Differential invariant signatures and flows in computer vision : a symmetry group approach

Includes bibliographical references (p. 40-44).Supported by the National Science Foundation. DMS-9204192 DMS-8811084 ECS-9122106 Supported by the Air Force Office of Scientific Research. AFOSR-90-0024 Supported by the Rothschild Foundation-Yad Hanadiv and by Image Evolutions, Ltd.Peter J. Olver, Guillermo Sapiro, Allen Tannenbaum

Image Segmentation Using Weak Shape Priors

The problem of image segmentation is known to become particularly challenging in the case of partial occlusion of the object(s) of interest, background clutter, and the presence of strong noise. To overcome this problem, the present paper introduces a novel approach segmentation through the use of "weak" shape priors. Specifically, in the proposed method, an segmenting active contour is constrained to converge to a configuration at which its geometric parameters attain their empirical probability densities closely matching the corresponding model densities that are learned based on training samples. It is shown through numerical experiments that the proposed shape modeling can be regarded as "weak" in the sense that it minimally influences the segmentation, which is allowed to be dominated by data-related forces. On the other hand, the priors provide sufficient constraints to regularize the convergence of segmentation, while requiring substantially smaller training sets to yield less biased results as compared to the case of PCA-based regularization methods. The main advantages of the proposed technique over some existing alternatives is demonstrated in a series of experiments.Comment: 27 pages, 8 figure

International Congress of Mathematicians: 2022 July 6–14: Proceedings of the ICM 2022

Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022. Published with the support of the International Mathematical Union and edited by Dmitry Beliaev and Stanislav Smirnov, these seven volumes present the most important developments in all fields of mathematics and its applications in the past four years. In particular, they include laudations and presentations of the 2022 Fields Medal winners and of the other prestigious prizes awarded at the Congress. The proceedings of the International Congress of Mathematicians provide an authoritative documentation of contemporary research in all branches of mathematics, and are an indispensable part of every mathematical library

Study on the Method of Constructing a Statistical Shape Model and Its Application to the Segmentation of Internal Organs in Medical Images

In image processing, segmentation is one of the critical tasks for diagnostic analysis and image interpretation. In the following thesis, we describe the investigation of three problems related to the segmentation algorithms for medical images: Active shape model algorithm, 3-dimensional (3-D) statistical shape model building and organic segmentation experiments. For the development of Active shape models, the constraints of statistical model reduced this algorithm to be difficult for various biological shapes. To overcome the coupling of parameters in the original algorithm, in this thesis, the genetic algorithm is introduced to relax the shape limitation. How to construct a robust and effective 3-D point model is still a key step in statistical shape models. Generally the shape information is obtained from manually segmented voxel data. In this thesis, a two-step procedure for generating these models was designed. After transformed the voxel data to triangular polygonal data, in the first step, attitudes of these interesting objects are aligned according their surface features. We propose to reflect the surface orientations by means of their Gauss maps. As well the Gauss maps are mapped to a complex plane using stereographic projection approach. The experiment was run to align a set of left lung models. The second step is identifying the positions of landmarks on polygonal surfaces. This is solved by surface parameterization method. We proposed two simplex methods to correspond the landmarks. A semi-automatic method attempts to “copy” the phasic positions of pre-placed landmarks to all the surfaces, which have been mapped to the same parameterization domain. Another automatic corresponding method attempts to place the landmarks equidistantly. Finally, the goodness experiments were performed to measure the difference to manually corresponded results. And we also compared the affection to correspondence when using different surface mapping methods. The third part of this thesis is applying the segmentation algorithms to solve clinical problems. We did not stick to the model-based methods but choose the suitable one or their complex according to the objects. In the experiment of lung regions segmentation which includes pulmonary nodules, we propose a complementary region growing method to deal with the unpredictable variation of image densities of lesion regions. In the experiments of liver regions, instead of using region growing method in 3-D style, we turn into a slice-by-slice style in order to reduce the overflows. The image intensity of cardiac regions is distinguishable from lung regions in CT image. But as to the adjacent zone of heart and liver boundary are generally blurry. We utilized a shape model guided method to refine the segmentation results.3-D segmentation techniques have been applied widely not only in medical imaging fields, but also in machine vision, computer graphic. At the last part of this thesis, we resume some interesting topics such as 3-D visualization for medical interpretation, human face recognition and object grasping robot etc.九州工業大学博士学位論文 学位記番号:工博甲第353号　学位授与年月日:平成25年9月27日Chapter 1: Introduction|Chapter 2: Framework of Medical Image Segmentation|Chapter 3: 2-D Organic Regions Using Active Shape Model and Genetic Algorithm|Chapter 4: Alignment of 3-D Models|Chapter 5: Corespondence of 3-D Models|Chapter 6:Experiments of Organic Segmentation|Chapter 7: Visualization Technology and Its Applications|Chapter 8: Conclusions and Future Works九州工業大学平成25年

Proceedings of minisemester on evolution of interfaces, Sapporo 2010

conf: Special Project A, Proceedings of minisemester on evolution of interfaces, Sapporo (Department of Mathematics, Hokkaido University, July 12- August 13, 2010