Graphics, Geometric Modeling  Math and Numerical Methods  Physics & Mech Eng  CFD  Image (Signal) Processing 
NOTES
Also, see other lists:
Term  Meaning 

Barycentric coordinate 
Coordinates of a point in space in terms of other points.
For example the barycentric coordinates of a point along a line between two points would be (t,1t).
The barycentric coordinates of a point inside a triangle is based on the following.
Draw lines from the point, P, to each of the three vertices of the triangle, A,B,C.
The barycentric coordinates of P are: (area(P,B,C)/area(A,B,C),area(P,A,C)/area(A,B,C),area(P,A,B)/area(A,B,C)) 
BCC  Body Centered Cubic  A celullar lattice that includes a node in the middle of each cell, popular in chemistry but also used in some volumetric approaches. For example, see Bodycentered cubic. 
Chamfer  the transition surface, between two major surfaces which meet at a convex corner, usually created by the manufacturing process. 
Characteristic polyhedron  The polyhedron formed by the control points for a surface patch 
Continuity (parametric continuity; also referred to as C1, C2, etc.)  parametric continuity: For two parametric curves ra(u) and rb(u) if ra(1) = rb(0) they are c0 continuous (the endpoints meet) if ra'(1) = rb'(0) they are c1 continuous (first derivative of the endpoints is same or tangents are the same) if ra''(1) = rb''(0) they are c2 continuous (second order continuous or change in tangents is the same at the end points) 
Continuity (geometric continuity; also referred to as G1, G2, etc.)  G1 continuity is maintained if the unit tangent vectors are identical (versus C1 continuity in which the tangent vectors are identical). G2 is a similar idea but a bit more complicated in the way the math works out. 
Contour tree  From http://www.dmu.ac.uk/~mt/research.html: "A Contour Tree is a hierarchical structure describing which plateaus are totally enclosed by other plateaus." Also see http://www.cs.ubc.ca/~hcarr/research/contourtrees.html. 
Control polygon  Any sequence (mesh) of points generally used to control the shape of a curve (surface)  as opposed to the term polygon used in modeling that usually refers to a sequence of points that define a closed border of a planar surface. 
Convex hull  The minimal bounding polygon (polyhedron) of a collection of points in 2space (3space) that is convex. You can also talk about the convex hull of higher order curves (surfaces) in which case the hull bounds the curves (surfaces). 
CSG  Constructive Solid Geometry. An object description kept as a binary tree in which leaf nodes are transformed instances of primitive objects such as sphere, cylinder, cube and internal nodes are boolean combinations of the subtrees, i.e., union, difference, intersection. 
Displacement map  Similar to a texture map except the surface of the object is actually displaced by the map. 
Extrinsic  an extrinsic property of a surface is a property of the surface which is relative to the space in which it is embedded. The height of a point is extrinsic; curvature at a point is not (it is intrinsic) 
Fair  (intuitive) Refers to a surface not having extraneous bumps and wiggles. 
Fillet  the transition surface, between two major surfaces which meet at a concave corner, usually created by the manufacturing process. 
Free form deformation (FFD)  A method to distort the shape of an object in which a 3D local coordinate grid is placed around an object. The vertices of the object are located within the grid by noting their coordinate definitions relative to it. The grid is then interactively distorted by the user. The object points are then remapped back into the distorted grid using tricubic interpolation thus distorting the object. 
Frenet frame  A.k.a., moving trihedron, moving triad. Local coordinate system defined at a point on a curve, p(u), made up of tangent vector (p^{u}), principle normal vector, (p^{uu}(DOT(p^{uu},p^{u})/p^{u})^{2})*p^{u}) and binormal (p^{u}Xp^{u}). 
Gamma correction  Modifying the color palette to compensate for nonlinear response of a monitor so that a linear change in digital color values results in linear change in light emitted from screen. 
Gaussian curvature  If k1 and k2 are the principle curvatures at a point, the Gaussian curvature is k1k2. 
Golden Rectangle  The golden rectangle is a rectangle with sides of 1 and 1+x such that, if you chop off a 1x1 square you'd be left with a rectangle with sides x and 1 and (here's the important part) the ratio of the sides of the original rectangle (1:1+x) is equal to the sides of the rectangle left after chopping off the square (x:1). It turns out that x = sqrt(5)/2  1/2 (or, said another way, the sides of the original rectangle are 1 and 1/2 + sqrt(5)/2. 
Hausdorff distance  "two sets are within Hausdorff distance r from each other iff any point of one set is within distance r from some point of the other set" (from www.cuttheknot.org"s page on Hausdorff distance) 
Intrinsic  an intrinsic property of a surface is a property of the surface which is not relative to the space in which it is embedded. Curvature at a point is an intrinsic propterty; the height of a point is not (it is extrinsic). 
