Clustering of Medical Images for Analysis: A Fuzzy Approach
Authors: Dakua Sarada Prasad , Navkar Nikhil , Abinahed Julien , Younes Georges , Al-Ansari Abdulla A. 
Published: July 2019

Background and Objective

Often times, clinicians use a three-dimensional set of medical images to diagnose and plan treatments, which typically include visual identification of structures such as bones and tissues [1]. This can be a challenging task as anatomical structures of interest can contain significant noise, and easily blend with neighboring tissues. We propose to tackle 2 cases: (a) treatment planning of pelvic fractures where a small size ring formed by the fused bones of the ischium, ilium, and pubis attached to the sacrum contains vital structures (including major blood vessels, nerves, digestive and reproductive organs) and should be carefully delineated, and (b) liver cancer treatment where malignant tissue has to be carefully removed. The pixel intensity of tumor is similar to those of healthy tissue and proper delineation is of utmost important before proceeding to plan therapy.

To address the aforementioned challenges, in this work we present a soft-clustering technique using Enhanced Fuzzy C-Means (EFCM) along with a bilateral filter to detect the region of interest. The key feature of the proposed algorithm combines domain and range filtering allowing the filter to maintain balance between preservation of relevant details and the degree of noise reduction. The approach allows traditional Fuzzy C-Means not only to exploit useful spatial information, but also to dynamically minimize clustering errors caused by common noise in medical images.

Methodology

A three-step workflow is used to process the medical images:

Step 1: After MR/CT images are acquired; clinician initially draws a rough outline around the region of interest (where the fracture or tumor is present) on the two-dimensional image slices. The manual input reduces the computational time to determine the desired tissue cluster by providing the region of interest instead of scanning/processing the entire image.

Step 2: In this step, a bilateral filter is used to remove noise while preserving details of the edges [2]. Linear filters, such as Gaussian, compute a weighted average of pixel values in the neighborhood. The weights decrease with distance from the neighborhood center. This works well for images where local neighboring pixels have similar values (slow spatial variation). As the noise that corrupts these neighboring pixels is mutually less correlated than the signal, the noise is averaged away while signal is preserved. However, the assumption of slow spatial variations fails at edges, which are consequently blurred by linear low-pass filtering. In this context, we use a non-linear/bilateral filter that combines both domain and range filtering. In smooth regions, the pixel values within a local neighborhood are similar to each other, and the normalized similarity function is close to one. Consequently, the bilateral filter acts essentially as a standard domain filter, averages away the weakly correlated differences between pixel values caused by noise, and preserves edge details.

Step 3: As a last step, EFCM clustering algorithm is applied to the noise-filtered image. Fuzzy C-Means clustering works by assigning membership to each data point with respect to the cluster centers [3]. A distance is computed between the cluster center and the data point. The membership of the data towards a particular cluster center varies linearly as per the distance. Closer the data to a cluster center, higher is its membership. The summation of membership of each data point across different clusters is equal to one. An objective function based on the Euclidean metric is then used to update the membership and cluster centers iteratively. However, the parameter estimation resulting from the described objective function may not be robust in a noisy environment. Therefore in this work, we develop an algorithm that uses a modified Euclidean term (described in Table I) that is robust against noise and allows meaningful clustering of compact pixels for image analysis by the clinicians (Fig. 1).

Results and Conclusion

The method proposed in this work was evaluated using two datasets: (a) CT images of pelvic fracture (two subjects) publicly available online for research purposes, on OsiriX website (http://www.osirix-viewer.com/datasets). The image acquisition details are as followed: Slice Thickness: 2 mm, Pixel Spacing: 0.29 mm ×  0.29 mm, Bit-depth: 12, and Acquisition Matrix: 512 × 512. (b) CT images containing liver with tumor from five anonymized subjects, obtained from Hamad Medical Corporation, Doha, Qatar. The image acquisition details are as followed: Slice Thickness: 3 mm, Pixel Spacing: 0.32 mm ×  0.32 mm, Bit-depth: 16, and Acquisition Matrix: 512 × 512.

The algorithms were implemented on MATLAB R2013a running on a workstation with 16 GB RAM and 2.8 GHz Intel processor. The average time required to perform segmentation was recorded as 8 ±  1.5 minutes. However the computational time could be further reduced, as implementation was done without optimization of the internal function calls. An initial assessment of the experimental results has shown satisfactory outcomes in both the cases to detect pelvic fracture and liver tumor (Fig. 1). The use of traditional linear filters on the datasets has failed to identify clusters with similar pixel intensity values. The use of bilateral filter with Euclidean modification proposed in this work has lead to desired soft clustering identifying the required anatomical structures in the images.

In future, we plan to optimize and validate the method extensively on different tissue-types using multiple imaging modalities.

References

[1] Vona G. et al., “Impact of cyto-morphological detection of circulating tumor cells in patients with liver cancer,” Hepatology, 39, 792–797, 2004.

[2] Sugimoto K. et al., “Compressive Bilateral Filtering,” IEEE Trans. on Image Processing, 24, 3357–3369, 2015.

[3] Havens T. C., “Fuzzy c-Means Algorithms for Very Large Data,” IEEE Trans. on Fuzzy Systems, 20, 1130–1146, 2012.