Image stitchingImage stitching or photo stitching is the process of combining multiple photographic s with overlapping fields of view to produce a segmented panorama or high-resolution image. Commonly performed through the use of computer software, most approaches to image stitching require nearly exact overlaps between images and identical exposures to produce seamless results, although some stitching algorithms actually benefit from differently exposed images by doing high-dynamic-range imaging in regions of overlap.
Homography (computer vision)In the field of computer vision, any two images of the same planar surface in space are related by a homography (assuming a pinhole camera model). This has many practical applications, such as , , or camera motion—rotation and translation—between two images. Once camera resectioning has been done from an estimated homography matrix, this information may be used for navigation, or to insert models of 3D objects into an image or video, so that they are rendered with the correct perspective and appear to have been part of the original scene (see Augmented reality).
Pose (computer vision)In the fields of computing and computer vision, pose (or spatial pose) represents the position and orientation of an object, usually in three dimensions. Poses are often stored internally as transformation matrices. The term “pose” is largely synonymous with the term “transform”, but a transform may often include scale, whereas pose does not. In computer vision, the pose of an object is often estimated from camera input by the process of pose estimation.
Geometric distributionIn probability theory and statistics, the geometric distribution is either one of two discrete probability distributions: The probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set ; The probability distribution of the number Y = X − 1 of failures before the first success, supported on the set . Which of these is called the geometric distribution is a matter of convention and convenience. These two different geometric distributions should not be confused with each other.
Conjugate priorIn Bayesian probability theory, if the posterior distribution is in the same probability distribution family as the prior probability distribution , the prior and posterior are then called conjugate distributions, and the prior is called a conjugate prior for the likelihood function . A conjugate prior is an algebraic convenience, giving a closed-form expression for the posterior; otherwise, numerical integration may be necessary. Further, conjugate priors may give intuition by more transparently showing how a likelihood function updates a prior distribution.
Beta distributionIn probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1) in terms of two positive parameters, denoted by alpha (α) and beta (β), that appear as exponents of the variable and its complement to 1, respectively, and control the shape of the distribution. The beta distribution has been applied to model the behavior of random variables limited to intervals of finite length in a wide variety of disciplines.
Jeffreys priorIn Bayesian probability, the Jeffreys prior, named after Sir Harold Jeffreys, is a non-informative prior distribution for a parameter space; its density function is proportional to the square root of the determinant of the Fisher information matrix: It has the key feature that it is invariant under a change of coordinates for the parameter vector . That is, the relative probability assigned to a volume of a probability space using a Jeffreys prior will be the same regardless of the parameterization used to define the Jeffreys prior.
HomographyIn projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces derive. It is a bijection that maps lines to lines, and thus a collineation. In general, some collineations are not homographies, but the fundamental theorem of projective geometry asserts that is not so in the case of real projective spaces of dimension at least two. Synonyms include projectivity, projective transformation, and projective collineation.
Feature (computer vision)In computer vision and , a feature is a piece of information about the content of an image; typically about whether a certain region of the image has certain properties. Features may be specific structures in the image such as points, edges or objects. Features may also be the result of a general neighborhood operation or feature detection applied to the image. Other examples of features are related to motion in image sequences, or to shapes defined in terms of curves or boundaries between different image regions.
Exponential distributionIn probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts.
Camera resectioningCamera resectioning is the process of estimating the parameters of a pinhole camera model approximating the camera that produced a given photograph or video; it determines which incoming light ray is associated with each pixel on the resulting image. Basically, the process determines the pose of the pinhole camera. Usually, the camera parameters are represented in a 3 × 4 projection matrix called the camera matrix. The extrinsic parameters define the camera pose (position and orientation) while the intrinsic parameters specify the camera image format (focal length, pixel size, and image origin).
Projective line over a ringIn mathematics, the projective line over a ring is an extension of the concept of projective line over a field. Given a ring A with 1, the projective line P(A) over A consists of points identified by projective coordinates. Let U be the group of units of A; pairs (a, b) and (c, d) from A × A are related when there is a u in U such that ua = c and ub = d. This relation is an equivalence relation. A typical equivalence class is written U[a, b]. P(A) = { U[a, b] : aA + bA = A }, that is, U[a, b] is in the projective line if the ideal generated by a and b is all of A.
Cayley transformIn mathematics, the Cayley transform, named after Arthur Cayley, is any of a cluster of related things. As originally described by , the Cayley transform is a mapping between skew-symmetric matrices and special orthogonal matrices. The transform is a homography used in real analysis, complex analysis, and quaternionic analysis. In the theory of Hilbert spaces, the Cayley transform is a mapping between linear operators . A simple example of a Cayley transform can be done on the real projective line.
CollineationIn projective geometry, a collineation is a one-to-one and onto map (a bijection) from one projective space to another, or from a projective space to itself, such that the of collinear points are themselves collinear. A collineation is thus an isomorphism between projective spaces, or an automorphism from a projective space to itself. Some authors restrict the definition of collineation to the case where it is an automorphism. The set of all collineations of a space to itself form a group, called the collineation group.
Repetitive strain injuryA repetitive strain injury (RSI) is an injury to part of the musculoskeletal or nervous system caused by repetitive use, vibrations, compression or long periods in a fixed position. Other common names include repetitive stress injury, repetitive stress disorders, cumulative trauma disorders (CTDs), and overuse syndrome. Some examples of symptoms experienced by patients with RSI are aching, pulsing pain, tingling and extremity weakness, initially presenting with intermittent discomfort and then with a higher degree of frequency.
Prior probabilityA prior probability distribution of an uncertain quantity, often simply called the prior, is its assumed probability distribution before some evidence is taken into account. For example, the prior could be the probability distribution representing the relative proportions of voters who will vote for a particular politician in a future election. The unknown quantity may be a parameter of the model or a latent variable rather than an observable variable.