KD tree  A binary tree which partitions kdimensional data. At each successive node, the data is divided into two buckets which splits the data along one of the dimensions (presumably the dimension with the largest range of values). 
Level set methods  A numerical technique to follow the evolution of interfaces. The evolving interface is defined by an initial shape and a speed function F, defined over the points of the interface. This is used to define a higher dimensional surface in which the interface is embedded. The interface is a cut of the surface. See level sets by J.A.Sethian 
Manifold 
A points set whose points are in onetoone correspondence with ntuples of real numbers, the coordinates of the points, is called an ndimensional differentiable manifold [CEM, p.573]. "A twodimensional surface in R^d (d>=2) is a 2manifold if each point on it has a neighborhood that is homeomorphic to an open twodimensional disk. In this paper we call 2manifolds simply manifolds. A manifold surface is called compact if it is bounded and closed. For example, a sphere is a compact manifold whereas a plane is not. A manifold is called orientable if it has two distinct sides. A sphere is orientable since it has two sides, 'inside' and 'outside'. A Mobius strip or a Klein bottle is not orientable." [DTTD] 
mean curvature  If k1 and k2 are the principle curvatures at a point, the mean curvature is (k1+k2)/2. 
Medial Axis Transform  Also called Skeletonization. Reducing a region to a skeletal remnant, for example by some type of thinning operation, that reflects the main topology of the main areas of the original region reflecting the connectivity and branching structures of these areas. Distance to the surface is associated with the skeletal points so that the original regions might be reconstructed. See HIPR2's Skeletonization/Medial Axis Transform 
Mipmap  A.k.a. pyramidal parametrics. Method of storing filtered versions (by powers of 2 in each dimension at each stage) of a texture map. 
Morse theory  From http://mathworld.wolfram.com/MorseTheory.html: "A generalization of calculus of variations which draws the relationship between the stationary points of a smooth realvalued function on a manifold and the global topology of the manifold." Also see What is Homotopy?. 
Polygon  Polygon usually refers to a sequence of points that define a closed border of a planar surface in threespace (compare to control polygon). However, in some contexts, the term polygon may not necessarily imply planarity. 
Principal Curvatures  The maximum and minumum bending of a surface at a point. See Wolfram's Mathworld Principal Curvatures. 
Quadrics, quadratic surfaces  A second order algebraic surface. Quadratic surfaces are also called quadrics. See Wolfram's Mathworld Quadratic Surfaces. 
Quaternions  Fourtuples used to describe orientation and rotations. Avoids gimbal lock, the drawback of Euler angles. [PPRU] 
Red Green Subdivision  A mesh refinement approach using a regular (red) subdivision and an irregular (green) subdivision. For example, see Simplicialbased multiresolution volume datasets management: an overview 
Reeb graph  A Reeb graph is a skeletal representatin of the topology of an object. 
Rfunction  A realvalued function of real variables that inherit some properties of Boolean functions. They can model objects implicitly. See Rfunctions. See Solid Modeling with Rfurnctions 
Simplex  (tentative) a simplex is the simplest geometric element of a particular dimension. For our purposes, it refers to a triangle or a tetrahedron. 
Spherical harmonics  Spherical harmonics are special functions of the spherical coordinates, theta and phi. These functions can be thought of as "standing waves on a sphere". (http://www.csd.abdn.ac.uk/~dritchie/graphics/) 
Steiner points  There are various definitions for Steiner points. The definition most related to graphics are points inserted into a planar straight edge graph to allow a Delaunay triangulation of the graph. See http://www2.cs.cmu.edu/~quake/triangle.defs.html. 
Superquadrics  Superquadrics and their geometric properties 
Tensor  A tensor is a quantity that is invariant under coordinate system transformation. See, for example, it's use in the discussion of Stress at a Point (pdf). Generalization of vectors and matrices. A tensor of rank 0 is a scalar, of rank 1 a vector, rank 2 is a matrix, rank 3 a 3D rectangular array and rank k a kdimenstional rectangular array. See Wolfram's Tensor. 
Tensor product  Let A=[a_{i}_{j}] be an m x p matrix and B = [b_{i}_{j}] an n x q matrix. Then the tensor product of A and B is the mn x pq matrix, C, which can be expressed as C = [a_{i}_{j}B]. See [TSHORES] 
Tensor product surface  A surface patch that is completely defined in terms of the corner conditions it is called a tensor product surface. A tensor product patch has a rectangular topology and is expressed in a symmetric form (w.r.t u and v) as can be seen in the standard bicubic patch. 
Thin plate spline  A spline defined by minimizing an energy function based on curvature. See Wolfram's Thin Plate Spline. 
