## The AIM@SHAPE Glossary

### Alphabetical list of terms

- magnetic resonance imaging
- Three-dimensional images produced by a non-invasive diagnostic procedure that uses magnetic field resonance. MRI is commonly used to obtain 3D pictures of internal body structures. In the case of dynamic MRI it is the the acquisition of a sequence of MRI images to monitor temporal changes in tissue structure.
- manifold
- A (separable Hausdoff) k-dimensional topological space M in which each point has a neighbourhood which is homeomorphic either to the k-dimensional open ball, or to the half-ball.
- marching cubes
- An algorithm that extracts an implicit surface represented by a 3D regular grid of data values. This grid is often referred to as a grid of voxels. The eight corners of a voxel give a total of alternative 256 different configurations for the corner status. By standard operations these can be group into 15 alternative configurations. Triangulations representing these 15 can be pre-computed, and thus efficiently used when tracing the implicit surface described by the grid of voxels.
- mask
- The subdivision rule for calculating a new vertex on the refined mesh, usually described by diagrams. Several masks are required to describe a subdivision scheme, e.g. mask for new vertices corresponding to old vertices, edges, faces, or boundary vertices.
- matching
- Finding the correspondence between two shapes, or finding the transformation that yields a good alignment between two shapes.
- mean curvature
- Given the principal curvatures k1 and k2, H = (k1 + k2)/2 is called the mean curvature.
- medial axis
- The medial axis of a bounded open subset X is the set of points that have at least two closest points in the complement of X.
- mesh
- A grid-like polygonal subdivision of the surface of a geometric model. More formally, it is an Euclidean d-dimensional cell complex G (actually gamma) such that any k-cell of G , with k
- meshing
- See Tessellation.
- mesh merging
- The combination of meshes resulting from different viewing directions into a single mesh.
- metadata
- From the Greek “meta”=beyond/after. Structured data about data. Metadata has become increasingly important in XML-based Web applications.
- minkowski sum
- Set of point with integer coefficients that can be obtained as sum of two vectors with integer coefficients taken from two other sets of vectors with integer.
- mocap
- See motion capture
- model composition
- A process by which a new 3D model (e.g. a mesh) is constructed by the seamless composition of two or more existing models.
- morphing
- The process of making a smooth transition between two shapes.
- morphological descriptor
- Describes the morphology of a human like: age, weight, height, gender, etc.
- morphology
- See Morphological Descriptor
- morph target
- It defines a different version of an object over time. A morph target is built by deforming/morphing a base shape of an object into a different shape that represents the same object in a different configuration. Morph targets can be used to animate 3D objects with skin interpolation.
- morse function
- A C2-differentiable function defined over a domain D in R2 such all the critical points are non-degenerate.
- morse-smale complex
- The stable (unstable) manifolds are pair-wise disjoint and decompose the domain D of a Morse-Smale function f into open cells, whose closure form a complex, called a Morse-Smale complex.
- morse-smale function
- A Morse function f is called a Morse-Smale function if and only if the stable and unstable manifolds intersect only transversally.
- morse theory
- A generalisation of calculus of variations which draws the relationship between the stationary points of a smooth real-valued function on a manifold and the global topology of the manifold.
- motion capture
- Methods for capturing movement data from a live source. The data are filtered and processed in order to replicate the same motion as the one performed by the live source on a control skeleton.
- mri
- See Magnetic Resonance Imaging.
- multigrid algorithms
- Algorithms designed to accelerate the convergence speed of basic relaxation iteration schemes (e.g. a Jacoby or Gauss-Seidel iteration) by computing corrections to the solution on coarser grids.
- multiresolution
- An analysis and/or synthesis technique that allows manipulation of geometry at different resolutions, enabling both local and global modification, modulation of details at different frequencies.
- multi-sensor data fusion
- Study of the techniques for the integration of data from multiple sensors.

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