Relative Convex Hull Determination from Convex Hulls in the Plane

A new algorithm for the determination of the relative convex hull in the plane of a simple polygon A with respect to another simple polygon B which contains A, is proposed. The relative convex hull is also known as geodesic convex hull, and the problem of its determination in the plane is equivalent to find the shortest curve among all Jordan curves lying in the difference set of B and A and encircling A. Algorithms solving this problem known from Computational Geometry are based on the triangulation or similar decomposition of that difference set. The algorithm presented here does not use such decomposition, but it supposes that A and B are given as ordered sequences of vertices. The algorithm is based on convex hull calculations of A and B and of smaller polygons and polylines, it produces the output list of vertices of the relative convex hull from the sequence of vertices of the convex hull of A.Comment: 15 pages, 4 figures, Conference paper published. We corrected two typing errors in Definition 2: $I_S$ has to be defined based on $O_S$, and $I_E$ has to be defined based on $O_E$ (not just using $O$). These errors appeared in the text of the original conference paper, which also contained the pseudocode of an algorithm where $I_S$ and $I_E$ appeared as correctly define

Revisiting Digital Straight Segment Recognition

This paper presents new results about digital straight segments, their recognition and related properties. They come from the study of the arithmetically based recognition algorithm proposed by I. Debled-Rennesson and J.-P. Reveill\`es in 1995 [Debled95]. We indeed exhibit the relations describing the possible changes in the parameters of the digital straight segment under investigation. This description is achieved by considering new parameters on digital segments: instead of their arithmetic description, we examine the parameters related to their combinatoric description. As a result we have a better understanding of their evolution during recognition and analytical formulas to compute them. We also show how this evolution can be projected onto the Stern-Brocot tree. These new relations have interesting consequences on the geometry of digital curves. We show how they can for instance be used to bound the slope difference between consecutive maximal segments

Incremental and Transitive Discrete Rotations

A discrete rotation algorithm can be apprehended as a parametric application $f\_\alpha$ from \ZZ[i] to \ZZ[i], whose resulting permutation ``looks like'' the map induced by an Euclidean rotation. For this kind of algorithm, to be incremental means to compute successively all the intermediate rotate d copies of an image for angles in-between 0 and a destination angle. The di scretized rotation consists in the composition of an Euclidean rotation with a discretization; the aim of this article is to describe an algorithm whic h computes incrementally a discretized rotation. The suggested method uses o nly integer arithmetic and does not compute any sine nor any cosine. More pr ecisely, its design relies on the analysis of the discretized rotation as a step function: the precise description of the discontinuities turns to be th e key ingredient that will make the resulting procedure optimally fast and e xact. A complete description of the incremental rotation process is provided, also this result may be useful in the specification of a consistent set of defin itions for discrete geometry

Extending the stixel world using polynomial ground manifold approximation

Stixel-based segmentation is specifically designed towards obstacle detection which combines road surface estimation in traffic scenes, stixel calculations, and stixel clustering. Stixels are defined by observed height above road surface. Road surfaces (ground manifolds) are represented by using an occupancy grid map. Stixel-based segmentation may improve the accuracy of real-time obstacle detection, especially if adaptive to changes in ground manifolds (e.g. with respect to non-planar road geometry). In this paper, we propose the use of a polynomial curve fitting algorithm based on the v-disparity space for ground manifold estimation. This is beneficial for two reasons. First, the coordinate space has inherently finite boundaries, which is useful when working with probability densities. Second, it leads to reduced computation time. We combine height segmentation and improved ground manifold algorithms together for stixel extraction. Our experimental results show a significant improvement in the accuracy of the ground manifold detection (an 8% improvement) compared to occupancy-grid mapping methods

Robust Vehicle Detection and Distance Estimation Under Challenging Lighting Conditions

Avoiding high computational costs and calibration issues involved in stereo-vision-based algorithms, this paper proposes real-time monocular-vision-based techniques for simultaneous vehicle detection and inter-vehicle distance estimation, in which the performance and robustness of the system remain competitive, even for highly challenging benchmark datasets. This paper develops a collision warning system by detecting vehicles ahead and, by identifying safety distances to assist a distracted driver, prior to occurrence of an imminent crash. We introduce adaptive global Haar-like features for vehicle detection, tail-light segmentation, virtual symmetry detection, intervehicle distance estimation, as well as an efficient single-sensor multifeature fusion technique to enhance the accuracy and robustness of our algorithm. The proposed algorithm is able to detect vehicles ahead at both day or night and also for short- and long-range distances. Experimental results under various weather and lighting conditions (including sunny, rainy, foggy, or snowy) show that the proposed algorithm outperforms state-of-the-art algorithms

