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Active Shape Model
Active shape models (ASMs) are statistical models of the shape of objects which iteratively deform to fit to an example of the object in a new image, developed by Tim Cootes and Chris Taylor in 1995. The shapes are constrained by the PDM (point distribution model) Statistical Shape Model to vary only in ways seen in a training set of labelled examples. The shape of an object is represented by a set of points (controlled by the shape model). The ASM algorithm aims to match the model to a new image. The ASM works by alternating the following steps: * Generate a suggested shape by looking in the image around each point for a better position for the point. This is commonly done using what is called a "profile model", which looks for strong edges or uses the Mahalanobis distance to match a model template for the point. * Conform the suggested shape to the point distribution model, commonly called a "shape model" in this context. The figure to the right shows an example. The techni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Model
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of Sample (statistics), sample data (and similar data from a larger Statistical population, population). A statistical model represents, often in considerably idealized form, the data-generating process. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables. As such, a statistical model is "a formal representation of a theory" (Herman J. Adèr, Herman Adèr quoting Kenneth A. Bollen, Kenneth Bollen). All Statistical hypothesis testing, statistical hypothesis tests and all Estimator, statistical estimators are derived via statistical models. More generally, statistical models are part of the foundation of statistical inference. Introduction Informally, a statistical model can be thought of as a statistical assumption (or set of statistical assumptions) with a certain property: that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shape
A shape or figure is a graphics, graphical representation of an object or its external boundary, outline, or external Surface (mathematics), surface, as opposed to other properties such as color, Surface texture, texture, or material type. A plane shape or plane figure is constrained to lie on a ''plane (geometry), plane'', in contrast to ''solid figure, solid'' 3D shapes. A two-dimensional shape or two-dimensional figure (also: 2D shape or 2D figure) may lie on a more general curved ''surface (mathematics), surface'' (a non-Euclidean two-dimensional space). Classification of simple shapes Some simple shapes can be put into broad categories. For instance, polygons are classified according to their number of edges as triangles, quadrilaterals, pentagons, etc. Each of these is divided into smaller categories; triangles can be equilateral, isosceles, obtuse triangle, obtuse, Triangle#By internal angles, acute, Triangle, scalene, etc. while quadrilaterals can be rectangles, rho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point Distribution Model
The point distribution model is a model for representing the mean geometry of a shape and some statistical modes of geometric variation inferred from a training set of shapes. Background The point distribution model concept has been developed by Cootes, Taylor ''et al.'' and became a standard in computer vision for the statistical study of shape and for segmentation of medical images where shape priors really help interpretation of noisy and low-contrasted pixels/voxels. The latter point leads to active shape models (ASM) and active appearance models (AAM). Point distribution models rely on landmark points. A landmark is an annotating point posed by an anatomist onto a given locus for every shape instance across the training set population. For instance, the same landmark will designate the tip of the index finger in a training set of 2D hands outlines. Principal component analysis (PCA), for instance, is a relevant tool for studying correlations of movement between groups of la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Shape Model
Statistical shape analysis is an analysis of the geometrical properties of some given set of shapes by statistical methods. For instance, it could be used to quantify differences between male and female gorilla skull shapes, normal and pathological bone shapes, leaf outlines with and without herbivory by insects, etc. Important aspects of shape analysis are to obtain a measure of distance between shapes, to estimate mean shapes from (possibly random) samples, to estimate shape variability within samples, to perform clustering and to test for differences between shapes. One of the main methods used is principal component analysis (PCA). Statistical shape analysis has applications in various fields, including medical imaging, computer vision, computational anatomy, sensor measurement, and geographical profiling. Landmark-based techniques In the point distribution model, a shape is determined by a finite set of coordinate points, known as landmark points. These landmark points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operation Of Shape Model In Active Shape Model
Operation or Operations may refer to: Arts, entertainment and media * ''Operation'' (game), a battery-operated board game that challenges dexterity * Operation (music), a term used in musical set theory * ''Operations'' (magazine), Multi-Man Publishing's house organ for articles and discussion about its wargaming products * ''The Operation'' (film), a 1973 British television film * ''The Operation'' (1990), a crime, drama, TV movie starring Joe Penny, Lisa Hartman, and Jason Beghe * ''The Operation'' (1992–1998), a reality television series from TLC * The Operation M.D., formerly The Operation, a Canadian garage rock band * "Operation", a song by Relient K from '' The Creepy EP'', 2001 Business * Business operations, the harvesting of value from assets owned by a business * Manufacturing operations, operation of a facility * Operations management, an area of management concerned with designing and controlling the process of production Military and law enforcement ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mahalanobis Distance
