3D edge detection of medical images using mathematical ...
3D Edge Detection of Medical Images Using Mathematical Morphological and Cellular Logic Array Processing Techniques # G. Rameshchandra, * G. Sathya , $ Towheed Sultana and @ E. G. Rajan # VNR Vignana Jyothi Institute of Engineering & Technology, Hyderabad, India, * New York Institute of Technology, United States of America $ Anna University of Technology Coimbatore, Coimbatore, India, @ Pentagram Research Centre, Hyderabad, India
Introduction
Results
In this paper, we introduce a novel and robust algorithm developed in the framework of „Cellular Logic Array Processing‟ for extracting volumetric edges from a reconstructed 3D image from a set of 2-D slices of original MRI/CT data. A sample MRI image of a human skull is used as a test data for analysis purposes. A comparative study of the algorithm introduced in this paper with already existing three morphological algorithms and one algorithm modified by us has been made and results reported here. In addition, a modified morphological filter based 3D edge detecting algorithm has also been introduced in this paper. Rajan and others introduced 2D and 3D image processing paradigms in the form of a pedagogy called „Image Algebra‟ in [2-5]. Zhao Ya-qian and others discussed in their work [1] various techniques for extracting edge features from a 2D digital image. Their work is mainly concerned with the processing of 2D images using morphological operations like dilation, erosion, closing, opening and morphological filters. The algorithm introduced in this paper is an outcome of a fundamental research carried out on the pedagogy „Image Algebra‟. Methods
The erosion based edge detection (EBED) algorithm #1 and dilation based edge detection (DBED) algorithm #2 indeed take less time to process, but they do not remove noise. The morphological filtering based algorithm #3 removes noise and detects edges. But it also removes some of the relevant sharp corners and small holes, since opening and closing operations are involved in the filtering process. Moreover, the morphological filtering algorithm #3 consumes approximately 8 times more processing time when compared to algorithms #1 and #2. In order to overcome these problems only, we have proposed here a modified morphological filtering called Opening based edge detection (OBED) algorithm #5.This algorithm removes noise, preserves important information which can be useful for medical image analysis and takes less processing time. On the other hand, the CLAP based 3D edge detection algorithm proposed in this paper, is found to be quality-wise better than other edge detection algorithms. The processing time of using the CLAP based edge detection algorithm #4 is approximately the same as that of using EBED and DBED algorithms. The CLAP based edge detection algorithm is compared with all other algorithms in the following table and graph.
The following morphological algorithms due to Zhao Ya-qian and others [1] are considered here for the purpose of comparative study. Algorithm #1: Let A be the original image and Z is the structuring element. Then the dilation of the image A by the structuring element Z is denoted by A⊕Z. Now the original image is subtracted from the dilated version of the image to obtain the edge map 𝐸𝑑 𝐴 . 𝐸𝑑 𝐴 = 𝐴 ⊕ 𝑍 − 𝐴 (1) Algorithm #2: The erosion of the image A by the structuring element Z is denoted by A⊝Z. Now the eroded image is subtracted from the original image to obtain the edge map. 𝐸𝑒 𝐴 = 𝐴 − 𝐴 ⊝ 𝑍 (2) Algorithm #3: Edge detection by subtracting the filtered version from the original 3D image using the operations of closing, opening and then once again closing, from the filtered version of the original image using the operations of closing, opening, closing and then dilation. The whole operation is expressed by the following equation. 𝐸𝑚 𝐴 = ((((A•Z)∘Z)•Z)⊕Z) - (((A•Z)∘Z)•Z) (3) Algorithm #4: Consider the 7-neighborhood 3-D mask shown in here Repeat sliding this7-neighborhood mask over the 3-D image. {at every stage of computation, find the maximum grayvalue G_max; find the minimum gray value G_min; if the difference between these two values D is less than or equal to a threshold value T specified by the user, then assign the value 0 to all the seven cells, else slide the mask further on} until the mask spans the entire 3-D image.
Algorithm #5 - Modified version of Algorithm #3 The processing time involved in detecting edges from a large 3D image is quite high. Moreover, one cannot afford to lose fine details of medical images in the process of noise removal. So, we suggest here the following modification in the Algorithm #3. Eo(A) = ((A∘Z)⊕Z) - (A∘Z) (4) TEMPLATE DESIGN © 2008
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EBED
Number of Voxels Before Processing 14834427
DBED
14834427
614731
16.00
MFED
14834427
302602
139.70
OBED
14834427
307344
46.93
CLAP-BED
14834427
426478
18.91
Algorithm
Number of Voxels After Processing
Processing Time (In Seconds)
565475
16.00
References 1. Zhao Yu-qian, Gui Wei-hua, Chen Zhen-cheng, Tang Jing-tian, Li Ling-yun, “Medical image edge detection based on mathematical morphology”, In Proc. 27thAnnu. Conf. Engineering in Medicine and Biology, Shangai, China, 2005, pp. 6492–6494. 2. Rajan, E. G., “Cellular logic array processing for high through put image processing systems”, Sadhana, Vol. 18, issue 2, pp. 279-300, Springer. 3. Rajan, E.G., “Symbolic computing: signal and image processing”, Anshan Publications, United Kingdom, 2005. 4. Rajan, E. G., “High-throughput cellular logic array processing of remotely sensed imageries, International Conference on Remote Sensing & GIS, JNTU, Hyderabad, 1992. 5. Rajan, E. G., “High-throughput cellular logic array processing of satellite data for geophysical surveying”, invited paper, no. A.1-S.1.08, World Space Congress, Washington, DC, September 1992.