Wavelets  A mathematical technique for the hierarchical decomposition of functions  also referred to as a multiresolution technique because it represents a function as a weighted sum of base functions which differ in the resolution of features which they capture. [WCG] 
Term  Meaning 

Bijective  "A onetoone function from a set A onto a set B is called a bijection. Bijections play a fundamental role in combinatorial mathematics. A bijection from a set onto itself is usually called a permutation of that set." [IC,p.16] 
Condensation  Also known as "particle filters" (vision community). See Particle filters for realtime object tracking 
Conjugant gradient method  An iterative solver for a sparse matrix system representing a system of linear equations. See Jonathan's paper 
Convex combination  A linear combination of elements where the weights are 1) all greater than or equal to zero and 2) they sum to one. See PlanetMath.org. Also see convex hull, above. 
Curl  measure of a vector field's tendency to rotate about a point. You can think of it as the cross product between a vector of first partial derivative operators and the function. 
Critical point  A critical point, (x,f(x)) , of a function f is if f(x) is defined and f '(x) is either zero or undefined. The xcoordinate of the critical point is called a critical value or a critical number. (From thinkquest.org) 
Divergence  The sum of first partial derivatives of a function (see Laplacian operator). See Wolfram's Laplacian. 
Direct Linear Transform (DLT)  Least squares solution for point correspondences between, for example in camera callibration, world space points and image space points. See Camera Callibration 
Dynamic programmng  "Dynamic Programming is an approach developed to solve sequential, or multistage, decision problems; hence, the name "dynamic" programming. But, as we shall see, this approach is equally applicable for decision problems where sequential property is induced solely for computational convenience." [DYNP] 
E(3)  3 dimensional Euclidean space 
Edge detection  See this page, for example. 
Eigenvalue  Value associated with an Eigenvector. It's magnitude (greater or less than one) tells whether the associated Eigenvector will diverge to infinity or collapse to zero after repeated applications of a matrix A. This is an important indicator for iterative solvers in which an error vector (expressed as a linear combination of Eigenvectors) needs to be forced to zero for a solution to be found. See Determinants, Eigen Vectors. 
Eigenvector  A vector which is not changed (except for a scale factor, the associated eigenvalue) by application of a matrix, Ax = kx where k (usually notated lambda) is called the eigenvalue. You might think of this as the axis of rotation if A were a 3D rotation matrix. See Determinants, Eigen Vectors. 
EMPCA  First see PCA. In a nutshell, to find C matrix that relates latent variables X to observed vectors Y use Y = CX: Estimate X by X = (C^{T}C)^{1}C^{T}Y, then estimate C by C^{new} = YX^{T}(XX^{T})^{1}. Do this iteratively. 
Eulerian formulation v. Lagrangian formulation  e.g., in fluid dynamics, whether the analysis is gridbased or particlebased. 
Euler integration  (tentative) Method of integrating a function by stepping in the direction of the function's derivative, i.e. f(x+dx) = f(x) + dx*f'(x), as in updating the position of a particle by it's velocity. 
Factor Analysis  "The main applications of factor analytic techniques are: (1) to reduce the number of variables and (2) to detect structure in the relationships between variables, that is to classify variables." From Principal Components and Factor Analysis 
Finite element method (FEM) Finite element analysis (FEA) 
A numerical method in which a surface or volume is broken down into relatively small descrete elements. The relationship of one element to adjacent elements with respect to some attribute is expressed as some differential (or difference) equation. This is expressed in matrix form and (possibly nonlinear) solution strategies are applied to produce a sequence to values for this attribute over time. See Internet Finite Element Resources. 
Forward differencing  Updating the descrete values of a variable by forming the expression which increments it from one value to the next. E.g. if p(t) = at+b, then dp = p(t+1)p(t) = a, so initializing p = p(0) = b, we have in sequence p = b, a+b, 2a+b, 3a+b, etc. This can be done with higher order equations. For example if p(t) = at^{2}+bt+c, then dp=p(t+1)p(t)=2at+a+b and ddp=dp(t+1)ddp(t)=2a so initializing p=p(0)=c and dp=dp(0)=a+b, we have (p,dp) = (c,a+b), (a+b+c,3a+b), (4a+2b+c,5a+b), (9a+3b+c,7a+b), etc. 
Golden Ratio Search  Search strategy similar to binary search but based on the golden ratio. (radical 5 minus 1 over 2) For the number, see Phi: That Golden Number; for the search strategy, see Golden Ratio Search 
Gradient  of a scalar field is a vector field where the vectors all point in the direction of higher values and the magnitude of the vectors represent the rate of change. 
Halton Sequence Generator  The Halton Sequence Generator is a quasirandom number sequence. 
Hessian  Similar to the Jacobian (really the second derivative version), it is defined as Hij = (2nd order partial of R)/((partial of ti)(partial of tj)). 
Harmonic mean  For a set of numbers x_{i}, it's one over the average of one over x_{i}. See MathWorld. 
Hidden Markov Models (HHMs)  See Hidden Markov Models. 
