Similarly, the computational complexity is the same for any other orientation. Therefore, we pre-compute the local CMs along all K orientations, i. We then start an iterative loop, consisting of two phases, where we update the label image, L , at each iteration. The generated L at each iteration becomes the new L 0 for the next iteration.
We start with the first phase and after a predefined number of phase-1 iterations, t , switch to the second phase. Then, during the phase-2 iterations, we stop the loop if there is no more change in L , or when the iteration number reaches a predefined maximum. Note that, due to the randomness introduced in the first phase, one may obtain slightly different results by repeating a segmentation experiment. We also compared it with three other unsupervised segmentation algorithms: the watershed segmentation 5 , a Gaussian-mixture-model-based hidden-Markov-random-field GMM-HMRF model 7 initialized with k-means clustering and the simple linear iterative clustering SLIC superpixel algorithm 8 with constant compactness.
For watershed segmentation, we created the edge map of the image using the Sobel filter, computed its h-minima transform, i. Next, for each method, we determined the optimal parameter values: in the 2D X-ray Image Segmentation and the 3D Abdominal MR Image Segmentation sections by heuristically choosing the least over-segmented result among those segmentation results that reflected all major anatomical regions and in the 3D Cardiovascular MR Image Segmentation section once by choosing the result with the highest mean Dice score and a second time by cross validation.
Label edges are shown in black for better contrast and clearer visualization in the figures. We also used a simple greedy algorithm to roughly match the colors of overlapping labels among subfigures for easier comparison. Here and in the 3D Abdominal MR Image Segmentation section, images were initially normalized to have intensity values between 0 and 1. The 1D image intensity profile along the horizontal blue line in Fig. The local CM curve red can be seen to be almost piecewise constant, with its values indicating the centers of the 1D intervals.
Left: Image intensity profile blue of the horizontal blue line in Fig. Informed consent was obtained after the nature and possible consequences of the studies were explained. The T1-weighted image had been acquired with the voxel size of 1. We upsampled the volume in the slice-selection direction with linear interpolation to obtain a 1.
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Lastly, for a quantitative assessment of the performance of the four methods, we used a public dataset of 10 cardiovascular MR images 13 acquired at 1. We divided each image by its intensity standard deviation and then normalized the images by the same constant so their maxima were on average 1 their minima were 0. Then, for each subject and each method, we chose the optimal segmentation result that produced the maximal Dice score averaged across the two labels. As can be seen, the proposed local-CM-based method resulted in a higher mean optimal Dice score than the competing methods did.
The vertical axis shows the best score achieved with respect to the remaining parameter. Alternatively, we also performed a leave-one-out cross validation CV by testing the methods on a left-out subject with the median of the optimal parameter values computed from the other 9 subjects, repeating it 10 times each time leaving out a different subject and averaging the Dice scores. We distributed the above experiments to different processors with inhomogeneous hardware.
Note that, to ensure convergence for all tests, we ran our method for a high total of iterations; however, one could reduce the number of phase-2 iterations and still obtain reasonable results. Further actions to gain speed would be to use a smaller number of orientations, K and to run the algorithm on a graphics processing unit GPU. As the figures demonstrate, the proposed local-CM-based method generally produced less over-segmented results than the rest of the methods did except in the background.
This may be because our method assigns each pixel label by considering — not only the neighboring pixels, but — the entire image. Increasing h improved the over-segmentation by the watershed method, but at the price of not capturing some boundaries.http://www.emirelektronik.com/wp-includes/333/2270.php
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The watershed method, however, resulted in better-defined borders between articular cartilages Fig. The GMM-HMRF model seems to emphasize more the image intensity than the geometry of a segment, hence leading to rather tissue- than organ-specific segmentation. This model is not so successful in segmenting individual bones Fig. Regarding the SLIC segmentation, the borders of its individual bone and organ labels do not seem as well-defined as the segmentation by the proposed method.
Also, as expected, larger regions such as the background are divided into many superpixels.
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To accurately evaluate the performance of the segmentation methods, we have avoided any postprocessing, such as region-merging techniques 6 that could potentially alleviate the over-segmentation issue. The latter may be because the ventricular myocardium and the blood pool are rather tissue types, whose image intensities are suitable for mixture models see above. Note that the Dice scores were produced without any shape prior or training.