The Mahalanobis distance is a measure of the distance between a point ''P'' and a distribution ''D'', introduced by P. C. Mahalanobis in 1936. Mahalanobis's definition was prompted by the problem of identifying the similarities of skulls based on measurements in 1927. It is a multi-dimensional generalization of the idea of measuring how many standard deviations away ''P'' is from the mean of ''D''. This distance is zero for ''P'' at the mean of ''D'' and grows as ''P'' moves away from the mean along each principal component axis. If each of these axes is re-scaled to have unit variance, then the Mahalanobis distance corresponds to standard Euclidean distance in the transformed space. The Mahalanobis distance is thus unitless, scale-invariant, and takes into account the correlations of the data set. Definition Given a probability distribution Q on \R^N, with mean \vec = (\mu_1, \mu_2, \mu_3, \dots , \mu_N)^\mathsf and positive-definite covariance matrix S, the Mahalanobis dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Active Appearance Model
An active appearance model (AAM) is a computer vision algorithm for matching a statistical model of object shape and appearance to a new image. They are built during a training phase. A set of images, together with coordinates of landmarks that appear in all of the images, is provided to the training supervisor. The model was first introduced by Edwards, Cootes and Taylor in the context of face analysis at the 3rd International Conference on Face and Gesture Recognition, 1998. Cootes, Edwards and Taylor further described the approach as a general method in computer vision at the European Conference on Computer Vision in the same year. The approach is widely used for matching and tracking faces and for medical image interpretation. The algorithm uses the difference between the current estimate of appearance and the target image to drive an optimization process. By taking advantage of the least squares techniques, it can match to new images very swiftly. It is related to the act ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Active Contour Model
Active contour model, also called snakes, is a framework in computer vision introduced by Michael Kass, Andrew Witkin, and Demetri Terzopoulos for delineating an object outline from a possibly noisy 2D image. The snakes model is popular in computer vision, and snakes are widely used in applications like object tracking, shape recognition, segmentation, edge detection and stereo matching. A snake is an energy minimizing, deformable spline influenced by constraint and image forces that pull it towards object contours and internal forces that resist deformation. Snakes may be understood as a special case of the general technique of matching a deformable model to an image by means of energy minimization. In two dimensions, the active shape model represents a discrete version of this approach, taking advantage of the point distribution model to restrict the shape range to an explicit domain learnt from a training set. Snakes do not solve the entire problem of finding contours in ima ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Procrustes Analysis
In statistics, Procrustes analysis is a form of statistical shape analysis used to analyse the distribution of a set of shapes. The name ''Procrustes'' ( el, Προκρούστης) refers to a bandit from Greek mythology who made his victims fit his bed either by stretching their limbs or cutting them off. In mathematics: * an orthogonal Procrustes problem is a method which can be used to find out the optimal ''rotation and/or reflection'' (i.e., the optimal orthogonal linear transformation) for the Procrustes Superimposition (PS) of an object with respect to another. * a constrained orthogonal Procrustes problem, subject to det(''R'') = 1 (where ''R'' is a rotation matrix), is a method which can be used to determine the optimal ''rotation'' for the PS of an object with respect to another (reflection is not allowed). In some contexts, this method is called the Kabsch algorithm. When a shape is compared to another, or a set of shapes is compared to an arbitrarily selected refe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point Distribution Model
The point distribution model is a model for representing the mean geometry of a shape and some statistical modes of geometric variation inferred from a training set of shapes. Background The point distribution model concept has been developed by Cootes, Taylor ''et al.'' and became a standard in computer vision for the statistical study of shape and for segmentation of medical images where shape priors really help interpretation of noisy and low-contrasted pixels/voxels. The latter point leads to active shape models (ASM) and active appearance models (AAM). Point distribution models rely on landmark points. A landmark is an annotating point posed by an anatomist onto a given locus for every shape instance across the training set population. For instance, the same landmark will designate the tip of the index finger in a training set of 2D hands outlines. Principal component analysis (PCA), for instance, is a relevant tool for studying correlations of movement between groups of la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
