morphometrics Morphometrics (from Greek μορΦή ''morphe'', "shape, form", and -μετρία ''metria'', "measurement") or morphometry refers to the quantitative analysis of ''form'', a concept that encompasses size and shape. Morphometric analyses are co ...

, landmark point or shortly landmark is a point in a

shape A shape is a graphics, graphical representation of an object's form or its external boundary, outline, or external Surface (mathematics), surface. It is distinct from other object properties, such as color, Surface texture, texture, or material ...

object in which correspondences between and within the populations of the object are preserved. In other disciplines, landmarks may be known as vertices,

anchor An anchor is a device, normally made of metal, used to secure a vessel to the bed of a body of water to prevent the craft from drifting due to wind or current. The word derives from Latin ', which itself comes from the Greek (). Anch ...

points, control points, sites, profile points, 'sampling' points, nodes, markers, fiducial markers, etc. Landmarks can be defined either manually by experts or automatically by a

computer program A computer program is a sequence or set of instructions in a programming language for a computer to Execution (computing), execute. It is one component of software, which also includes software documentation, documentation and other intangibl ...

. There are three basic types of landmarks: anatomical landmarks, mathematical landmarks or pseudo-landmarks. An

anatomical landmark Anatomical terminology is a specialized system of terms used by anatomists, zoologists, and health professionals, such as doctors, surgeons, and pharmacists, to describe the structures and functions of the body. This terminology incorpor ...

is a biologically-meaningful point in an

organism An organism is any life, living thing that functions as an individual. Such a definition raises more problems than it solves, not least because the concept of an individual is also difficult. Many criteria, few of them widely accepted, have be ...

. Usually experts define anatomical points to ensure their correspondences within the same

species A species () is often defined as the largest group of organisms in which any two individuals of the appropriate sexes or mating types can produce fertile offspring, typically by sexual reproduction. It is the basic unit of Taxonomy (biology), ...

. Examples of anatomical landmark in shape of a

skull The skull, or cranium, is typically a bony enclosure around the brain of a vertebrate. In some fish, and amphibians, the skull is of cartilage. The skull is at the head end of the vertebrate. In the human, the skull comprises two prominent ...

are the eye corner, tip of the nose, jaw, etc. Anatomical landmarks determine homologous parts of an organism, which share a common ancestry. Mathematical landmarks are points in a shape that are located according to some mathematical or geometrical property, for instance, a high

curvature In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or su ...

point or an

extreme point In mathematics, an extreme point of a convex set S in a Real number, real or Complex number, complex vector space is a point in S that does not lie in any open line segment joining two points of S. The extreme points of a line segment are calle ...

. A computer program usually determines mathematical landmarks used for an automatic

pattern recognition Pattern recognition is the task of assigning a class to an observation based on patterns extracted from data. While similar, pattern recognition (PR) is not to be confused with pattern machines (PM) which may possess PR capabilities but their p ...

. Pseudo-landmarks are constructed points located between anatomical or mathematical landmarks. A typical example is an equally spaced set of points between two anatomical landmarks to get more sample points from a shape. Pseudo-landmarks are useful during shape matching, when the matching process requires a large number of points.

References

* {{cite book, author=I.L. Dryden and K.V. Mardia, title=Statistical Shape Analysis, publisher=John Wiley & Sons, date=1988, isbn=0-471-95816-6 Computer vision

See also

References