Robust curvature extrema detection based on new numerical derivation

International audienceExtrema of curvature are useful key points for different image analysis tasks. Indeed, polygonal approximation or arc decomposition methods used often these points to initialize or to improve their algorithms. Several shape-based image retrieval methods focus also their descriptors on key points. This paper is focused on the detection of extrema of curvature points for a raster-to-vector-conversion framework. We propose an original adaptation of an approach used into nonlinear control for fault-diagnosis and fault-tolerant control based on algebraic derivation and which is robust to noise. The experimental results are promising and show the robustness of the approach when the contours are bathed into a high level speckled noise

Probabilistic Solutions to Differential Equations and their Application to Riemannian Statistics

We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Such methods have concrete value in the statistics on Riemannian manifolds, where non-analytic ordinary differential equations are involved in virtually all computations. The probabilistic formulation permits marginalising the uncertainty of the numerical solution such that statistics are less sensitive to inaccuracies. This leads to new Riemannian algorithms for mean value computations and principal geodesic analysis. Marginalisation also means results can be less precise than point estimates, enabling a noticeable speed-up over the state of the art. Our approach is an argument for a wider point that uncertainty caused by numerical calculations should be tracked throughout the pipeline of machine learning algorithms.Comment: 11 page (9 page conference paper, plus supplements

Active skeleton for bacteria modeling

The investigation of spatio-temporal dynamics of bacterial cells and their molecular components requires automated image analysis tools to track cell shape properties and molecular component locations inside the cells. In the study of bacteria aging, the molecular components of interest are protein aggregates accumulated near bacteria boundaries. This particular location makes very ambiguous the correspondence between aggregates and cells, since computing accurately bacteria boundaries in phase-contrast time-lapse imaging is a challenging task. This paper proposes an active skeleton formulation for bacteria modeling which provides several advantages: an easy computation of shape properties (perimeter, length, thickness, orientation), an improved boundary accuracy in noisy images, and a natural bacteria-centered coordinate system that permits the intrinsic location of molecular components inside the cell. Starting from an initial skeleton estimate, the medial axis of the bacterium is obtained by minimizing an energy function which incorporates bacteria shape constraints. Experimental results on biological images and comparative evaluation of the performances validate the proposed approach for modeling cigar-shaped bacteria like Escherichia coli. The Image-J plugin of the proposed method can be found online at http://fluobactracker.inrialpes.fr.Comment: Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging and Visualizationto appear i

Topological Navigation of Simulated Robots using Occupancy Grid

Formerly I presented a metric navigation method in the Webots mobile robot simulator. The navigating Khepera-like robot builds an occupancy grid of the environment and explores the square-shaped room around with a value iteration algorithm. Now I created a topological navigation procedure based on the occupancy grid process. The extension by a skeletonization algorithm results a graph of important places and the connecting routes among them. I also show the significant time profit gained during the process

Euler Characteristic Curves and Profiles: a stable shape invariant for big data problems

Tools of Topological Data Analysis provide stable summaries encapsulating the shape of the considered data. Persistent homology, the most standard and well studied data summary, suffers a number of limitations; its computations are hard to distribute, it is hard to generalize to multifiltrations and is computationally prohibitive for big data-sets. In this paper we study the concept of Euler Characteristics Curves, for one parameter filtrations and Euler Characteristic Profiles, for multi-parameter filtrations. While being a weaker invariant in one dimension, we show that Euler Characteristic based approaches do not possess some handicaps of persistent homology; we show efficient algorithms to compute them in a distributed way, their generalization to multifiltrations and practical applicability for big data problems. In addition we show that the Euler Curves and Profiles enjoys certain type of stability which makes them robust tool in data analysis. Lastly, to show their practical applicability, multiple use-cases are considered.Comment: 32 pages, 19 figures. Added remark on multicritical filtrations in section 4, typos correcte

AUTOMATED DETECTION AND VECTORIZATION OF ROAD ELEMENTS IN HIGH RESOLUTION ORTHOGRAPHIC IMAGES

This paper proposes, describes, and applies an algorithm for the automatic detection of selected elements of road infrastructure, along with the option to determine their spatial information. The principle is based on the evaluation of the color spectrum of the selected object on orthographic images. As a source image used for the processing, output from low-altitude aerial photogrammetry or terrestrial laser scanning can be used, together with the option to implement digital elevation models into the processing. The approach is based on the detection of the color composition of the selected element of the road, followed by clustering of the identified elements within the image and mathematical transformation of the clusters into a spatial vector form. Prior to the processing, the target objects are filtered out based on user input, for which vectorization is performed. The outputs are in the form of contours or the determined basic structure of the object. The main difference compared to existing methods is that the vectorization is only performed on the selected, pre-filtered parts of the raster image with identified target objects, not the whole image. This approach makes it possible to effectively and automatically identify and analyze, e.g., the edge of the road, road markings, or road features. This enables the subsequent implementation of the identified outputs into more complex spatial models of the road or its proximity. Additionally, the processing of the data to create a digital model of the environment can be automated, with a significant saving of time and related costs

New Confocal Hyperbola-based Ellipse Fitting with Applications to Estimating Parameters of Mechanical Pipes from Point Clouds

This manuscript presents a new method for fitting ellipses to two-dimensional data using the confocal hyperbola approximation to the geometric distance of points to ellipses. The proposed method was evaluated and compared to established methods on simulated and real-world datasets. First, it was revealed that the confocal hyperbola distance considerably outperforms other distance approximations such as algebraic and Sampson. Next, the proposed ellipse fitting method was compared with five reliable and established methods proposed by Halir, Taubin, Kanatani, Ahn and Szpak. The performance of each method as a function of rotation, aspect ratio, noise, and arc-length were examined. It was observed that the proposed ellipse fitting method achieved almost identical results (and in some cases better) than the gold standard geometric method of Ahn and outperformed the remaining methods in all simulation experiments. Finally, the proposed method outperformed the considered ellipse fitting methods in estimating the geometric parameters of cylindrical mechanical pipes from point clouds. The results of the experiments show that the confocal hyperbola is an excellent approximation to the true geometric distance and produces reliable and accurate ellipse fitting in practical settings