the improved performance of our fully automatic method

Automatic Generator of Minimal Problem Solvers

Finding solutions to minimal problems for estimating epipolar geometry and camera motion leads to solving systems of algebraic equations. Often, these systems are not trivial and therefore special algorithms have to be designed to achieve numerical robustness and computational efficiency. The state of the art approach for constructing such algorithms is the Gröbner basis method for solving systems of polynomial equations. Previously, the Gröbner basis solvers were designed ad hoc for concrete problems and they could not be easily applied to new problems. In this paper we propose an automatic procedure for generating Gröbner basis solvers which could be used even by non-experts to solve technical problems. The input to our solver generator is a system of polynomial equations with a finite number of solutions. The output of our solver generator is the Matlab or C code which computes solutions to this system for concrete coefficients. Generating solvers automatically opens possibilities to solve more complicated problems which could not be handled manually or solving existing problems in a better and more efficient way. We demonstrate that our automatic generator constructs efficient and numerically stable solvers which are comparable or outperform known manually constructed solvers. The automatic generator is available a