Holonomic constraint  (tentative) A constraint based on one level of derivative of a variable. For example a constraint based only on positional information. 
Homeomorphic  (tentative) A onetoone onto mapping 
Homographic  A onetoone onto mapping between two figures. 
Homotopy  "A continuous transformation from one function to another. A homotopy between two functions f and g from a space X to a space Y is a continuous map G from such that and , where denotes set pairing. Another way of saying this is that a homotopy is a path in the mapping space from the first function to the second. " (From mathworld.worlfram.com) Also see What is Homotopy? 
Illconditioned  A problem in which a small change in measurements might produce a large change in the solution. 
Illposed  A problem in which there might not be a solution or there is more than on solution or the solution might not depend continuously on the data. See Illposed Inverse problems 
Implicit Euler integration  Instead of updating a function from it's current position f(x) by stepping in the direction of its tangent (f(x+dx)=f(x)+f'(x)*dx, find a point which is a step away in x whose derivative points directly away from the current point: f(x+dx)f(x)=f'(x+dx)*dx. This take more computation per step but presumably it allows bigger steps to be taken. For example, see Implicit integration  the linear case. (Compare to Euler integration) 
Independent component analysis (ICA)  ICA describes how the observed data are generated by a process of linearly mixing the components. See this Tutorial 
Injective  "A function f is called a onetoone function or injection if it associates different values in the range with different values in the domain." [IC, p.15] 
Isomap  A dimensionality reduction technique that computes the geodesic distance between two points by constructing a nearest neighbor graph from a set of points and computing distances between nonnearest neighbors from the graph. This is followed by a standard Multidimensional Scaling (MDS) dimensionality reduction technique. See this article from Science Magazine. 
Jacobian 
A matrix, J, in which each entry i,j relates the change of variable t_{j} to the change in variable v_{i} so that V = J T. Essentially it is the multidimensional version of dx/dt. T would be a vector of unknowns; V is given. If J is not square, can be solved using the pseudo inverse by multiplying both sides by the transpose of J (to form the square matrix J^{T}J on the right) and then multiplying both sides by the inverse (J^{T}J)^{1} to get J^{+}V = T where J^{+}, the pseudo inverse of J, is (J^{T}J)^{1}J^{T} 
Kalman Filter  A recursive solution to the discretedata linear filtering problem. See The Kalman Filter 
Lagrange multipliers 
(from [LAGR])
Lagrange multipliers provide a method of finding maxima or minima of a function subject to constraints. This method is
particularly useful when more than one constraint is involved. To solve a problem with Lagrange multipliers,

Laplace operator  sum of the second partial derivatives of a function 
Levenberg_marquardt method  From Mathworld: "LevenbergMarquardt is a popular alternative to the GaussNewton method of finding the minimum of a function F(x) that is a sum of squares of nonlinear functions." 
Linear discriminant analysis  LDA tutorial 
Linear dynamical systems 
Lectures by Prof. Boyd at Stanford Wikipedia's Linear dynamical system 
Linear leastsquares  fitting a set of data points to a linear combination of any specified functions [CEM] 
Linear programming Linear optimization 
optimizing a linear function bounded by linear constraints. The Simplex Method is the standard way to efficiently organize the computations. 
Linear regression  fitting a set of data points to a straight line model [CEM] 
Lloyd's algorithm  repositioning a set of points to the centroid of their respective Voronoi cell in order to more evenly distribute them. See Answers.com's Lloyd's algorithm 
Lipschitz condition  A condition of an upper bound on the change in a function given a change in parametric value: f(u2)f(u1) <= L*u2u1 for some finite number L in some region R of f. The Lipschitz condition is implied if the function f has fintion partial derivatives [GCTD] 
LU Decomposition  Decomposing a square matrix A into lower and upper triangular matrices such that A = L U. Further, the diagonal of L can be set uniformly to '1'. This decomposition can be used to solve a linear set of equations Ax=b by solving Ux = y and then Ay = b. These can be easily solved with backward and forward substitution. This decomposition can also be used to compute the inverse of a matrix by successively setting the b vector to columns of the identity matrix. 
Markovian property  "For a process to be Markovian, the future must depend only at the present and past should not have any effect on the future." [DYNP] 
Maximum likelihood  Given a model, M, that is parameterized by the set of parameters S, the probability of generating a dataset D is P(DS). If you don't know the parameter setting but can observe data, then determine the parameters by calculating the maximum P(SD). Compute the maximum by setting the dirivative of the equation for P(SD) to zero. Often it is easier to deal with the log of the P(SD), for example, when P() is a function of a Gaussian distribution and, therefore, has an exponential term in it. 
Monte Carlo integration  evaluates the function at a random sample of points and estimates its integral based on that random sample. For example, if the area under a curve is desired for a function y=f(x), 0 < x < 1 and 0 < f(x) < 1, then a bunch of (xi,yi) points are generated in the interval; the percentage of points for which yi < f(xi) is used as the estimation for the area under the curve. 
