Motion from point matches : multiplicity of solutions

In this paper, we study the multiplicity of solutions of the motion problem. Given n point matches between two frames, how many solutions are there to the motion problem ? We show that the maximum number of solutions is 10 when 5 point matches are available. This settles a question which has been around in the computer vision community for a while. We follow two tracks. The first one attempts to recover the motion parameters by studying the essential matrix and has been followed by a number of researchers in the field. A natural extension of this is to use algebraic geometry to characterize the set of possible essential matrices. We present some new results based on this approach. The second one, based on projective geometry, dates from the previous century. We show that the two approaches are compatible and yield the same result. We then describe a computer implementation of the second approach that uses Maple, a language for symbolic computation. The program allows us to compute exactly the solutions for any configuration of 5 points. Some experiments are described

Hierarchical aesthetic quality assessment using deep convolutional neural networks

Aesthetic image analysis has attracted much attention in recent years. However, assessing the aesthetic quality and assigning an aesthetic score are challenging problems. In this paper, we propose a novel framework for assessing the aesthetic quality of images. Firstly, we divide the images into three categories: “scene”, “object” and “texture”. Each category has an associated convolutional neural network (CNN) which learns the aesthetic features for the category in question. The object CNN is trained using the whole images and a salient region in each image. The texture CNN is trained using small regions in the original images. Furthermore, an A & C CNN is developed to simultaneously assess the aesthetic quality and identify the category for overall images. For each CNN, classification and regression models are developed separately to predict aesthetic class (high or low) and to assign an aesthetic score. Experimental results on a recently published large-scale dataset show that the proposed method can outperform the state-of-the-art methods for each category

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When the geometry of 3D space is reconstructed from a pair of views, using the "Fundamental matrix" as the object of analysis, then it is known (as early as the 1940s) that there exists a "critical surface" for which the solution of 3-space is ambiguous. We show that when 3-space is reconstructed from a triplet of views, using the "Trilinear Tensor" as the object of analysis, there are no critical surfaces. In addition to theoretical interest of solving an open problem, this result has profound practical significance. The numerical instability associated with Structure from Motion is largely attributed to the existence of "critical volumes" that arise from the existence of critical surfaces coupled with errors in the image measurements. The lack of critical surfaces in the context of three views (provided that the trilinear tensor is used) suggests that better stability in the presence of errors can be gained. 1 Introduction The geometric relation between three-dimensional (3D) shape..

Comparing Probabilistic and Geometric Models On Lidar Data

A bottleneck in the use of Geographic Information Systems (GIS) is the cost of data acquisition. In our case, we are interested in producing GIS layers containing useful information for river flood impact assessment. Geometric models can be used to describe regions of the data which correspond to man-made constructions. Probabilistic models can be used to describe vegetation and other features. Our purpose is to compare geometric and probabilistic models on small regions of interest in lidar data, in order to choose which type of models renders a better description in each region. To do so, we use the Minimum Description Length principle of statistical inference, which states that best descriptions are those which better compress the data. By comparing computer programs that generate the data under different assumptions, we can decide which type of models conveys more useful information about each region of interest.

Vehicle Trajectory Approximation and Classification

We present a variational technique for finding low curvature smooth approximations to trajectories in the plane. The method is applied to short segments of a vehicle trajectory in a known ground plane. Estimates of the speed and steering angle are obtained for each segment and the motion during the segment is assigned to one of the four classes: ahead, left, right, stop. A hidden Markov model for the motion of the car is constructed and the Viterbi algorithm is used to find the sequence of internal states for which the observed behaviour of the vehicle has the highest probability

Fusion of Multiple Tracking Algorithms for Robust People Tracking

This paper shows how the output of a number of detection and tracking algorithms can be fused to achieve robust tracking of people in an indoor environment. The new tracking system contains three co-operating parts: i) an Active Shape Tracker using a PCA-generated model of pedestrian outline shapes, ii) a Region Tracker, featuring region splitting and merging for multiple hypothesis matching, and iii) a Head Detector to aid in the initialisation of tracks. Data from the three parts are fused together to select the best tracking hypotheses. The new method is validated using sequences from surveillance cameras in a underground station. It is demonstrated that robust realtime tracking of people can be achieved with the new tracking system using standard PC hardware