Eye Status Based on Eyelid Detection: A Driver Assistance System

Fatigue and driver drowsiness monitoring is an important subject for designing driver assistance systems. The measurement of eye closure is a fundamental step for driver awareness detection. We propose a method which is based on eyelid detection and the measurement of the distance between the eyelids. First, the face and the eyes of the driver are localized. After extracting the eye region, the proposed algorithm detects eyelids and computes the percentage of eye closure. Experimental results are performed on the BioID database. Our comparisons show that the proposed method outperforms state-of-the-art methods

Real-time Anomaly Detection and Localization in Crowded Scenes

In this paper, we propose a method for real-time anomaly detection and localization in crowded scenes. Each video is defined as a set of non-overlapping cubic patches, and is described using two local and global descriptors. These descriptors capture the video properties from different aspects. By incorporating simple and cost-effective Gaussian classifiers, we can distinguish normal activities and anomalies in videos. The local and global features are based on structure similarity between adjacent patches and the features learned in an unsupervised way, using a sparse autoencoder. Experimental results show that our algorithm is comparable to a state-of-the-art procedure on UCSD ped2 and UMN benchmarks, but even more time-efficient. The experiments confirm that our system can reliably detect and localize anomalies as soon as they happen in a video

Effects of Ground Manifold Modeling on the Accuracy of Stixel Calculations

This paper highlights the role of ground manifold modeling for stixel calculations; stixels are medium-level data representations used for the development of computer vision modules for self-driving cars. By using single-disparity maps and simplifying ground manifold models, calculated stixels may suffer from noise, inconsistency, and false-detection rates for obstacles, especially in challenging datasets. Stixel calculations can be improved with respect to accuracy and robustness by using more adaptive ground manifold approximations. A comparative study of stixel results, obtained for different ground-manifold models (e.g., plane-fitting, line-fitting in v-disparities or polynomial approximation, and graph cut), defines the main part of this paper. This paper also considers the use of trinocular stereo vision and shows that this provides options to enhance stixel results, compared with the binocular recording. Comprehensive experiments are performed on two publicly available challenging datasets. We also use a novel way for comparing calculated stixels with ground truth. We compare depth information, as given by extracted stixels, with ground-truth depth, provided by depth measurements using a highly accurate LiDAR range sensor (as available in one of the public datasets). We evaluate the accuracy of four different ground-manifold methods. The experimental results also include quantitative evaluations of the tradeoff between accuracy and run time. As a result, the proposed trinocular recording together with graph-cut estimation of ground manifolds appears to be a recommended way, also considering challenging weather and lighting conditions

Simultaneous analysis of driver behaviour and road condition for driver distraction detection

The design of intelligent driver assistance systems is of increasing importance for the vehicle-producing industry and road-safety solutions. This article starts with a review of road-situation monitoring and driver's behaviour analysis. This article also discusses lane tracking using vision (or other) sensors, and the strength or weakness of different methods of driver behaviour analysis (e.g. iris or pupil status monitoring, and EEG spectrum analysis). This article focuses then on image analysis techniques and develops a multi-faceted approach in order to analyse driver's face and eye status via implementing a real-time AdaBoost cascade classifier with Haar-like features. The proposed method is tested in a research vehicle for driver distraction detection using a binocular camera. The developed algorithm is robust in detecting different types of driver distraction such as drowsiness, fatigue, drunk driving or the performance of secondary tasks

Classifying the Arithmetical Complexity of Teaching Models

This paper classifies the complexity of various teaching models by their position in the arithmetical hierarchy. In particular, we determine the arithmetical complexity of the index sets of the following classes: (1) the class of uniformly r.e. families with finite teaching dimension, and (2) the class of uniformly r.e. families with finite positive recursive teaching dimension witnessed by a uniformly r.e. teaching sequence. We also derive the arithmetical complexity of several other decision problems in teaching, such as the problem of deciding, given an effective coding $\{\mathcal L_0,\mathcal L_1,\mathcal L_2,\ldots\}$ of all uniformly r.e. families, any $e$ such that $\mathcal L_e = \{L^e_0,L^e_1,\ldots,\}$, any $i$ and $d$, whether or not the teaching dimension of $L^e_i$ with respect to $\mathcal L_e$ is upper bounded by $d$.Comment: 15 pages in International Conference on Algorithmic Learning Theory, 201