Multidimensional Scaling  "Multidimensional scaling (MDS) can be considered to be an alternative to factor analysis (see Factor Analysis). In general, the goal of the analysis is to detect meaningful underlying dimensions that allow the researcher to explain observed similarities or dissimilarities (distances) between the investigated objects." From Multidimensional Scaling 
Multiresolution analysis (MRA)  (tentative) analyzing a function at multiple resolutions (e.g. wavelets). 
Newton's method NewtonRaphson method 
root finding by geometrically extending the tanget line at a current point Xi, until it crosses zero, then setting the next guess, Xi+1, to the abscissa of that zerocrossing. See http://uranus.eng.auth.gr/lessons/1/5.html 
Particle Filters  Also known as "condensation". See Particle filters for realtime object tracking 
Penalty Method  A method of enforcing contraints by using momentary stiff springs to reestablish violated constraints, e.g., collision. 
Positive definite matrix  A real symmetric matrix with postive eigenvalues. Equivalently, a symmetric matrix for which x^{T}Ax > 0 [LAA,p.250; 5] See matrix properties. 
Principle component analysis (PCA) 
Break down data into it's principle components. That is, determine an ordered set of orthogonal vectors such that the data varies along the direction of the first vector by the greatest amount, then varies along the direction of the second vector by the next greatest amount, etc. Steps: 1) get data, 2) subtract out mean, 3) calculate the covariance matrix, 4) get the eigenvectors and eigenvalues of the covariance matrix, 4) order the eigenvectors according to the magnitude of their associated eigenvalues. The eigenvectors are essentially new coordinate frame in which a data point can be expressed by projecting the data point onto the eigenvectors. For data compression, choose only the top so many of the eigenvectors and project a data point onto each of these vectors. See A tutorial on Principal Components Analysis [PDF]. 
Quadratic programming  solving for Sj by minimizing R(Sj) subject to Ci(Sj) by taking a 2nd order NewtonRaphson step in R (irrespective of Ci), then projecting that onto the nullspace of a firstorder step to drive the Ci to zero. 
Radial Basis Function Network 
Uses Gaussians or Gaussianlike functions, (monotonic, radially symmetric), h_{i}(x), to approximate a function y = f(x) = ∑w_{i} h_{i}(x). The weights are learned by a training set of data and finding a leastsquares fit to the data. It is a singlelayer linear neural network. See Introduction to Radial Basis Function Networks 
R^{3}  triples of real numbers 
Riccati Equations  See Riccati Equations 
Runga Kutta  (tentative) An integration method (used as opposed to the Euler method) in which a derivative half step is taken and the derivative there is used to update the value of the function, e.g. f(x+dx) = f(x) + f'(x+(dx/2)*f'(x)). This is second order Runga Kutta. Fourth order Runga Kutta is commonly used. [NR] 
S^{3}  3D vectors on the unit sphere 
SE(3)  Special Euclidean group  position and orientation in 3D space 
Secant method  a root finding method. See Secant Method. 
self organizing map (SOM)  "The basic SelfOrganizing Map (SOM) can be visualized as a sheetlike neuralnetwork array, the cells (or nodes) of which become specifically tuned to various input signal patterns or classes of patterns in an orderly fashion. The learning process is competitive and unsupervised..." (http://www.mlab.uiah.fi/~timo/som/thesissom.html) 
SO(3)  Special orthogonal group  3x3 matrices, columns are unit length, mutually orthogonal, determinant is 1.0. (rigid rotations) 
Sigmoidal  The usual definition is 'curved like the letter S'. However, dictionaries may also include 'curved like the letter C' and 'shaped like a sigma'. 
Simulated Annealing  A search strategy in which random perturbations from a local search are allowed but attenuated over time, simulating the physical process of annealing as liquids freeze. See Simulated Annealing. 
Singular point  "Some discontinuities are singular points. A singular point of a curve is any point at which the curve does not have a unique tangent. From this, it follows that the function will not be differentiable at a singular point. A singular point of a curve can occur where the curve is pointed, where it crosses itself, or where it branches in two directions." (From geocities.com/mathfair2002/) 
Singular value decomposition  Solution method for Ax = b. Similar to LU decomposition in that the matrix A is decomposed into more than one matrix. In this case it is decomposed into 3 matrices, A = UWV. W is a diagonal matrix. The magnitude of the diagonal values indicates relative importance of the values of A. If a value of W is 0 or close to 0, then A is singular. This can be used to reduce the dimensionality of the problem by removing 'unimportant' values of A from consideration. 
Stationary point  A point at which the derivative of a function vanishes, f'(x) = 0. (From mathworld.worlfram.com) 
steepest descent  Interative technique in finding a solution to Ax=b. You take a step in the direction of steepest descent (gradient). The magnitude of the step you take is determined by the place along the direction your stepping in which the gradient is orthogonal to that direction. [ICGM] 
Stochastic sampling  Taking one or more pseudo random samples of an area as representation of an area which would otherwise be integrated. 
