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Tool Investigation

    In this section, we introduce the tools that have been investigated in our study and summerize their function.
  1. Facet Model Surface Detection Program

    2. The facet model uses the polynomial function to fit the gray level data. The commonly used general forms for the  facet model include piecewise constant (flat facet model), piecewise linear (slope facet model), piecewise quadric, and piecewise cubic. Masks can be generated to calculate the fitting coefficents. Once the facet model is built, a various tasks can be performed, including enhancement and edge detection. We have extended Haralick's two dimensional directional derivatives to three dimensional case. A set of three dimensional facet models were designed to detect surface points directly from a series of CT images. Subpixel accuracy can be achieved by locating the zero-crossing point along the direction of gradient. The program was developed for another project of dimensional measurement of engine blades. Details can be found in [1].
     
  2. Active Contour Model Contour Extraction and Registration Program

    3. Active contour models, also known as "Snakes", have been applied to numerous image analysis and computer vision problems to search contours. A snake is an open or closed elastic curve represented by a set of points on a sequence. Finding contours of distinct features is done by deforming and moving the elastic curve gradually from an initial shape residing in the image towards the position where distinct features such as boundary points are to be extracted. This deformation process is guided by iteratively searching for a local minimum of an energy function, which consists of the internal energy (a smoothing constraint of the snake curve) and the external energy that indicates the degree of matching of features (such as high image intensity for bright regions or large gradient value for edges). While our snake is the same as many others reported in the literature, our snake has a additional energy constraint for the external energy. This additional constraint is to highlight the changes in the boundary between two subsequent image layers by using the gray level difference value as a guide to indicate the movement needed by the upper image boundary curve in order to obtain the lower image boundary. This computer program was developed for another project of tracking the pig heart boundary of real time ultrasound video. It is a modification from GSnake*. Details can be found in [2].
     
  3. Level Set Contour Extraction Program

    4. Level Set segmentation method [3] is an iterative method to locate the boundary of an object in the image. In this method, an initial set of contour points is first selected, and then every contour point of the set evolves at a velocity in the normal direction of the contour at each iteration. In general the magnitude of the velocity is related to the curvature of the contour and local image features. In our study, the magnitude of the velocity is inversely proportional to the gradient. Human intervention is needed to stop the process. However, there are two weaknesses in using this method: (1) The stopping rule of the process has to be externally introduced. (2) The resulting performance is related to the selection of the initial contour. In our effort to overcome these difficulties, we introduce a searching process to estimate the best velocity set at each iteration. A preliminary application of the resulting algorithm is reported in this paper.
     
  4. Point Processing Program: Surfacer**

    5. Surfacer is a 3-D data manipulation software package for processing, interpreting, and analyzing 3-D data. Surfacer has three basic functionalities: point processing, curve and surface generation, and entity analysis. For point processing, a variety of point processing tools are provided, including: filtering, segmentation, feature extraction, editing, sorting, and scaling. For curve and surface generation, a number of utilities are provided for generating high-quality curve and surface models directly from point data, from point data and curves, from curves alone, or from surface geometry. For entity analysis, utilities for verifying the quality of surfaces and curves are provided. In our applications, only point processing function is used.
     
  5. Three Dimensional Reconstruction Program: Nuages ***

    6. Nuages is a tool for 3D reconstruction from parallel closed contours. The input contours are represented by a set coordinates of the points. The program generates a set of triangles representing the surface of a 3D polyhedra, and/or a set of tetrahedra filling the 3D polyhedra. Multiple contours are allowed to exist on the same plane but there should be no interception between contours. The program supports many file formats, including wavefront .obj format, DXF format, VRML format, and Object File Format (.off) format. Nuages is available on the internet.
     
  6. Geometry Viewing Program: Geomview****

    7. Geomview is an interactive program for geometry visualization. The input data can have be: polyhedra with shared vertices(.off), quadrilaterals, rectangular meshes, vectors, and Bezier surface patches of arbitrary degree including rational patches. Multiple objects and cameras are allowed. The control of the objects are independent and interactive. Following functions are provided: motion control, appearances (including lighting, shading, and materials), edge or vertex level, snapshots, and adding or deleting objects. Geomview is also available on the internet.
 
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