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Watershed (image Processing)
In the study of image processing, a watershed is a transformation defined on a grayscale image. The name refers metaphorically to a geological ''watershed'', or drainage divide, which separates adjacent drainage basins. The watershed transformation treats the image it operates upon like a topographic map, with the brightness of each point representing its height, and finds the lines that run along the tops of ridges. There are different technical definitions of a watershed. In graphs, watershed lines may be defined on the nodes, on the edges, or hybrid lines on both nodes and edges. Watersheds may also be defined in the continuous domain. There are also many different algorithms to compute watersheds. Watershed algorithms are used in image processing primarily for object segmentation purposes, that is, for separating different objects in an image. This allows for counting the objects or for further analysis of the separated objects. Image:Relief of gradient of heart MRI.png, Rel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Processing
An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensional picture, that resembles a subject. In the context of signal processing, an image is a distributed amplitude of color(s). In optics, the term “image” may refer specifically to a 2D image. An image does not have to use the entire visual system to be a visual representation. A popular example of this is of a greyscale image, which uses the visual system's sensitivity to brightness across all wavelengths, without taking into account different colors. A black and white visual representation of something is still an image, even though it does not make full use of the visual system's capabilities. Images are typically still, but in some cases can be moving or animated. Characteristics Images may be two or three-dimensional, such as a pho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Morse Theory
Discrete Morse theory is a combinatorial adaptation of Morse theory developed by Robin Forman. The theory has various practical applications in diverse fields of applied mathematics and computer science, such as configuration spaces, homology computation, denoising, mesh compression, and topological data analysis. Notation regarding CW complexes Let X be a CW complex and denote by \mathcal its set of cells. Define the ''incidence function'' \kappa\colon\mathcal \times \mathcal \to \mathbb in the following way: given two cells \sigma and \tau in \mathcal, let \kappa(\sigma,~\tau) be the degree of the attaching map from the boundary of \sigma to \tau. The boundary operator is the endomorphism \partial of the free abelian group generated by \mathcal defined by :\partial(\sigma) = \sum_\kappa(\sigma,\tau)\tau. It is a defining property of boundary operators that \partial\circ\partial \equiv 0. In more axiomatic definitions one can find the requirement that \forall \sigma,\tau^ \in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ImageJ
ImageJ is a Java-based image processing program developed at the National Institutes of Health and the Laboratory for Optical and Computational Instrumentation (LOCI, University of Wisconsin). Its first version, ImageJ 1.x, is developed in the public domain, while ImageJ2 and the related projects SciJava, ImgLib2, and SCIFIO are licensed with a permissive BSD-2 license. ImageJ was designed with an open architecture that provides extensibility via Java plugins and recordable macros. Custom acquisition, analysis and processing plugins can be developed using ImageJ's built-in editor and a Java compiler. User-written plugins make it possible to solve many image processing and analysis problems, from three-dimensional live-cell imaging to radiological image processing, multiple imaging system data comparisons to automated hematology systems. ImageJ's plugin architecture and built-in development environment has made it a popular platform for teaching image processing. ImageJ can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirichlet Problem
In mathematics, a Dirichlet problem is the problem of finding a function which solves a specified partial differential equation (PDE) in the interior of a given region that takes prescribed values on the boundary of the region. The Dirichlet problem can be solved for many PDEs, although originally it was posed for Laplace's equation. In that case the problem can be stated as follows: :Given a function ''f'' that has values everywhere on the boundary of a region in R''n'', is there a unique continuous function ''u'' twice continuously differentiable in the interior and continuous on the boundary, such that ''u'' is harmonic in the interior and ''u'' = ''f'' on the boundary? This requirement is called the Dirichlet boundary condition. The main issue is to prove the existence of a solution; uniqueness can be proved using the maximum principle. History The Dirichlet problem goes back to George Green, who studied the problem on general domains with general boundary condi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Walker (computer Vision)
The random walker algorithm is an algorithm for image segmentation. In the first description of the algorithm,Grady, L.:Random walks for image segmentation. PAMI, 2006 a user interactively labels a small number of pixels with known labels (called seeds), e.g., "object" and "background". The unlabeled pixels are each imagined to release a random walker, and the probability is computed that each pixel's random walker first arrives at a seed bearing each label, i.e., if a user places K seeds, each with a different label, then it is necessary to compute, for each pixel, the probability that a random walker leaving the pixel will first arrive at each seed. These probabilities may be determined analytically by solving a system of linear equations. After computing these probabilities for each pixel, the pixel is assigned to the label for which it is most likely to send a random walker. The image is modeled as a graph, in which each pixel corresponds to a node which is connected to neighbo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