Surjective  "A function f from A onto B is defined as a function from A to B such that each member of B is associated with at least one member of A. A function from A onto B is also called a surjection from A to B." [IC, p. 16] 
SVM Support Vector Machine 
SVM is a particular type of Kernel machine (a large class of learning algorithms). Uses inner product of feature vectors. Use a kernel function that nonlinearly map features into (hopefully) linearly separable space. From: Tutorial (pdf). Also see www.kernelmachines.org and www.suportvector.net. 
Twist vector  A twist vector expresses rigid body motion. It is a 6 component vector that consists of angular velocity and linear velocity. 
Underconstrained  A problem is underconstrained if the constraints allow for more than one solution. 
Variational calculus  Variational calculus studies the variation of an integral over a path under perturbations of the path q(t). We substitute the initial path q(t) with the new path q(t) = q(t) + q(t). [MECH]. 
Verlet integration  Calculate forces at current position, use to calculate velocity at next halfway time step, and use to update positions. Velocities leapfrog over positions. See http://www.cse.clrc.ac.uk/msi/software/Democritus/Theory/verlet.html 
Viterbi search algorithm  An algorithm to compute the most likely sequnce of states in a hidden Markov model given a sequence of observed outputs. It uses best possible paths to intermediate states and updates incrementally. See Viterbi Algorithm. 
Wrench vector  Similar to a twist vector, it is a 6 component force vector consisting of a linear component and angular component. 
Term  Meaning 

Acceleration  The rate of change of velocity with respect to time. 
Bernoulli's equation  An equation that relates pressure, density, velocity, elevation and gravitational acceleration. See Bernoulli's Equation 
Cauchy stress  Cauchy stress is the force per unit area of the deformed solid, also called true stress. See Stress at a Point (pdf) or the Mechanics of Solids. 
Continuum Mechanics  The study of the behavior of material as a uniform continuum, neglecting it's sstructure on a smaller scale. See Introduction to Continuum Mechanics 
Critical damping  "A critically damped system approaches equilibrium as fast as possible without any overshoot or oscillation." From http://icva.hep.ph.ic.ac.uk/CMS/UG/Vibrations+Waves/damped/critical_damping.html. Also see: http://web.mit.edu/8.03esg/watkins/8.03/damlim.pdf 
Damping 
For our purposes, a force applied proportionate to and in the opposite direction of velocity.
Most often encountered with springs. The damping term is added to help control the motion and preventing it from getting out of hand. Consider F = kx  dv where k is the spring constant, x is the deviation from rest length, v is velocity and d is the damping constant. 
Density  Mass per unit volume (under specified conditions of pressure and temperature). [DICT] 
Dirichlet Boundary Conditions  In a fluid simultion, expressing the boundary conditions in terms of fluid velocity. See Dirichlet Boundary Conditions for example. 
Elastic Collisions  A material is elastic in the area in which Hooke's Law holds. The elastic limit is the where the elastic region ends. Perfectly elastic collisions are those in which no kinetic energy is lost and momentum is conserved. See Elastic Collisions 
Eulerian framework  Looking at a timevarying spatial function by breaking space into cells and keepting track of what happens inside of each cell. Compare to a Lagrangian framework. 
Force  The capacity to do work or cause physical change. [DICT] 
Friction  Resistance of one object moving relative to, and in contact with, another. Friction is a force linearly related to velocity, and is a function of normal force and the materials in contact. 
Gravity  The natural force of attraction between any two massive bodies, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. [DICT] 
Green's Strain  Characterizes a deformation by the change in square of infintesimal line element lengths between the deformed and undeformed surface. See (ps) for example. 
Hertzian contact  Contact modeling between two linear elastic objects. See Robotics and Human Augmented Systems 
Hooke's Law  Force is proportional to displacement as in a spring. They are related by a constant of proportionality. It is usually written as F = k*x where x is the difference between rest length (as in a spring) and current length. 
Inelastic Collisions  inelastic means that some energy is lost in the collision. See Inelastic Collisions 
Inertia  Inertia is the measure of selfresistance to acceleration. (http://www.ebtx.com/ntx/ntx13.htm) 
Lagrangian framework  Looking at a timevarying spatial function by tracking particles through space. Compare to a Eularian framework. 
Laplace operator  The summation of second order partial differentials. See The Laplace Operator. 
