On the size of quadtrees generalized to d-dimensional binary pictures

AbstractSome results about the size of quadtrees and linear quadtrees, used to represent binary 2n × 2n digital pictures, are generalized to d-dimensional 2n × … × 2n pictures. Among these results are a comparison of the space-efficiency of linear vs regular trees, in terms of both the number of nodes of the tree and the number of bits needed to store each node, and an upper bound on the number of nodes as a function of n and the perimeter of the picture

Highly efficient computer oriented octree data structure and neighbors search in 3D GIS spatial

Three Dimensional (3D) have given new perspective in various field such as urban planning, hydrology, infrastructure modeling, geology etc due to its capability of handling real world object in more realistic manners, rather than two-dimensional (2D) approach. However, implementation of 3D spatial analysis in the real world has proven difficult due to the complexity of algorithm, computational power and time consuming. Existing GIS system enables 2D and two-and-a-half dimensional (2.5D) spatial datasets, but less capable of supporting 3D data structures. Recent development in Octree see more effort to improve weakness of octree in finding neighbor node by using various address encoding scheme with specific rule to eliminate the need of tree traversal. This paper proposed a new method to speed up neighbor searching and eliminating the needs of complex operation to extract spatial information from octree by preserving 3D spatial information directly from Octree data structure. This new method able to achieve O(1) complexity and utilizing Bit Manipulation Instruction 2 (BMI2) to speedup address encoding, extraction and voxel search 700% compared with generic implementation

3D Shape Descriptor-Based Facial Landmark Detection: A Machine Learning Approach

Facial landmark detection on 3D human faces has had numerous applications in the literature such as establishing point-to-point correspondence between 3D face models which is itself a key step for a wide range of applications like 3D face detection and authentication, matching, reconstruction, and retrieval, to name a few. Two groups of approaches, namely knowledge-driven and data-driven approaches, have been employed for facial landmarking in the literature. Knowledge-driven techniques are the traditional approaches that have been widely used to locate landmarks on human faces. In these approaches, a user with sucient knowledge and experience usually denes features to be extracted as the landmarks. Data-driven techniques, on the other hand, take advantage of machine learning algorithms to detect prominent features on 3D face models. Besides the key advantages, each category of these techniques has limitations that prevent it from generating the most reliable results. In this work we propose to combine the strengths of the two approaches to detect facial landmarks in a more ecient and precise way. The suggested approach consists of two phases. First, some salient features of the faces are extracted using expert systems. Afterwards, these points are used as the initial control points in the well-known Thin Plate Spline (TPS) technique to deform the input face towards a reference face model. Second, by exploring and utilizing multiple machine learning algorithms another group of landmarks are extracted. The data-driven landmark detection step is performed in a supervised manner providing an information-rich set of training data in which a set of local descriptors are computed and used to train the algorithm. We then, use the detected landmarks for establishing point-to-point correspondence between the 3D human faces mainly using an improved version of Iterative Closest Point (ICP) algorithms. Furthermore, we propose to use the detected landmarks for 3D face matching applications

Fast swept-volume distance for robust collision detection

The need for collision detection arises in several robotics areas, including motion-planning, online collision avoidance, and simulation. At the heart of most current methods are algorithms for interference detection and/or distance computation. A few recent algorithms and implementations are very fast, but to use them for accurate collision detection, very small step sizes can be necessary, reducing their effective efficiency. We present a fast, implemented technique for doing exact distance computation and interference detection for translationally-swept bodies. For rotationally swept bodies, we adapt this technique to improve accuracy, for any given step size, in distance computation and interference detection. We present preliminary experiments that show that the combination of basic and swept-body calculations holds much promise for faster accurate collision detection