An Interval Iteration Based Multilevel Thresholding Algorithm for Brain MR Image Segmentation

Abstract

In this paper, we propose an interval iteration multilevel thresholding method (IIMT). This approach is based on the Otsu method but iteratively searches for sub-regions of the image to achieve segmentation, rather than processing the full image as a whole region. Then, a novel multilevel thresholding framework based on IIMT for brain MR image segmentation is proposed. In this framework, the original image is first decomposed using a hybrid L1 − L0 layer decomposition method to obtain the base layer. Second, we use IIMT to segment both the original image and its base layer. Finally, the two segmentation results are integrated by a fusion scheme to obtain a more refined and accurate segmentation result. Experimental results showed that our proposed algorithm is effective, and outperforms the standard Otsu-based and other optimization-based segmentation methods.

An Efficient and Fast Sparse Grid Algorithm for High-Dimensional Numerical Integration

“…When d > 30, the classical MC method fails to produce a computed result with a relative error of order 10 −5 . As explained in [20], the MC method requires more than 10 10 randomly sampled integration points and then needs independently to compute their function values, which is a tall order to do on a regular workstation. Next, we come to address a natural question that asks how high the dimension d can be handled by the MDI-SG method.…”

“…To some certain extent, those methods are effective for computing integrals in low and medium dimensions (i.e., d 100), but it is still a challenge for them to compute integrals in very high dimensions (i.e., d ≈ 1000). This is the second installment in a sequel [20] which aims at developing fast numerical algorithms for high-dimensional numerical integration. As mentioned above, the straightforward implementation of the TP method will evidently run into the CoD dilemma.…”

“…As mentioned above, the straightforward implementation of the TP method will evidently run into the CoD dilemma. To circumvent the difficulty, we proposed in [20] a multilevel dimension iteration algorithm (called MDI-TP) for accelerating the TP method.…”

Self-Adaptive Image Thresholding within Nonextensive Entropy and the Variance of the Gray-Level Distribution

“…The Otsu algorithm [4] is widely adopted to deal with images having a bimodal histogram distribution and can be easily extended to multi-level image segmentation [5][6][7][8][9]. The entropy-based algorithm [10][11][12][13][14] is another option for image segmentation since the gray-level histogram can be considered as a kind of probability distribution, and maximization of the corresponding entropies is a nature-inspired means of finding the optimal thresholds.…”