Load  
Mass  A property of matter equal to the measure of an object's resistance to changes in either the speed or direction of its motion. The mass of an object is not dependent on gravity and therefore is different from but proportional to its weight. [DICT] 
Material derivative  "The time rate of change of a quantity such as temperature or velocity of a material particle is known as a material derivative, and is denoted by a superimposed dot or by D/Dt." See Material Derivative 
Moment  The (first) moment of a quantity is quantity*distance. The second moment of a quantity is quantity*distance^{2}. 
momentum  Momentum = Mass times velocity. Angular momentum = mass × velocity × distance (from point object is spinning or orbiting around) (http://www.astronomynotes.com/angmom/angmom.htm) Momentum (both linear and angular) is conserved in a closed system. 
Normal Force  The force perpencidular to the surface of contact between two bodies. 
Poison's Ratio  Poison's Ratio: n = e perpendicular/e parallel Ratio of longitudinal strain perpendicular/parallel to maximum compressive stress. () 
Pressure  Force applied uniformly over a surface, measured as force per unit of area. [DICT] 
Shear  Deformation of an object which can be characterized by the relative movement of parallel surfaces in opposite directions. 
Strain  The axial strain is defined as the fractional change in length. Strain = (deformation of member) divided by the (original length of member). (http://physics.uwstout.edu/statics/) 
Stress  What is known as Axial (or Normal) Stress, often symbolized by the Greek letter sigma, is defined as the force perpendicular to the cross sectional area of the member divided by the cross sectional area. Typcially, stress is given by: Sigma = F/A. Axial stress is really the 'pressure' in a solid member. (http://physics.uwstout.edu/statics/) 
Surface traction  Applied distributed forces on the surface of an object. 
Tension  A force working to elongate an object. 
Traction  A force, such as adhesive friction, pulling one object towards another 
viscosity  Resistance to flow. 
Young's Modulus  The value of Young's modulus  which is a measure of the amount of force needed to produce a unit deformation  depends on the material. Young's Modulus for Steel is 30 x 106 lb/in2, for Aluminum E = 10 x 106 lb/in2, and for Brass E = 15 x 106 lb/in2. (http://physics.uwstout.edu/statics/) 
compressible  where the density changes (e.g. gas) 

density  mass per unit area 
diffusion  a physical process in which some property of a gas is transported by the random motion of molecules. It is realted to the stress tensor and the viscosity of the gas. 
dilatant  type of fluid that flow easily with a low velocity at low strain rates, but becomes more like a solid as the strain reate increases (e.g. quicksand). 
hydrostatic  property of fluid at rest 
ideal fluid  fluid that has no viscosity and does not flow in a turbulent manner 
ideal flow  when the friction due to viscosity is negligible 
incompressible  where the density is fixed (e.g. water) 
isotropic  the same in all directions 
laminar flow  purely viscous flow (no turbulence); the fluid flows in laminas or layers 
Newtonian  type of fluid where the shear stress is linearly proportional to the velocity gradient 
pressure  in a static fluid, the normal compressive force per unit area acting on a surface immersed in the fluid. 
steady flow  flow in which the velocity components and thermodynamic properties at every point in space do not change with time 
surface tension  the apparent stress in the surface layer of a liquid 
thixotropic  type of fluid in which stressstrain rate relationship depends on prior working or straining (e.g. printer's ink) 
velocity gradient  change in velocity 
viscoelastic  fluids in which the shear stress is a function not only of the velocity gradient but also of ordinary strain as well. 
viscosity  a measure of a fluid's resistance to shear when the fluid is in motion 
Notation (due to text limitations):
d/dt  partial differential 

r  density (usually rho) 
p  pressure 
u  velocity 
conservation of mass: the net rate of mass flow out of the control surface, r*(du/dx+du/dy+du/dz), is equal to the time rate of decrease of mass inside the control volume, dr/dt, so:
dr/dt = r*(du/dx + du/dy + du/dz)
0 = (du/dx + du/dy + du/dz)
momentum equation: Ignoring the effect of viscosity results in what's called the Euler Equations. The force on the differential element will change the momentum (mass * velocity) of the stuff inside the element.
dp/dx = d(r*u)/dt = r*(du/dt + du/dx*dx/dt) dx/dt = u and substituting, dp/dx = r*(du/dt + u*du/dx)
Term  Meaning 

Arithmetic encoding  A form of entropy encoding that encodes the entire message into a single number (or fraction). It's context based if the entropy of a symbol changes based upon its context (the preceeding symbol, for example). See Wikipedia's Arithemtic encoding. 
Canny Edge Detector  "The Canny operator works in a multistage process. First of all the image is smoothed by Gaussian convolution. Then a simple 2D first derivative operator (somewhat like the Roberts Cross) is applied to the smoothed image to highlight regions of the image with high first spatial derivatives. Edges give rise to ridges in the gradient magnitude image. The algorithm then tracks along the top of these ridges and sets to zero all pixels that are not actually on the ridge top so as to give a thin line in the output, a process known as nonmaximal suppression. The tracking process exhibits hysteresis controlled by two thresholds: T1 and T2 with T1 > T2. Tracking can only begin at a point on a ridge higher than T1. Tracking then continues in both directions out from that point until the height of the ridge falls below T2. This hysteresis helps to ensure that noisy edges are not broken up into multiple edge fragments." From Canned Edge Detector. 
