Object association with belief functions, an application with vehicles

The problem tackled in this article consists in associating perceived objects detected at a certain time with known objects previously detected, knowing uncertain and imprecise information regarding the association of each perceived objects with each known objects. For instance, this problem can occur during the association step of an obstacle tracking process, especially in the context of vehicle driving aid. A contribution in the modeling of this association problem in the belief function framework is introduced. By interpreting belief functions as weighted opinions according to the Transferable Belief Model semantics, pieces of information regarding the association of known objects and perceived objects can be expressed in a common global space of association to be combined by the conjunctive rule of combination, and a decision making process using the pignistic transformation can be made. This approach is validated on real data.     

Object detection based on a robust and accurate statistical multi-point-pair model

In this paper, we propose a robust and accurate background model, called grayscale arranging pairs (GAP). The model is based on the statistical reach feature (SRF), which is defined as a set of statistical pair-wise features. Using the GAP model, moving objects are successfully detected under a variety of complex environmental conditions. The main concept of the proposed method is the use of multiple point pairs that exhibit a stable statistical intensity relationship as a background model. The intensity difference between pixels of the pair is much more stable than the intensity of a single pixel, especially in varying environments. Our proposed method focuses more on the history of global spatial correlations between pixels than on the history of any given pixel or local spatial correlations. Furthermore, we clarify how to reduce the GAP modeling time and present experimental results comparing GAP with existing object detection methods, demonstrating that superior object detection with higher precision and recall rates is achieved by GAP.     

Discovery of Intrinsic Primitives on Triangle Meshes

The discovery of meaningful parts of a shape is required for many geometry processing applications, such as parameterization, shape correspondence, and animation. It is natural to consider primitives such as spheres, cylinders and cones as the building blocks of shapes, and thus to discover parts by fitting such primitives to a given surface. This approach, however, will break down if primitive parts have undergone almost‐isometric deformations, as is the case, for example, for articulated human models. We suggest that parts can be discovered instead by finding intrinsic primitives, which we define as parts that posses an approximate intrinsic symmetry. We employ the recently‐developed method of computing discrete approximate Killing vector fields (AKVFs) to discover intrinsic primitives by investigating the relationship between the AKVFs of a composite object and the AKVFs of its parts. We show how to leverage this relationship with a standard clustering method to extract k intrinsic primitives and remaining asymmetric parts of a shape for a given k. We demonstrate the value of this approach for identifying the prominent symmetry generators of the parts of a given shape. Additionally, we show how our method can be modified slightly to segment an entire surface without marking asymmetric connecting regions and compare this approach to state‐of‐the‐art methods using the Princeton Segmentation Benchmark.     

Global Structure Optimization of Quadrilateral Meshes

We introduce a fully automatic algorithm which optimizes the high‐level structure of a given quadrilateral mesh to achieve a coarser quadrangular base complex. Such a topological optimization is highly desirable, since state‐of‐the‐art quadrangulation techniques lead to meshes which have an appropriate singularity distribution and an anisotropic element alignment, but usually they are still far away from the high‐level structure which is typical for carefully designed meshes manually created by specialists and used e.g. in animation or simulation. In this paper we show that the quality of the high‐level structure is negatively affected by helical configurations within the quadrilateral mesh. Consequently we present an algorithm which detects helices and is able to remove most of them by applying a novel grid preserving simplification operator (GP‐operator) which is guaranteed to maintain an all‐quadrilateral mesh. Additionally it preserves the given singularity distribution and in particular does not introduce new singularities. For each helix we construct a directed graph in which cycles through the start vertex encode operations to remove the corresponding helix. Therefore a simple graph search algorithm can be performed iteratively to remove as many helices as possible and thus improve the high‐level structure in a greedy fashion. We demonstrate the usefulness of our automatic structure optimization technique by showing several examples with varying complexity.     

Contouring Discrete Indicator Functions

We present a method for calculating the boundary of objects from Discrete Indicator Functions that store 2‐material volume fractions with a high degree of accuracy. Although Marching Cubes and its derivatives are effective methods for calculating contours of functions sampled over discrete grids, these methods perform poorly when contouring non‐smooth functions such as Discrete Indicator Functions. In particular, Marching Cubes will generate surfaces that exhibit aliasing and oscillations around the exact surface. We derive a simple solution to remove these problems by using a new function to calculate the positions of vertices along cell edges that is efficient, easy to implement, and does not require any optimization or iteration. Finally, we provide empirical evidence that the error introduced by our contouring method is significantly less than is introduced by Marching Cubes.     

