A Fast and Precise Method for Searching Rectangular Tumor Regions in Brain MR Images

TL;DR

This work tackles fast and precise localization of rectangular ROI in brain MRI for applications like MRSI, by combining a segmentation network (U-Net with an EfficientNet encoder) with a $9$-dimensional exhaustive search over $V$, $R$, and $\Theta$. It leverages $3$D summed-area tables to compute ROI sums in $O(1)$ time per candidate and introduces a new $f_{proposed}$ metric that biases toward cube-like shapes and higher tumor fractions. On BraTS-derived data, the method achieves dramatic speedups (about $8$ seconds vs $11$–$40$ minutes) and improves ROI quality over conventional metrics, with controllable trade-offs between volume accuracy and tumor fraction via $\lambda_2$. The approach offers a practical, scalable tool for rapid, reliable rectangular ROI placement in brain tumor diagnosis and MR-guided planning.

Abstract

Purpose: To develop a fast and precise method for searching rectangular regions in brain tumor images. Methods: The authors propose a new method for searching rectangular tumor regions in brain MR images. The proposed method consisted of a segmentation network and a fast search method with a user-controllable search metric. As the segmentation network, the U-Net whose encoder was replaced by the EfficientNet was used. In the fast search method, summed-area tables were used for accelerating sums of voxels in rectangular regions. Use of the summed-area tables enabled exhaustive search of the 3D offset (3D full search). The search metric was designed for giving priority to cubes over oblongs, and assigning better values for higher tumor fractions even if they exceeded target tumor fractions. The proposed computation and metric were compared with those used in a conventional method using the Brain Tumor Image Segmentation dataset. Results: When the 3D full search was used, the proposed computation (8 seconds) was 100-500 times faster than the conventional computation (11-40 minutes). When the user-controllable parts of the search metrics were changed variously, the tumor fractions of the proposed metric were higher than those of the conventional metric. In addition, the conventional metric preferred oblongs whereas the proposed metric preferred cubes. Conclusion: The proposed method is promising for implementing fast and precise search of rectangular tumor regions, which is useful for brain tumor diagnosis using MRI systems. The proposed computation reduced processing times of the 3D full search, and the proposed metric improved the quality of the assigned rectangular tumor regions.

Figures (6)

• Figure 1: The overview of the proposed method. The proposed method consisted of segmentation and search steps. In the segmentation step, all voxels were classified as tumor and non-tumor voxels. In the search step, an optimal rectangular region was searched in 9-dimensional space consisting of a 3D offset, a 3D size, and a 3D angle.
• Figure 2: The neural network used in tumor segmentation. Its input images were multi-contrast images. Its output labels were binary values consisting of 1 (tumor) and 0 (non-tumor). The network structure was the U-NetUNet structure whose encoder was replaced by the EfficientNetEfficientNet.
• Figure 3: A summed-area table in a 2D case. As shown in (a), a summed-area table can be computed by summing rectangular regions from the left-top pixel to all pixels. As shown in (b), a sum of a rectangular region can be computed by a fixed number of add/subtract operations if the summed-area table is precomputed. For the sake of conciseness, a 2D summed-area table is explained in these figures. Actual implementation used 3D summed-area tables.
• Figure 4: A summary of the proposed search method. The search of rectangular regions optimized 9D space using summed-area tables. Summed-area tables were generated for individual 3D angles. Whenever one of 6 parameters consisting of the 3D angle and 3D size was focused for searching, remaining 5 parameters were not changed. For each candidate of the focused parameter, the optimal 3D offset was also searched. Each focused parameter was searched in parallel using multi-threading.
• Figure 5: Representative images, tumor labels, and rectangular regions in the cases of searching $30 \times 30 \times 30$$\text{mm}^3$ regions. The segmentation images represent estimated tumor regions. The rectangular regions were filled with green. As shown in the cases of the rectangular regions using the conventional metric (conv.m), the conventional metric preferred oblongs. The extracted shapes of the rectangular regions were similar in the cases of both 1-dimensional search (p1D) and 3-dimensional search (p3D). The shapes of the rectangular regions using the proposed metric (prop.m) were close to cubes since the proposed metric gave priority to cubes over oblongs. When the segmentation network with 2 inputs was used instead of that with 4 inputs, the results were slightly changed as shown in segmentation-2 and prop.m-2.