Gabor wavelets  See Gabor Wavelets. I've come across them in articles talking about face recognition. 
Hough transform 
from Amos Storkey: The Hough Transform is a global method for finding straight lines hidden in larger amounts of other data. It is an important technique in image processing. To understand the Hough Transform, it is important to know what the Hough space is. Each point (d,T) in Hough space corresponds to a line at angle T and distance d from the origin in the original data space. The value of a function in Hough space gives the point density along a line in the data space. The Hough Transform utilises this by the following method. For each point in the original space consider all the lines which go through that point at a particular discrete set of angles, chosen a priori. For each angle T, calculate the distance to the line through the point at that angle and discretise that distance using an a priori chosen discretisation, giving value d. 
Hu moments 
See the definition of moments (including central moments) below if you are not familiar with it. Hu moments are based on scale invariant central moments. If the central moments are c_{pq}, the scale invariant central moments are:n_{pq} = c_{pq}/c_{00}^{((p+q)/2)+1} Some Hu moments are computed from these. Some Hu moments are scale and translation invariance, some are reflectance invariance, some provide reflectin discrimination, etc. Some of the Hu moments are: n_{20}+n_{02}; (n_{20}n_{02})^{2}+4n_{11}^{2}; (n_{30}3n_{12})^{2}+(3n_{21}n_{03})^{2} See the Appendix in Realtime Motion Template Gradients using Intel CVLib by Jim Davis and Gary Bradski. 
KL transform  KarhunenLoee (KL) transformation is also known as the principal component transformation, the eigenvector transformation or the Hotelling transformation. See Image Processing  the KL transform 
LIC Line Integrals 
See Line Integrals. 
LIC Linear Integral Convolution 
"Basically this plugin will smear a image at each pixel along a line which direction and length is calculated from a vector field. This vector field is calculated as the direction or gradient at each pixel of the hue, saturation or brightness of another image." From Line Integral Convolution. 
LIC Linear Predictive Code  LPC 
Estimating a value based on a linear function of previous values. Used in speech synthsis. See Texttospeech technology 
Moments 
For a descretized image, f(x,y), the twodimensional moment of order p+q is: m_{pq} = ∑∑x^{p}y^{q}f(x,y). m_{00} is the mass of an object. (m_{10}/m_{00}, m_{01}/m_{00}) is the center of mass of an object. Central moments are computed relative to the center of mass of an object. 
Morphological operators  Binary image operators; the operators can also be defined for greyscale images. The fundamental ones are dilation and erosion. Both use structuring element, also called a kernel, that is positioned over each pixel's neighborhood. In Dilation the pixel is set to one if the intersection of the image neighborhood and the kernel is nonempty. In Erosion, a pixel is set to '1' when the intersection with the kernel and the neighborhood is equal to the neighborhood. Closure is defined by Dilation followed by Erosion. Opening is defined by Erosion followed by Dilation. See Morphology by HIPR. Also see Wolfram's Binary Morphological Operators 
Noise  Fluctuations and additions to a signal from influences outside the system being studied. See Wikipedia's noise. Also see Wikipedia's the colors of noise 
Optical flow 
Assuming intensities of points do not change (much) in short periods of time, optical flow attempts to for displacement vectors of points between successive images of a sequence.
See

Roberts Cross Operator  2D spatial gradient measure on an image. It consists of a pair of 2x2 convolution masks. One mask is columms of: +1, 0; 0, 1. The other is the first rotated by 90 degrees: 0, 1; +1, 0. See Roberts Cross Edge Detector 
Sobel Edge Detector 
2D spatial gradient measure on an image.
It consists of a pair of 3x3 convolution masks.
One mask has columns of: 1,2,1; 0,0,0; and +1,+2,+1.
The other mask has rows of: 1,2,1; 0,0,0; and +1,+2,+1.
See Sogel Edge Detector
"Two 3x3 convolution masks are applied to each pixel, one color at a time  one with a horizontal trend and one with a vertical trend. The result of the each convolution is treated a vector representing the edge through the current pixel. If the magnitude of the sum of these two orthogonal vectors is greater than some userspecified threshold, the pixel is marked in black as an edge. Otherwise, the pixel is set to white." (From Sobel Edge Detection Filter) Also see this demo. 
Stationary signal  Is a signal that repeats with the same periodicity. 
Watershed algorithm  Regionpartitioning algorithm inspired by geographical construction of catch basins  where basins meet, watershed lines are constructed. See "The Watershed Transform: Definitions, Algorithms and Parallelization Strategies" by Roerdink and Meijster. 
Zernike moments  See Complex Zernike moments 