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Patch-Based Label Fusion with Structured Discriminant Embedding for Hippocampus Segmentation

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Abstract

Automatic and accurate segmentation of hippocampal structures in medical images is of great importance in neuroscience studies. In multi-atlas based segmentation methods, to alleviate the misalignment when registering atlases to the target image, patch-based methods have been widely studied to improve the performance of label fusion. However, weights assigned to the fused labels are usually computed based on predefined features (e.g. image intensities), thus being not necessarily optimal. Due to the lack of discriminating features, the original feature space defined by image intensities may limit the description accuracy. To solve this problem, we propose a patch-based label fusion with structured discriminant embedding method to automatically segment the hippocampal structure from the target image in a voxel-wise manner. Specifically, multi-scale intensity features and texture features are first extracted from the image patch for feature representation. Margin fisher analysis (MFA) is then applied to the neighboring samples in the atlases for the target voxel, in order to learn a subspace in which the distance between intra-class samples is minimized and the distance between inter-class samples is simultaneously maximized. Finally, the k-nearest neighbor (kNN) classifier is employed in the learned subspace to determine the final label for the target voxel. In the experiments, we evaluate our proposed method by conducting hippocampus segmentation using the ADNI dataset. Both the qualitative and quantitative results show that our method outperforms the conventional multi-atlas based segmentation methods.

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Acknowledgements

This work is supported in part by NSFC project 61701324, Sience&Technology Department of Sichuan Province 2016JZ0014, Open Fund Project of Fujian Provincial Key Laboratory of Information Processing and Intelligent Control (Minjiang University) (No. MJUKF201715).

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Authors and Affiliations

  1. College of Computer Science, Sichuan University, Chengdu, China

    Yan Wang & Jiliu Zhou

  2. Fujian Provincial Key Laboratory of Information Processing and Intelligent Control (Minjiang University), Fuzhou, 350121, China

    Yan Wang

  3. Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, China

    Guangkai Ma

  4. Department of Computer Science, Chengdu University of Information Technology, Chengdu, China

    Xi Wu & Jiliu Zhou

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  1. Yan Wang
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  2. Guangkai Ma
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  3. Xi Wu
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Correspondence to Yan Wang.

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Appendix

Appendix

Given a sampled voxel z, the texture information from the image H we extract in this paper includes:

  1. 1.

    Outputs of FODs:

$$ \left\{H\left(\boldsymbol{z}+\boldsymbol{u}\right)-H\left(\boldsymbol{z}-\boldsymbol{u}\right),\boldsymbol{u}=\left(r\cos \theta \sin \phi, r\sin \theta \sin \phi, r\cos \phi \right)\right\} $$
  1. 2.

    Outputs of SODs:

$$ \left\{H\left(\boldsymbol{z}+\boldsymbol{u}\right)+H\left(\boldsymbol{z}-\boldsymbol{u}\right)-2H\left(\boldsymbol{z}\right),\boldsymbol{u}=\left(r\cos \theta \sin \phi, r\sin \theta \sin \phi, r\cos \phi \right)\right\} $$
  1. 3.

    Outputs of 3D Hyper plan filters:

$$ \left\{{\Psi_1}^{\ast}\left(H\left({C}_{3,3,1}\left(\boldsymbol{z}+\boldsymbol{u}\right)\right)-H\left({C}_{3,3,1}\left(\boldsymbol{z}-\boldsymbol{u}\right)\right)\right),\boldsymbol{u}=\left(0,0,1\right),{\Psi}_1=\left[\begin{array}{ccc}1& 1& 1\\ {}1& 1& 1\\ {}1& 1& 1\end{array}\right]\right\} $$
  1. 4.

    Outputs of 3D Sobel filters:

$$ \left\{{\Psi_2}^{\ast}\left(H\left({C}_{3,3,1}\left(\boldsymbol{z}+\boldsymbol{u}\right)\right)-H\left({C}_{3,3,1}\left(\boldsymbol{z}-\boldsymbol{u}\right)\right)\right),\boldsymbol{u}=\left(0,0,1\right),{\Psi}_2=\left[\begin{array}{ccc}1& 2& 1\\ {}2& 3& 2\\ {}1& 2& 1\end{array}\right]\right\} $$
  1. 5.

    Outputs of Laplacian filters:

$$ \sum \limits_{{\boldsymbol{z}}_1\in {O}_p\left(\boldsymbol{z}\right)}\left(H\left({\boldsymbol{z}}_1\right)-H\left(\boldsymbol{z}\right)\right),{O}_p\left(\boldsymbol{z}\right)\subseteq {C}_{3,3,3}\left(\boldsymbol{z}\right) $$
  1. 6.

    Outputs of range difference filters:

$$ {\max}_{{\boldsymbol{z}}_1\in {O}_p\left(\boldsymbol{z}\right)}\left(H\left({\boldsymbol{z}}_1\right)\right)-\underset{{\boldsymbol{z}}_1\in {O}_p\left(\boldsymbol{z}\right)}{\min}\left(H\left({\boldsymbol{z}}_1\right)\right),{O}_p\left(\boldsymbol{z}\right)\subseteq {C}_{3,3,3}\left(\boldsymbol{z}\right) $$

where Ca, b, c(z) represents a cube centered at z with size of a × b × c, u is the offset vector, r is the length of u, θ and ϕ are two rotation angles of u, Op(z) denotes the voxels in the p-neighborhood of z, ∗ denotes the convolution operation. FODs and SODs detect intensity change along a line segment. Here, we set r ∈ {1, 2, 3}, θ ∈ {0, π/4, π/2, 3π/4}, and ϕ ∈ {0, π/4, π/2}. 3D Hyperplane filters and 3D Sobel filters are the extensions of FODs and SODs in the plane. Filters along two other directions are also implemented. Laplacian filters are isotropic and detect second-order intensity changes. Range difference filters compute the difference between maximal and minimal values in the neighborhood for each voxel. In this paper, we determine the size of a neighborhood p ∈ {7, 19, 27}.

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Wang, Y., Ma, G., Wu, X. et al. Patch-Based Label Fusion with Structured Discriminant Embedding for Hippocampus Segmentation. Neuroinform 16, 411–423 (2018). https://doi.org/10.1007/s12021-018-9364-2

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