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

The AD Vacuum System: Construction and Commissioning

CERN has built a new experimental facility, called the Antiproton Decelerator (AD), by transforming two existing machines: the "Antiproton Collector" (AC) and the "Antiproton Accumulator" (AA). To achieve adequate beam performance once the antiproton beam is decelerated to its final value of 0.1 GeV/c, it was necessary to lower the average pressure by nearly two orders of magnitude. For this purpose, a large number of additional pumps were installed and a very careful preparation was applied to a variety of special machine equipment which, in its original construction, was not designed for ultra-high vacuum operation. An important improvement in the outgassing rates was achieved through an extended, mild bake-out of tanks and vacuum vessels containing large amounts of ferrite material and multi-layer thermal insulation. This paper describes the necessary modifications of the vacuum system and in more detail the various steps taken to obtain the required pressure in the low 10-10 mbar range. It will also report on the unexpected difficulties which were encountered by re-using vacuum components that were not initially designed for bake-out

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

Hybrid filter blending to maintain facial expressions in rendered human portraits

Artistic rendering of human portraits is different and more challenging than that of landscapes or flowers. Issues are eye, nose, and mouth regions (i.e., facial features) where we need to represent their natural emotions. Shades or darkness around eyes, or shininess at nose tips may negatively impact the rendering result if not properly dealt with. Similarly, a lighter colour around the mouth region caused by lighting might produce some disturbing artefacts. The proposed computerised method attempts to be adaptive to those sensitive areas by utilising a face analysis module. First, the program detects main facial segments and features. Then it utilises a blending of various filtering parameters aiming at an adequate final portrait that represents the subject's original facial expression, while still supporting a non-photorealistic artistic rendering as the perceived impression

Comparison of two 3D tracking paradigms for freely flying insects

In this paper, we discuss and compare state-of-the-art 3D tracking paradigms for flying insects such as Drosophila melanogaster. If two cameras are employed to estimate the trajectories of these identical appearing objects, calculating stereo and temporal correspondences leads to an NP-hard assignment problem. Currently, there are two different types of approaches discussed in the literature: probabilistic approaches and global correspondence selection approaches. Both have advantages and limitations in terms of accuracy and complexity. Here, we present algorithms for both paradigms. The probabilistic approach utilizes the Kalman filter for temporal tracking. The correspondence selection approach calculates the trajectories based on an overall cost function. Limitations of both approaches are addressed by integrating a third camera to verify consistency of the stereo pairings and to reduce the complexity of the global selection. Furthermore, a novel greedy optimization scheme is introduced for the correspondence selection approach. We compare both paradigms based on synthetic data with ground truth availability. Results show that the global selection is more accurate, while the previously proposed tracking-by-matching (probabilistic) approach is causal and feasible for longer tracking periods and very high target densities. We further demonstrate that our extended global selection scheme outperforms current correspondence selection approaches in tracking accuracy and tracking time

PCA-based lung motion model

Organ motion induced by respiration may cause clinically significant targeting errors and greatly degrade the effectiveness of conformal radiotherapy. It is therefore crucial to be able to model respiratory motion accurately. A recently proposed lung motion model based on principal component analysis (PCA) has been shown to be promising on a few patients. However, there is still a need to understand the underlying reason why it works. In this paper, we present a much deeper and detailed analysis of the PCA-based lung motion model. We provide the theoretical justification of the effectiveness of PCA in modeling lung motion. We also prove that under certain conditions, the PCA motion model is equivalent to 5D motion model, which is based on physiology and anatomy of the lung. The modeling power of PCA model was tested on clinical data and the average 3D error was found to be below 1 mm.Comment: 4 pages, 1 figure. submitted to International Conference on the use of Computers in Radiation Therapy 201