SSD: Smooth Signed Distance Surface Reconstruction

We introduce a new variational formulation for the problem of reconstructing a watertight surface defined by an implicit equation, from a finite set of oriented points; a problem which has attracted a lot of attention for more than two decades. As in the Poisson Surface Reconstruction approach, discretizations of the continuous formulation reduce to the solution of sparse linear systems of equations. But rather than forcing the implicit function to approximate the indicator function of the volume bounded by the implicit surface, in our formulation the implicit function is forced to be a smooth approximation of the signed distance function to the surface. Since an indicator function is discontinuous, its gradient does not exist exactly where it needs to be compared with the normal vector data. The smooth signed distance has approximate unit slope in the neighborhood of the data points. As a result, the normal vector data can be incorporated directly into the energy function without implicit function smoothing. In addition, rather than first extending the oriented points to a vector field within the bounding volume, and then approximating the vector field by a gradient field in the least squares sense, here the vector field is constrained to be the gradient of the implicit function, and a single variational problem is solved directly in one step. The formulation allows for a number of different efficient discretizations, reduces to a finite least squares problem for all linearly parameterized families of functions, and does not require boundary conditions. The resulting algorithms are significantly simpler and easier to implement, and produce results of quality comparable with state‐of‐the‐art algorithms. An efficient implementation based on a primal‐graph octree‐based hybrid finite element‐finite difference discretization, and the Dual Marching Cubes isosurface extraction algorithm, is shown to produce high quality crack‐free adaptive manifold polygon meshes.     

River Networks for Instant Procedural Planets

Realistic terrain models are required in many applications, especially in computer games. Commonly, procedural models are applied to generate the corresponding models and let users experience a wide variety of new environments. Existing algorithms generate landscapes immediately with view‐dependent resolution and without preprocessing. Unfortunately, landscapes generated by such algorithms lack river networks and therefore appear unnatural. Algorithms that integrate realistic river networks are computationally expensive and cannot be used to generate a locally adaptive high resolution landscape during a fly‐through. In this paper, we propose a novel algorithm to generate realistic river networks. Our procedural algorithm creates complete planets and landscapes with realistic river networks within seconds. It starts with a coarse base geometry of a planet without further preprocessing and user intervention. By exploiting current graphics hardware, the proposed algorithm is able to generate adaptively refined landscape geometry during fly‐throughs.     

Skeleton computation of orthogonal polyhedra

Skeletons are powerful geometric abstractions that provide useful representations for a number of geometric operations. The straight skeleton has a lower combinatorial complexity compared with the medial axis. Moreover, while the medial axis of a polyhedron is composed of quadric surfaces the straight skeleton just consist of planar faces. Although there exist several methods to compute the straight skeleton of a polygon, the straight skeleton of polyhedra has been paid much less attention. We require to compute the skeleton of very large datasets storing orthogonal polyhedra. Furthermore, we need to treat geometric degeneracies that usually arise when dealing with orthogonal polyhedra. We present a new approach so as to robustly compute the straight skeleton of orthogonal polyhedra. We follow a geometric technique that works directly with the boundary of an orthogonal polyhedron. Our approach is output sensitive with respect to the number of vertices of the skeleton and solves geometric degeneracies. Unlike the existing straight skeleton algorithms that shrink the object boundary to obtain the skeleton, our algorithm relies on the plane sweep paradigm. The resulting skeleton is only composed of axis‐aligned and 45° rotated planar faces and edges.     

A Multiscale Approach to Optimal Transport

In this paper, we propose an improvement of an algorithm of Aurenhammer, Hoffmann and Aronov to find a least square matching between a probability density and finite set of sites with mass constraints, in the Euclidean plane. Our algorithm exploits the multiscale nature of this optimal transport problem. We iteratively simplify the target using Lloyd's algorithm, and use the solution of the simplified problem as a rough initial solution to the more complex one. This approach allows for fast estimation of distances between measures related to optimal transport (known as Earth‐mover or Wasserstein distances). We also discuss the implementation of these algorithms, and compare the original one to its multiscale counterpart.     

Inexact graph matching based on kernels for object retrieval in image databases

In the framework of online object retrieval with learning, we address the problem of graph matching using kernel functions. An image is represented by a graph of regions where the edges represent the spatial relationships. Kernels on graphs are built from kernel on walks in the graph. This paper firstly proposes new kernels on graphs and on walks, which are very efficient for graphs of regions. Secondly we propose fast solutions for exact or approximate computation of these kernels. Thirdly we show results for the retrieval of images containing a specific object with the help of very few examples and counter-examples in the framework of an active retrieval scheme.