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3D segmentation of white matter lesions by combining pixons-based techniques with polya urn models
NemoImage
11, Number
5, 2000,
Part 2 of 2 Parts
IDE~P
METHODS
- ANALYSIS
3D Segmentationof White Matter Lesions by Combining Pixons-Based Techniqueswith Polya Urn Models Tianzi Jiang*t,
Qing Lut, Yong Fan?, Frithjof
Kruggel*
“Max-Planck Institute of Cognitive Neuroscience, Stephanstrass 1, D-04103, Leipzig, Germany ?-National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing 100080, China The pixon model was first introduced by Pina and Puetter [l] to reconstruct astronomical images. The pixons are variable-sized cells which locally define the resolutions of data. The size, shape and position of all pixons over an image are collected into a pixon map. It gives a multi-resolution description of the image with various spatial scales. Pixons are ideally suited detect and quantify white matter lesions which occur with degenerative brain diseases. Mechanisms for the classification and qualification of such lesions will help in drawing therapeutical decisions. we have made an attempt to apply this powerful tool to segmentation of white matter lesions. For this purpose, we assumed the following a priori knowledge for white matter lesions: (1) lesions are completely surrounded by white matter; (2) lesions are small; (3) lesions are hypointense in Tl-weighted images; and (4) lesions are spherical or ellipsoid of different sizes. As a preliminary of our research, we have first investigated the mechanisms of pixons. In order to design a suitable multiscale description for a 3D image this stage is absolutely necessary because all previous works related to pixons were conducted in 2D case. We started our research into this problem with 2D slice because it is much easier than 3D case and there have been some related works on 2D slice for references. Therefore, we can directly compare the efficacy of our methods with the existing compartments. Then we have extended our results to 3D case by the following methods. We assumed that 3D structures are consisted of their 2D slices. Therefore, we can reconstruct 3D results from the corresponding results of several 2D slices. We found out a suitable way concentrating 2D results into 3D segmentation. We have also made another attempt that we use pixon-based methods to process 3D MR datasets directly. To this end, we have first designed a proper multiscale of 3D image. In order to further the efficacy of our segmentation, we have also extended 2D Polya urn models, which was first used for 2D image segmentation by Banejee et al [2], to 3D to process 3D MR datasets directly. We find that Polya urn model is an analogue of relaxation label-a stochastic version of relaxation label-a refinement procedure to improve the final segmentation results. The performance of Polya urn process for 2D segmentation is attractive.The following two approaches were used in this paper: (1) the region growing method to obtain a rough segmentation and then the 3D urn model to refine the results; (2) Pixon-Based MRF models were used to find the segmentation and 3D urn models were adopted to refine the segmentation. Moreover, we have extended approach 2 stated above to find the white matter areas, and then adopt region growing to find the lesions in these areas. It is because the prior knowledge tells us that lesions lie in the WM. For a Polya urn model, a central problem is to determine a suitable neighborhood and sampling rule for urns. We dealt with this problem as follows. For the determination of neighborhood of urn, we can collect all the neighboring urns into one super urn. We used one of the following two rules as our sampling rule: (a) Perform like the roulette rule in genetic algorithm and a random number is generated. Thus the color with major number of balls was more possible to be chosen. (2) The color with the major number of balls was chosen. A comparison between this two rules as well as the rules used by Banejee et al [2] for WMLs segmentation are undergoing. References 1. Pina R. K. and Puetter, R. C., Publications of the Astronomical Society of the Pacific, 2. Banerjee, A., Burlina, P., and Alajaji. F., IEEE Trans. lmage Proc., 1999, 8:1243-1253.
S616
1993, 105: 630-637.
11, Number
5, 2000,
Part 2 of 2 Parts
IDE~P
METHODS
- ANALYSIS
3D Segmentationof White Matter Lesions by Combining Pixons-Based Techniqueswith Polya Urn Models Tianzi Jiang*t,
Qing Lut, Yong Fan?, Frithjof
Kruggel*
“Max-Planck Institute of Cognitive Neuroscience, Stephanstrass 1, D-04103, Leipzig, Germany ?-National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing 100080, China The pixon model was first introduced by Pina and Puetter [l] to reconstruct astronomical images. The pixons are variable-sized cells which locally define the resolutions of data. The size, shape and position of all pixons over an image are collected into a pixon map. It gives a multi-resolution description of the image with various spatial scales. Pixons are ideally suited detect and quantify white matter lesions which occur with degenerative brain diseases. Mechanisms for the classification and qualification of such lesions will help in drawing therapeutical decisions. we have made an attempt to apply this powerful tool to segmentation of white matter lesions. For this purpose, we assumed the following a priori knowledge for white matter lesions: (1) lesions are completely surrounded by white matter; (2) lesions are small; (3) lesions are hypointense in Tl-weighted images; and (4) lesions are spherical or ellipsoid of different sizes. As a preliminary of our research, we have first investigated the mechanisms of pixons. In order to design a suitable multiscale description for a 3D image this stage is absolutely necessary because all previous works related to pixons were conducted in 2D case. We started our research into this problem with 2D slice because it is much easier than 3D case and there have been some related works on 2D slice for references. Therefore, we can directly compare the efficacy of our methods with the existing compartments. Then we have extended our results to 3D case by the following methods. We assumed that 3D structures are consisted of their 2D slices. Therefore, we can reconstruct 3D results from the corresponding results of several 2D slices. We found out a suitable way concentrating 2D results into 3D segmentation. We have also made another attempt that we use pixon-based methods to process 3D MR datasets directly. To this end, we have first designed a proper multiscale of 3D image. In order to further the efficacy of our segmentation, we have also extended 2D Polya urn models, which was first used for 2D image segmentation by Banejee et al [2], to 3D to process 3D MR datasets directly. We find that Polya urn model is an analogue of relaxation label-a stochastic version of relaxation label-a refinement procedure to improve the final segmentation results. The performance of Polya urn process for 2D segmentation is attractive.The following two approaches were used in this paper: (1) the region growing method to obtain a rough segmentation and then the 3D urn model to refine the results; (2) Pixon-Based MRF models were used to find the segmentation and 3D urn models were adopted to refine the segmentation. Moreover, we have extended approach 2 stated above to find the white matter areas, and then adopt region growing to find the lesions in these areas. It is because the prior knowledge tells us that lesions lie in the WM. For a Polya urn model, a central problem is to determine a suitable neighborhood and sampling rule for urns. We dealt with this problem as follows. For the determination of neighborhood of urn, we can collect all the neighboring urns into one super urn. We used one of the following two rules as our sampling rule: (a) Perform like the roulette rule in genetic algorithm and a random number is generated. Thus the color with major number of balls was more possible to be chosen. (2) The color with the major number of balls was chosen. A comparison between this two rules as well as the rules used by Banejee et al [2] for WMLs segmentation are undergoing. References 1. Pina R. K. and Puetter, R. C., Publications of the Astronomical Society of the Pacific, 2. Banerjee, A., Burlina, P., and Alajaji. F., IEEE Trans. lmage Proc., 1999, 8:1243-1253.
S616
1993, 105: 630-637.