Methods and systems for fast automatic brain matching via spectral correspondence
View Patent ↗Methods and systems determine a correspondence of two sets of data, each data set represents an object. A weighted graph is created from each data set, and a Laplacian is determined for each weighted graph, from which spectral components are determined. The spectral components determine a coordinate of a node in a weighted graph. Nodes of a weighted graph are weighted with a quantified feature related to anode. A coordinate related to a quantified feature of a node is added to the coordinate based on the spectral components. Spectral components related to a weighted graph are reordered to a common ordering. Reordered spectral components related to the first and second data set are aligned and a correspondence is determined. An object may be a brain and a feature may be a sulcal depth. Other objects for which a correspondence may be determined include an electrical network, an image and a social network.
1. A method for determining a correspondence between a first set of data and a second set of data, representing a first brain and a second brain, respectively, comprising:
a processor creating a first mesh from the first set of data and a second mesh from the second set of data;
the processor determining a Laplacian matrix for a weighted graph representing a mesh;
determining by eigendecomposition a first and a second spectrum related to the first and second mesh;
assigning to each node in each mesh a coordinate based on one or more spectral components of the related spectrum;
assigning to each node in each mesh an additional coordinate based on a quantified feature of the node;
aligning the reordered first and second spectrum to determine a correspondence between the first and second mesh.
2. The method of claim 1 , wherein the Laplacian matrix reflects a weight of a node in its related weighted graph that expresses a quantified feature of the node.
3. The method of claim 2 , wherein the quantified feature is selected from the group consisting of a sulcal depth, a brain curvature and a cortical thickness.
4. The method of claim 2 , wherein weighting of nodes in the Laplacian matrix is achieved by evaluating an expression:
{tilde over (L)}=GL , with
{tilde over (L)} representing the Laplacian matrix modified for node weights, L representing a Laplacian matrix that is unmodified for node weights and G representing a matrix of node weights.
5. The method of claim 4 , wherein the matrix represented by G is dependent on at least one set of weighting factors of nodes, each weighting factor in the set being dependent on a quantified feature of that node.
6. The method of claim 1 , wherein the quantified feature of the additional coordinate is selected from the group consisting of a sulcal depth, a brain curvature and a cortical thickness.
7. A system to determine a correspondence between a first set of data and a second set of data, representing a first brain and a second brain, respectively, comprising:
a memory, enabled to store the first set of data, the second set of data and instructions;
a processor, enabled to retrieve instructions from the memory to perform the steps:
creating a first mesh from the first set of data and a second mesh from the second set of data;
determining a first and a second Laplacian matrix for a weighted graph of the first and the second mesh, respectively;
determining by eigendecomposition a first and a second spectrum related to the first and second mesh;
assigning to each node in each mesh a coordinate based on one or more spectral components of the related spectrum;
assigning to each node in each mesh an additional coordinate based on a quantified feature of the node; and
aligning the first and second spectrum to determine a correspondence between the first and second mesh.
8. The system of claim 7 , wherein the first and second Laplacian matrix each reflects a weight of a node in its related weighted graph that expresses a quantified feature of the node.
9. The system of claim 8 , wherein the quantified feature is selected from the group consisting of a sulcal depth, a brain curvature and a cortical thickness.
10. The system of claim 8 , wherein weighting of nodes in the Laplacian matrix is achieved by evaluating an expression:
{tilde over (L)}=GL , with
{tilde over (L)} representing the Laplacian matrix modified for node weights, L representing a Laplacian matrix that is unmodified for node weights and G representing a matrix of node weights.
11. The system of claim 10 , wherein the matrix represented by G is dependent on at least one set of weighting factors of nodes, each weighting factor in the set being dependent on a quantified feature of that node.
12. The system of claim 7 , wherein the quantified feature of the additional coordinate is selected from the group consisting of a sulcal depth, a brain curvature and a cortical thickness.