Nonetheless, given that we tuned one or two parameters for each method, our evaluation of the four methods can be considered as mostly but not totally unsupervised.
We have empirically computed the optimal parameter values in our experiments and provided them throughout the Results section. In practice, these values can be a good starting point for the interested reader who wants to try the proposed CM-based segmentation on a new image that has intensities normalized between 0 and 1. To reduce the runtime, the algorithm can be run with considerably lower numbers of orientations K and iterations, while still producing reasonable results.
Moreover, our publicly available codes the Data Availability section are GPU-compatible, making it possible to significantly speed up the computation. Our algorithm uses the CM of a region as a reference point, whose label it iteratively propagates to the rest of the pixels in that region. If such a reference point is located inside the region, it will be unique to the region. This is, yet, not guaranteed to be the case in higher dimensions, unless the region is convex. Being always inside the region, 1D CMs can be used as reference points with labels that are unique to the region.
A drawback of this approximation though is that, in a highly nonconvex region, more iterations may be needed for the label to propagate entirely. In some cases, the algorithm may even converge to a locally optimal result where a non-convex region is over-segmented. The two labels computed for the background in Fig. Nevertheless, choosing a large enough number of phase-1 iterations t can alleviate this issue and, in fact, many nonconvex regions can be seen to have been successfully segmented by the proposed method.
Lastly, if an initial segmentation for some parts of the image is available, it can be used to initialize the labels instead of random assignment. The labels in those regions can be chosen to either remain fixed or get updated in the iterations. This is especially useful for semi-automatic segmentation, where the user provides some information to the algorithm on which pixels should be grouped together. We have introduced a new unsupervised medical image segmentation approach that groups the pixels in each region based on the local CMs of the region.
Through qualitative and quantitative validation, we have shown the proposed method to often outperform three existing unsupervised segmentation methods. The rest of the coauthors declare no potential competing interests. Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. National Center for Biotechnology Information , U. Sci Rep. Published online Aug Iman Aganj , 1, 2 Mukesh G. Harisinghani , 1, 3 Ralph Weissleder , 1, 3 and Bruce Fischl 1, 2.
Mukesh G. Author information Article notes Copyright and License information Disclaimer. Iman Aganj, Email: ude. Corresponding author. Received May 9; Accepted Aug This article has been cited by other articles in PMC. Abstract Image segmentation is a critical step in numerous medical imaging studies, which can be facilitated by automatic computational techniques. Introduction Image segmentation is the process of partitioning the set of image pixels into subsets, where the pixels in each subset are related, e.
Computational Complexity Reduction To make the problem tractable, we must choose w such that, while it serves the abovementioned pixel-grouping purpose, the computational cost of C can also be reduced. Open in a separate window. Figure 1. Image Segmentation We now employ the aforementioned 1D local CM computation method to develop an iterative algorithm for unsupervised segmentation of a 2D or 3D image with N pixels.
Figure 2. Figure 3. Figure 4. Figure 5. The two most common tasks in whole slide tissue image analysis are the segmentation of microscopic structures, like nuclei and cells, in tumor and non-tumor regions and the classification of image regions and whole images. Computerized detection and segmentation of nuclei is one of the core operations in histopathology image analysis.
This operation is crucial to extracting, mining, and interpreting sub-cellular morphologic information from digital slide images. Cancer nuclei differ from other nuclei in many ways and influence tissue in a variety of ways. Accurate quantitative characterizations of the shape, size, and texture properties of nuclei are key components of the study of the tumor systems biology and the complex patterns of interaction between tumor cells and other cells.
Image classification, carried out with or without segmentation, assigns a class label to an image region or an image. It is a key step in computing a categorization via imaging features of patients into groups for cohort selection and correlation analysis. Methods for segmentation and classification have been proposed by several research projects Gurcan et al.
Xing and Yang provide a good review of segmentation algorithms for histopathology images. A CNN algorithm was developed by Zheng et al. A method based on ensembles of support vector machines for detection and classification of cellular patterns in tissue images was proposed by Manivannan et al.
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Al-Milaji et al. Xu et al. These features are aggregated to classify whole slide tissue images. A method that learns class-specific dictionaries for classification of histopathology images was proposed by Vu et al. Kahya et al. Their method employs sparse support vector machines and Wilcoxon rank sum test to assign and assess weights of imaging features.