Catalyst Project: Computer algorithms and simulations for CT image reconstruction and segmentation utilizing optimal sampling lattices and efficient domains

催化剂项目支持历史悠久的黑人学院和大学致力于建立教职员工的研究能力，以加强科学、技术、工程和数学本科教育和研究。预计该奖项将进一步提高教职员工的研究能力，改善学院的研究和教学，并让本科生参与研究经验。Vorhees学院的这个项目旨在开发使用最佳采样网格的计算机断层扫描(CT)图像重建和分割方法，并为本科生提供一个机会，通过计算机建模方面的研究经验来加强他们的教育。这位研究人员与南卡罗来纳大学的教职员工建立了强有力的合作关系。计算机断层扫描是创建身体内部图像的重要工具。图像重建是从扫描数据中计算出内部图像，图像分割可以帮助定位图像中的内部物体或它们的边界。通常的CT计算是在像素为正方形或立方体的笛卡尔晶格上进行的。而最优采样点阵，如二维六边形和三维面心立方和体心立方点阵，与传统的笛卡尔点阵相比，提供了更高的采样效率和更好的邻接关系。在这个项目中，对于2D情况，将使用过滤反投影法在六边形点阵和规则六边形区域上从扫描数据重建图像。然后对重建图像采用图割等图像分割方法。由于CT机旋转以执行来自不同方向的扫描，因此被扫描的2D对象可以被假定为圆形。由于圆形区域可以比正方形更紧密地嵌入到正六边形中，因此可能涉及更少的格点，并且可以有效地对格点进行索引以用于图像分割。因此，可以减少图像分割的计算时间，提高图像分割的质量。计算机模拟将在图像分割质量和计算效率方面对新算法进行评估。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Catalyst Projects provide support for Historically Black Colleges and Universities to work towards establishing research capacity of faculty to strengthen science, technology, engineering and mathematics undergraduate education and research. It is expected that the award will further the faculty member's research capability, improve research and teaching at the institution, and involve undergraduate students in research experiences. This project at Vorhees College seeks to develop computed tomography (CT) image reconstruction and segmentation methods using optimal sampling lattices and provides an opportunity for undergraduate students to enhance their education through research experiences in computer modeling. The researcher has established a strong collaboration with faculty at the University of South Carolina. Computed tomography is an important tool to create the internal image of a physical body. Image reconstruction is to compute the internal image from the scanned data and image segmentation may help to locate the internal objects or their boundaries in the image. The usual CT computations are done on a Cartesian lattice whose pixels are squares or cubes. However optimal sampling lattices, such as 2D hexagonal and 3D face centered cubic and body centered cubic lattices, provide more efficient sampling and better adjacency relation than the traditional Cartesian lattices. In this project, for the 2D case, images will be reconstructed from scanned data using the filtered back-projection method over a hexagonal lattice and in a regular hexagonal region. Then image segmentation methods such as graph-cuts on the reconstructed images are applied. Because a CT machine rotates to perform scans from different directions, a 2D object to be scanned may be assumed to be circular. Since the circular region can be embedded into a regular hexagon more tightly than into a square, fewer number of lattice points may be involved and the lattice points can be efficiently indexed for image segmentation. Hence the computational time for image segmentation may be reduced and the quality may be improved. Computer simulations will be done to evaluate the new algorithms in terms of image segmentation quality and computational efficiency.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.