In virtual colonoscopy, CT scans are typically acquired with the patient in both supine (facing up) and prone (facing down) positions. The registration of these two scans is desirable so that the user (physician) can clarify situations or confirm polyp findings at a location in one scan with the same location in the other, thereby improving polyp detection rates and reducing false positives. However, this supine-prone registration is challenging because of the substantial distortions in the colon shape due to the patient’s position shifting. We present an efficient algorithm and framework for performing this registration through the use of conformal geometry to guarantee the registration is a diffeomorphism (a one-to-one and onto mapping). The taenia coli and colon flexures are automatically extracted for each supine and prone surface employing the colon geometry. The two colon surfaces are divided into several segments using the flexures. Each of the colon segments is conformally flattened to the rectangular domain using holomorphic differentials with the taenia coli. For both, the mean curvature are color encoded as texture images, from which feature points are automatically detected using graph cut segmentation, mathematic morphological operations, and principal component analysis. Using these corresponding features, the conformal flattening is adjusted to be quasi-conformal such that the features become aligned. We demonstrate the efficiency and efficacy of our registration method by illustrating matched views on both the 2D flattened colon images and in the 3D volume rendered colon interior view. We evaluate the correctness of the results by measuring the distance between features on the registered colons.
We propose a new colon flattening algorithm that is efficient, shape-preserving, and robust to topological noise. Unlike previous approaches, which require a mandatory topological denoising to remove fake handles, our algorithm directly flattens the colon surface without any denoising. In our method, we replace the original Euclidean metric of the colon surface with a heat diffusion metric that is insensitive to topological noise. Using this heat diffusion metric, we then solve a Laplacian equation followed by an integration step to compute the final flattening. We demonstrate that our method is shape-preserving and the shape of the polyps are well preserved. The flattened colon also provides an efficient way to enhance the navigation and inspection in virtual colonoscopy. We further show how the existing colon registration pipeline is made more robust by using our colon flattening. We have tested our method on several colon wall surfaces and the experimental results demonstrate the robustness and the efficiency of our method.
We introduce a simple, yet powerful method called the Cumulative Heat Diffusion for shape-based volume analysis, while drastically reducing the computational cost compared to conventional heat diffusion. Unlike the conventional heat diffusion process, where the diffusion is carried out by considering each node separately as the source, we simultaneously consider all the voxels as sources and carry out the diffusion, hence the term cumulative heat diffusion. In addition, we introduce a new operator that is used in the evaluation of cumulative heat diffusion called the Volume Gradient Operator (VGO). VGO is a combination of the LBO and a data-driven operator which is a function of the half gradient. The half gradient is the absolute value of the difference between the voxel intensities. The VGO by its definition captures the local shape information and is used to assign the initial heat values. Furthermore, VGO is also used as the weighting parameter for the heat diffusion process. We demonstrate that our approach can robustly extract shape-based features and thus forms the basis for an improved classification and exploration of features based on shape.
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