Introduction
Results
In this paper, we introduce a novel and robust algorithm developed in the framework of „Cellular Logic Array Processing‟ for extracting volumetric edges from a reconstructed 3D image from a set of 2-D slices of original MRI/CT data. A sample MRI image of a human skull is used as a test data for analysis purposes. A comparative study of the algorithm introduced in this paper with already existing three morphological algorithms and one algorithm modified by us has been made and results reported here. In addition, a modified morphological filter based 3D edge detecting algorithm has also been introduced in this paper. Rajan and others introduced 2D and 3D image processing paradigms in the form of a pedagogy called „Image Algebra‟ in [2-5]. Zhao Ya-qian and others discussed in their work [1] various techniques for extracting edge features from a 2D digital image. Their work is mainly concerned with the processing of 2D images using morphological operations like dilation, erosion, closing, opening and morphological filters. The algorithm introduced in this paper is an outcome of a fundamental research carried out on the pedagogy „Image Algebra‟. Methods
The erosion based edge detection (EBED) algorithm #1 and dilation based edge detection (DBED) algorithm #2 indeed take less time to process, but they do not remove noise. The morphological filtering based algorithm #3 removes noise and detects edges. But it also removes some of the relevant sharp corners and small holes, since opening and closing operations are involved in the filtering process. Moreover, the morphological filtering algorithm #3 consumes approximately 8 times more processing time when compared to algorithms #1 and #2. In order to overcome these problems only, we have proposed here a modified morphological filtering called Opening based edge detection (OBED) algorithm #5.This algorithm removes noise, preserves important information which can be useful for medical image analysis and takes less processing time. On the other hand, the CLAP based 3D edge detection algorithm proposed in this paper, is found to be quality-wise better than other edge detection algorithms. The processing time of using the CLAP based edge detection algorithm #4 is approximately the same as that of using EBED and DBED algorithms. The CLAP based edge detection algorithm is compared with all other algorithms in the following table and graph.
The following morphological algorithms due to Zhao Ya-qian and others [1] are considered here for the purpose of comparative study. Algorithm #1: Let A be the original image and Z is the structuring element. Then the dilation of the image A by the structuring element Z is denoted by A⊕Z. Now the original image is subtracted from the dilated version of the image to obtain the edge map 𝐸𝑑 𝐴 . 𝐸𝑑 𝐴 = 𝐴 ⊕ 𝑍 − 𝐴 (1) Algorithm #2: The erosion of the image A by the structuring element Z is denoted by A⊝Z. Now the eroded image is subtracted from the original image to obtain the edge map. 𝐸𝑒 𝐴 = 𝐴 − 𝐴 ⊝ 𝑍 (2) Algorithm #3: Edge detection by subtracting the filtered version from the original 3D image using the operations of closing, opening and then once again closing, from the filtered version of the original image using the operations of closing, opening, closing and then dilation. The whole operation is expressed by the following equation. 𝐸𝑚 𝐴 = ((((A•Z)∘Z)•Z)⊕Z) - (((A•Z)∘Z)•Z) (3) Algorithm #4: Consider the 7-neighborhood 3-D mask shown in here Repeat sliding this7-neighborhood mask over the 3-D image. {at every stage of computation, find the maximum grayvalue G_max; find the minimum gray value G_min; if the difference between these two values D is less than or equal to a threshold value T specified by the user, then assign the value 0 to all the seven cells, else slide the mask further on} until the mask spans the entire 3-D image.
Algorithm #5 - Modified version of Algorithm #3 The processing time involved in detecting edges from a large 3D image is quite high. Moreover, one cannot afford to lose fine details of medical images in the process of noise removal. So, we suggest here the following modification in the Algorithm #3. Eo(A) = ((A∘Z)⊕Z) - (A∘Z) (4) TEMPLATE DESIGN © 2008
www.PosterPresentations.com
EBED
Number of Voxels Before Processing 14834427
DBED
14834427
614731
16.00
MFED
14834427
302602
139.70
OBED
14834427
307344
46.93
CLAP-BED
14834427
426478
18.91
Algorithm
Number of Voxels After Processing
Processing Time (In Seconds)
565475
16.00
References 1. Zhao Yu-qian, Gui Wei-hua, Chen Zhen-cheng, Tang Jing-tian, Li Ling-yun, “Medical image edge detection based on mathematical morphology”, In Proc. 27thAnnu. Conf. Engineering in Medicine and Biology, Shangai, China, 2005, pp. 6492–6494. 2. Rajan, E. G., “Cellular logic array processing for high through put image processing systems”, Sadhana, Vol. 18, issue 2, pp. 279-300, Springer. 3. Rajan, E.G., “Symbolic computing: signal and image processing”, Anshan Publications, United Kingdom, 2005. 4. Rajan, E. G., “High-throughput cellular logic array processing of remotely sensed imageries, International Conference on Remote Sensing & GIS, JNTU, Hyderabad, 1992. 5. Rajan, E. G., “High-throughput cellular logic array processing of satellite data for geophysical surveying”, invited paper, no. A.1-S.1.08, World Space Congress, Washington, DC, September 1992.
