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Pruning (morphology)
The pruning algorithm is a technique used in digital image processing based on mathematical morphology. It is used as a complement to the skeleton and thinning algorithms to remove unwanted parasitic components (spurs). In this case 'parasitic' components refer to branches of a line which are not key to the overall shape of the line and should be removed. These components can often be created by edge detection algorithms or digitization. Common uses for pruning include automatic recognition of hand-printed characters. Often inconsistency in letter writing creates unwanted spurs that need to be eliminated for better characterization. Mathematical Definition The standard pruning algorithm will remove all branches shorter than a given number of points. If a parasitic branch is shorter than four points and we run the algorithm with ''n = 4'' the branch will be removed. The second step ensures that the main trunks of each line are not shortened by the procedure. Structuring Elements ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Image Processing
Digital image processing is the use of a digital computer to process digital images through an algorithm. As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing. It allows a much wider range of algorithms to be applied to the input data and can avoid problems such as the build-up of noise and distortion during processing. Since images are defined over two dimensions (perhaps more) digital image processing may be modeled in the form of multidimensional systems. The generation and development of digital image processing are mainly affected by three factors: first, the development of computers; second, the development of mathematics (especially the creation and improvement of discrete mathematics theory); third, the demand for a wide range of applications in environment, agriculture, military, industry and medical science has increased. History Many of the techniques of digital image processing, or digita ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Morphology
Mathematical morphology (MM) is a theory and technique for the analysis and processing of geometrical structures, based on set theory, lattice theory, topology, and random functions. MM is most commonly applied to digital images, but it can be employed as well on graphs, surface meshes, solids, and many other spatial structures. Topological and geometrical continuous-space concepts such as size, shape, convexity, connectivity, and geodesic distance, were introduced by MM on both continuous and discrete spaces. MM is also the foundation of morphological image processing, which consists of a set of operators that transform images according to the above characterizations. The basic morphological operators are erosion, dilation, opening and closing. MM was originally developed for binary images, and was later extended to grayscale functions and images. The subsequent generalization to complete lattices is widely accepted today as MM's theoretical foundation. History Mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Skeleton
In shape analysis, skeleton (or topological skeleton) of a shape is a thin version of that shape that is equidistant to its boundaries. The skeleton usually emphasizes geometrical and topological properties of the shape, such as its connectivity, topology, length, direction, and width. Together with the distance of its points to the shape boundary, the skeleton can also serve as a representation of the shape (they contain all the information necessary to reconstruct the shape). Skeletons have several different mathematical definitions in the technical literature, and there are many different algorithms for computing them. Various different variants of skeleton can also be found, including straight skeletons, morphological skeletons, etc. In the technical literature, the concepts of skeleton and medial axis are used interchangeably by some authors,, Section 11.1.5, p. 650 while some other authors, Section 9.9, p. 382., Section 17.5.2, p. 234. regard them as relate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edge Detection
Edge detection includes a variety of mathematical methods that aim at identifying edges, curves in a digital image at which the image brightness changes sharply or, more formally, has discontinuities. The same problem of finding discontinuities in one-dimensional signals is known as ''step detection'' and the problem of finding signal discontinuities over time is known as ''change detection''. Edge detection is a fundamental tool in image processing, machine vision and computer vision, particularly in the areas of feature detection and feature extraction. Motivations The purpose of detecting sharp changes in image brightness is to capture important events and changes in properties of the world. It can be shown that under rather general assumptions for an image formation model, discontinuities in image brightness are likely to correspond to: * discontinuities in depth, * discontinuities in surface orientation, * changes in material properties and * variations in scene illumi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digitizing
DigitizationTech Target. (2011, April). Definition: digitization. ''WhatIs.com''. Retrieved December 15, 2021, from https://whatis.techtarget.com/definition/digitization is the process of converting information into a digital (i.e. computer-readable) format.Collins Dictionary. (n.d.). Definition of 'digitize'. Retrieved December 15, 2021, from https://www.collinsdictionary.com/dictionary/english/digitize The result is the representation of an object, image, sound, document, or signal (usually an analog signal) obtained by generating a series of numbers that describe a discrete set of points or samples. The result is called '' digital representation'' or, more specifically, a '' digital image'', for the object, and ''digital form'', for the signal. In modern practice, the digitized data is in the form of binary numbers, which facilitates processing by digital computers and other operations, but digitizing simply means "the conversion of analog source material into a numerica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Handwriting Recognition
