Narrow Results

We consider the following geometric pattern matching problem: Given two sets of points in the plane, P and Q, and some (arbitrary) δ > 0, find the largest subset B ⊂ P and a similarity transformation T (translation, rotation and scale) such that h(T(B),Q) < δ, where h(.,.) is the directional Hausdorff distance. This problem stems from real world applications, where δ is determined by the practical uncertainty in the position of the points (pixels). We reduce the problem to finding the depth (maximally covered point) of an arrangement of polytopes in transformation space. The depth is the cardinality of B, and the polytopes that cover the deepest point correspond to the points in B. We present an algorithm that approximates the maximum depth with high probability, thus getting a large enough common point set in P and Q.

The algorithm is implemented in the GPU framework, thus it is very fast in practice. We present experimental results and compare their runtime with those of an algorithm running on the CPU.

Improving the image quality and the rendering speed have always been a challenge to the programmers involved in large scale volume rendering especially in the field of medical image processing. The paper aims to perform volume rendering using the graphics processing unit (GPU), in which, with its massively parallel capability has the potential to revolutionize this field. This work is now better with the help of GPU accelerated system. The final results would allow the doctors to diagnose and analyze the 2D computed tomography (CT) scan data using three dimensional visualization techniques. The system is used in multiple types of datasets, from 10 MB to 350 MB medical volume data. Further, the use of compute unified device architecture (CUDA) framework, a low learning curve technology, for such purpose would greatly reduce the cost involved in CT scan analysis; hence bring it to the common masses. The volume rendering has been done on Nvidia Tesla C1060 (there are 240 CUDA cores, which provides execution of data parallely) card and its performance has also been benchmarked.