Statistical shape analysis is a geometrical

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

 analysis from a set of shape

Shape

The shape of an object located in some space is a geometrical description of the part of that space occupied by the object, as determined by its external boundary – abstracting from location and orientation in space, size, and other properties such as colour, content, and material...

s in which statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

 are measured to describe geometrical properties from similar shapes or different groups, for instance, the difference between male and female Gorilla skull shapes, normal and pathological

Pathology

Pathology is the precise study and diagnosis of disease. The word pathology is from Ancient Greek , pathos, "feeling, suffering"; and , -logia, "the study of". Pathologization, to pathologize, refers to the process of defining a condition or behavior as pathological, e.g. pathological gambling....

 bone shapes, etc. Some of the important aspects of shape analysis are to obtain a measure of distance between shapes, to estimate average shapes from a (possibly random) sample and to estimate shape variability in a sample. One of the main methods used is principal component analysis.

Modeling

The first step after collecting a set of shapes is creating a proper shape model for further statistical analysis. A shape

Shape

The shape of an object located in some space is a geometrical description of the part of that space occupied by the object, as determined by its external boundary – abstracting from location and orientation in space, size, and other properties such as colour, content, and material...

 is determined by a finite number of coordinate points, known as landmark point

Landmark point

In morphometrics, landmark point or shortly landmark is a point in a shape object in which correspondences between and within the populations of the object are preserved. In other disciplines, landmarks may be known as vertices, anchor points, control points, sites, profile points, 'sampling'...

s; the Cartesian coordinates

Cartesian coordinate system

A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length...

 is the most commonly used one.

Shape deformation

In physics

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, deformation is a change of a shape due to an applied force. Investigating shape deformation can reveal the transformation

Transformation (mathematics)

In mathematics, a transformation could be any function mapping a set X on to another set or on to itself. However, often the set X has some additional algebraic or geometric structure and the term "transformation" refers to a function from X to itself that preserves this structure.Examples include...

 between two similar shapes and give information about local and global shape differences. Mathematically, a deformation is defined as a mapping from a shape t to y by a transformation function Φ, i.e. .(See Definition 10.2 of )