Handwriting recognition (HWR), also known as handwritten text recognition (HTR), is the ability of a computer to receive and interpret intelligible handwritten input from sources such as paper documents, photographs, touch-screens and other devices. The image of the written text may be sensed "off line" from a piece of paper by optical scanning (optical character recognition) or intelligent word recognition. Alternatively, the movements of the pen tip may be sensed "on line", for example by a pen-based computer screen surface, a generally easier task as there are more clues available. A handwriting recognition system handles formatting, performs correct segmentation into characters, and finds the most plausible words. Offline recognition Offline handwriting recognition involves the automatic conversion of text in an image into letter codes that are usable within computer and text-processing applications. The data obtained by this form is regarded as a static representation of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thinning (morphology)
Thinning is the transformation of a digital image into a simplified, but topologically equivalent image. It is a type of topological skeleton, but computed using mathematical morphology operators. Example Let E=Z^2, and consider the eight composite structuring elements, composed by: :C_1=\ and D_1=\, :C_2=\ and D_2=\ and the three rotations of each by 90^o, 180^o, and 270^o. The corresponding composite structuring elements are denoted B_1,\ldots,B_8. For any ''i'' between 1 and 8, and any binary image ''X'', define ::X\otimes B_i=X\setminus (X\odot B_i), where \setminus denotes the set-theoretical difference and \odot denotes the hit-or-miss transform. The thinning of an image ''A'' is obtained by cyclically iterating until convergence: :A\otimes B_1\otimes B_2\otimes\ldots\otimes B_8\otimes B_1\otimes B_2\otimes\ldots. Thickening Thickening is the dual of thinning that is used to grow selected regions of foreground pixels. In most cases in image processing thickening i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dilation (morphology)
Dilation (usually represented by ⊕) is one of the basic operations in mathematical morphology. Originally developed for binary images, it has been expanded first to grayscale images, and then to complete lattices. The dilation operation usually uses a structuring element for probing and expanding the shapes contained in the input image. Binary dilation In binary morphology, dilation is a shift-invariant (translation invariant) operator, equivalent to Minkowski addition. A binary image is viewed in mathematical morphology as a subset of a Euclidean space R''d'' or the integer grid Z''d'', for some dimension ''d''. Let ''E'' be a Euclidean space or an integer grid, ''A'' a binary image in ''E'', and ''B'' a structuring element regarded as a subset of R''d''. The dilation of ''A'' by ''B'' is defined by ::A \oplus B = \bigcup_ A_b, where ''A''''b'' is the translation of ''A'' by ''b''. Dilation is commutative, also given by A \oplus B = B\oplus A = \bigcup_ B_a. If ''B'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Union (set Theory)
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other. A refers to a union of zero (0) sets and it is by definition equal to the empty set. For explanation of the symbols used in this article, refer to the table of mathematical symbols. Union of two sets The union of two sets ''A'' and ''B'' is the set of elements which are in ''A'', in ''B'', or in both ''A'' and ''B''. In set-builder notation, :A \cup B = \. For example, if ''A'' = and ''B'' = then ''A'' ∪ ''B'' = . A more elaborate example (involving two infinite sets) is: : ''A'' = : ''B'' = : A \cup B = \ As another example, the number 9 is ''not'' contained in the union of the set of prime numbers and the set of even numbers , because 9 is neither prime nor even. Sets cannot have duplicate elements, so the union of the sets and is . Multip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. As of 2020, MATLAB has more than 4 million users worldwide. They come from various backgrounds of engineering, science, and economics. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was based on his 1960s PhD thesis. Moler became a math professor at the University of New Mexico and starte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pruning
Pruning is a horticultural, arboricultural, and silvicultural practice involving the selective removal of certain parts of a plant, such as branches, buds, or roots. The practice entails the ''targeted'' removal of diseased, damaged, dead, non-productive, structurally unsound, or otherwise unwanted plant material from crop and landscape plants. Some try to remember the categories as "the 4 D's": the last general category being "deranged". In general, the smaller the branch that is cut, the easier it is for a woody plant to compartmentalize the wound and thus limit the potential for pathogen intrusion and decay. It is therefore preferable to make any necessary formative structural pruning cuts to young plants, rather than removing large, poorly placed branches from mature plants. In nature, meteorological conditions such as wind, ice and snow, and salinity can cause plants to self-prune. This natural shedding is called abscission. Specialized pruning practices may be ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pruning MATLAB Example
Pruning is a horticultural, arboricultural, and silvicultural practice involving the selective removal of certain parts of a plant, such as branches, buds, or roots. The practice entails the ''targeted'' removal of diseased, damaged, dead, non-productive, structurally unsound, or otherwise unwanted plant material from crop and landscape plants. Some try to remember the categories as "the 4 D's": the last general category being "deranged". In general, the smaller the branch that is cut, the easier it is for a woody plant to compartmentalize the wound and thus limit the potential for pathogen intrusion and decay. It is therefore preferable to make any necessary formative structural pruning cuts to young plants, rather than removing large, poorly placed branches from mature plants. In nature, meteorological conditions such as wind, ice and snow, and salinity can cause plants to self-prune. This natural shedding is called abscission. Specialized pruning practices may be appl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
