**Author**: Qianqian Fang <fangq at nmr.mgh.harvard.edu>

- Photon Migration Lab
- Martinos Center for Biomedical Imaging
- Massachusetts General Hospital (Harvard Medical School)
- Bldg. 149, 13th St., Charlestown, MA 02148

- 1. Introduction
- 2. List of functions
- 3. Acknowledgement

"Metch", coined from "mesh" and "match", is a Matlab/Octave-based mesh/volume registration toolbox. It provides straightforward functions to register point clouds (or surfaces) to a triangular/cubic surface mesh by calculating an optimal affine transformation (in terms of matrix A for scaling and rotation, and b for translation). It also allows one to project a point cloud onto the surface using surface norms and guarantee the conformity of the points to the surface.

A GUI to register a point cloud to a mesh or volumetric image

parameters: node: node coordinate of the surface mesh (nn x 3) elem: element list of the surface mesh (3 columns for triangular mesh, 4 columns for cubic surface mesh)

the input can also be two parameters in form of metchgui(volume,points), where volume is a 3D image (array).

outputs: alldata: a structrure containing all processing outputs the fields include: .node: the input node .elem: the input surface mesh elements .volume: if the input volumetric image .A0: the affine rotation for selected point pairs (after Initialize) .b0: the affine translation for selected point pairs (after Initialize) .A: the affine rotation for the point cloud (after Optimize) .b: the affine translation for the point cloud (after Optimize) .points: the input point cloud .pointsinit: the point cloud after initialization .pointsopt: the point cloud after optimization .pointsproj: the point cloud after projecting to the surface .initplot: the handle to the point cloud plot after init .optplot: the handle to the point cloud plot after optimization .projplot: the handle to the point cloud plot after projection

If user supplys an output variable, the GUI will not return until the user hits the "close" button or close the window; if user does not supply any output, the call will return immediately; any data user intends to save, he has to click on "Save Session" button and provides a mat-file file name. A single structure named "metchsession" will be stored in this file.

This function is matlab-only.

this is the same as metchgui.m except it does not need metchgui.fig in order to run. It can also be run on lower versions of matlab.

Perform point cloud registration to a triangular surface (surface can be either triangular or cubic), Gauss-Newton method is used for the calculation

parameters: node: node coordinate of the surface mesh (nn x 3) elem: element list of the surface mesh (3 columns for triangular mesh, 4 columns for cubic surface mesh) p: points to be registered, 3 columns for x,y and z respectively pmask: a mask vector with the same length as p, determines the method to handle the point, if pmask(i)=-1, the point is a free node and can be move by the optimization, if pmask(i)=0, the point is fixed; if pmask(i)=n>0, the distance between p(i,:) and node(n,:) will be part of the object function and be optimized A0: a 3x3 matrix, as the initial guess for the affine A matrix (rotation&scaling) b0: a 3x1 vector, as the initial guess for the affine b vector (translation) cmask: a binary 12x1 vector, determines which element of [A(:);b] will be optimized maxiter: a integer, specifying the optimization iterations

outputs: newpos: the registered positions for p, newpos=A*p'+b

project a point cloud on to the surface mesh (surface can only be triangular)

parameters: v: node coordinate of the surface mesh (nn x 3) f: element list of the surface mesh (3 columns for triangular mesh, 4 columns for cubic surface mesh) pt: points to be projected, 3 columns for x,y and z respectively nv: nodal norms (vector) calculated from nodesurfnorm.m with dimensions of (size(v,1),3) cn: a integer vector with the length of p, denoting the closest surface nodes (indices of v) for each point in p. this value can be calculated from dist2surf.m

if nv and cn are not supplied, proj2mesh will project the point cloud onto the surface by the direction pointing to the centroid of the mesh

outputs: newpt: the projected points from p elemid: a vector of length of p, denotes which surface trangle (in elem) contains the projected point weight: the barycentric coordinate for each projected points, these are the weights

calculate an affine transform (A matrix and b vector) to map n vertices from one space to the other using least square solutions

parameters: pfrom: nx3 matrix, each row is a 3d point in original space pto: nx3 matrix, each row is a 3d point in the mapped space

outputs: A: 3x3 matrix, the calculated affine A matrix b: 3x1 vector, the calculated affine b vector

the solution will satisfy the following equation: A*pfrom'+b=pto

calculate the distances from a point cloud to a surface, and return the indices of the closest surface node

parameters: node: node coordinate of the surface mesh (nn x 3) nv: nodal norms (vector) calculated from nodesurfnorm.m with dimensions of (size(node,1),3), this can be calcuated from nodesurfnorm.m pt: points to be calculated, 3 columns for x,y and z respectively

outputs: d2surf: a vector of length of p, the distances from p(i) to the surface cn: a integer vector with the length of p, the indices of the closest surface node

calculate the plane equation coefficients for a plane (determined by 3 points), the plane equation is a*x+b*y+c*z+d=0

parameters: plane: a 3x3 matrix, each row is a 3d point in form of (x,y,z) this is used to define a plane outputs: a,b,c,d: the coefficients of the plane equation

calculate the intersection of a 3d line (passing two points) with a plane (determined by 3 points)

parameters: p0: a 3d point in form of (x,y,z) p1: another 3d point in form of (x,y,z), p0 and p1 determins the line plane: a 3x3 matrix, each row is a 3d point in form of (x,y,z) this is used to define a plane outputs: isinside: a boolean variable, 1 for the intersection is within the 3d triangle determined by the 3 points in plane; 0 is outside pt: the coordinates of the intersection pint coord: 1x3 vector, if isinside=1, coord will record the barycentric coordinate for the intersection point within the triangle; otherwise it will be all zeros.

calculate a nodal norm for each vertix on a surface mesh (surface can only be triangular or cubic)

parameters: node: node coordinate of the surface mesh (nn x 3) elem: element list of the surface mesh (3 columns for triangular mesh, 4 columns for cubic surface mesh) pt: points to be projected, 3 columns for x,y and z respectively

outputs: nv: nodal norms (vector) calculated from nodesurfnorm.m with dimensions of (size(v,1),3)

calculate the surface norms for each element (surface can be either triangular or cubic)

parameters: node: node coordinate of the surface mesh (nn x 3) elem: element list of the surface mesh (3 columns for triangular mesh, 4 columns for cubic surface mesh) outputs: ev: norm vector for each surface element

This toolbox was developed with the support from NIH grant titled "Dynamic Inverse Solutions for Multimodal Imaging" (R01EB006385)