Ray casting implicit fractal surfaces with reduced affine arithmetic

A method is presented for ray casting implicit surfaces defined by fractal combinations of procedural noise functions. The method is robust and uses affine arithmetic to bound the variation of the implicit function along a ray. The method is also efficient due to a modification in the affine arithmetic representation that introduces a condensation step at the end of every non-affine operation. We show that our method is able to retain the tight estimation capabilities of affine arithmetic for ray casting implicit surfaces made from procedural noise functions while being faster to compute and more efficient to store

Geometry Processing of Conventionally Produced Mouse Brain Slice Images

Brain mapping research in most neuroanatomical laboratories relies on conventional processing techniques, which often introduce histological artifacts such as tissue tears and tissue loss. In this paper we present techniques and algorithms for automatic registration and 3D reconstruction of conventionally produced mouse brain slices in a standardized atlas space. This is achieved first by constructing a virtual 3D mouse brain model from annotated slices of Allen Reference Atlas (ARA). Virtual re-slicing of the reconstructed model generates ARA-based slice images corresponding to the microscopic images of histological brain sections. These image pairs are aligned using a geometric approach through contour images. Histological artifacts in the microscopic images are detected and removed using Constrained Delaunay Triangulation before performing global alignment. Finally, non-linear registration is performed by solving Laplace's equation with Dirichlet boundary conditions. Our methods provide significant improvements over previously reported registration techniques for the tested slices in 3D space, especially on slices with significant histological artifacts. Further, as an application we count the number of neurons in various anatomical regions using a dataset of 51 microscopic slices from a single mouse brain. This work represents a significant contribution to this subfield of neuroscience as it provides tools to neuroanatomist for analyzing and processing histological data.Comment: 14 pages, 11 figure

A fully automatic CAD-CTC system based on curvature analysis for standard and low-dose CT data

Computed tomography colonography (CTC) is a rapidly evolving noninvasive medical investigation that is viewed by radiologists as a potential screening technique for the detection of colorectal polyps. Due to the technical advances in CT system design, the volume of data required to be processed by radiologists has increased significantly, and as a consequence the manual analysis of this information has become an increasingly time consuming process whose results can be affected by inter- and intrauser variability. The aim of this paper is to detail the implementation of a fully integrated CAD-CTC system that is able to robustly identify the clinically significant polyps in the CT data. The CAD-CTC system described in this paper is a multistage implementation whose main system components are: 1) automatic colon segmentation; 2) candidate surface extraction; 3) feature extraction; and 4) classification. Our CAD-CTC system performs at 100% sensitivity for polyps larger than 10 mm, 92% sensitivity for polyps in the range 5 to 10 mm, and 57.14% sensitivity for polyps smaller than 5 mm with an average of 3.38 false positives per dataset. The developed system has been evaluated on synthetic and real patient CT data acquired with standard and low-dose radiation levels

Simple and Robust Boolean Operations for Triangulated Surfaces

Boolean operations of geometric models is an essential issue in computational geometry. In this paper, we develop a simple and robust approach to perform Boolean operations on closed and open triangulated surfaces. Our method mainly has two stages: (1) We firstly find out candidate intersected-triangles pairs based on Octree and then compute the inter-section lines for all pairs of triangles with parallel algorithm; (2) We form closed or open intersection-loops, sub-surfaces and sub-blocks quite robustly only according to the cleared and updated topology of meshes while without coordinate computations for geometric enti-ties. A novel technique instead of inside/outside classification is also proposed to distinguish the resulting union, subtraction and intersection. Several examples have been given to illus-trate the effectiveness of our approach.Comment: Novel method for determining Union, Subtraction and Intersectio

Progressive refinement rendering of implicit surfaces

The visualisation of implicit surfaces can be an inefficient task when such surfaces are complex and highly detailed. Visualising a surface by first converting it to a polygon mesh may lead to an excessive polygon count. Visualising a surface by direct ray casting is often a slow procedure. In this paper we present a progressive refinement renderer for implicit surfaces that are Lipschitz continuous. The renderer first displays a low resolution estimate of what the final image is going to be and, as the computation progresses, increases the quality of this estimate at an interactive frame rate. This renderer provides a quick previewing facility that significantly reduces the design cycle of a new and complex implicit surface. The renderer is also capable of completing an image faster than a conventional implicit surface rendering algorithm based on ray casting