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Digital Image Processing

Digital image processing

Digital image processing is the use of computer algorithms to perform image processing on digital images. Digital image processing has the same advantages (over analog image processing) as digital signal processing has (over analog signal 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 signal distortion during processing. The most common kind of digital image processing is digital image editing.

History

Because of the computational load of dealing with images containing millions of pixels, digital image processing was largely of academic interest until the 1970s, when dedicated hardware became available that could process images in real time, for some dedicated problems such as television standards conversion. As general-purpose computers became faster, they started to take over the role of dedicated hardware for all but the most specialized and compute-intensive operations. With the fast computers and signal processors available in the 2000s, digital image processing has become the most common form of image processing, and is generally used because it is not only the most versatile method, but also the cheapest.

Digital processing of camera images

Images taken by popular digital cameras often need processing to improve their quality, a distinct advantage digital cameras have over film cameras. The digital image processing is done by special software programs that manipulate the images is many ways. This process is perfomed in a "digital darkroom", which is not really a darkroom as it is accomplished via a computer and keyboard.

Uses

Digital image processing allows the use of much more complex algorithms for image processing, and hence can offer both more sophisticated performance at simple tasks, and the implementation of methods which would be impossible by analog means. In particular, digital image processing is the only practical technology for:
- Classification
- Feature extraction
- Pattern recognition
- Projection
- Multi-scale signal analysis Some techniques which are used in digital image processing include:
- Principal components analysis
- Independent component analysis
- Self-organizing maps
- Hidden Markov models
- Neural networks

External link

-
- [http://www.dsprelated.com/groups/imagedsp/1.php Image Processing forum (image coding, compression, digital effects, mpeg, etc)]
- [http://grail.cs.washington.edu/ GRAIL, the Graphics and Imaging Laboratory of the University of Washington]
- [http://viva.ee.virginia.edu/ Virginia Image and Video Analysis group]
- [http://web.uvic.ca/ail/ Advanced Imaging Laboratory of the University of Victoria]
- [http://filters.sourceforge.net/ FILTERS : a free open source image processing library] Category:Computer vision Category:Image processing th:การประมวลผลภาพดิจิทัล

Algorithm

In mathematics and computer science an algorithm (the word is derived from the name of the Persian mathematician Al-Khwarizmi) is a finite set of well-defined instructions for accomplishing some task which, given an initial state, will terminate in a corresponding recognizable end-state (contrast with heuristic). Algorithms can be implemented by computer programs, although often in restricted forms; mistakes in implementation and limitations of the computer can prevent a computer program from correctly executing its intended algorithm. The concept of an algorithm is often illustrated by the example of a recipe, although many algorithms are much more complex; algorithms often have steps that repeat (iterate) or require decisions (such as logic or comparison). Correctly performing an algorithm will not solve a problem if the algorithm is flawed or not appropriate to the problem. For example, a hypothetical algorithm for making a potato salad will fail if there are no potatoes present, even if all the motions of preparing the salad are performed as if the potatoes were there. Different algorithms may complete the same task with a different set of instructions in more or less time, space, or effort than others. For example, given two different recipes for making potato salad, one may have peel the potato before boil the potato while the other presents the steps in the reverse order, yet they both call for these steps to be repeated for all potatoes and end when the potato salad is ready to be eaten. Certain countries, such as the USA, controversially allow some algorithms to be patented, provided a physical embodiment is possible (for example, a multiplication algorithm may be embodied in the arithmetic unit of a microprocessor).

Formalized algorithms

Algorithms are essential to the way computers process information, because a computer program is essentially an algorithm that tells the computer what specific steps to perform (in what specific order) in order to carry out a specified task, such as calculating employees’ paychecks or printing students’ report cards. Thus, an algorithm can be considered to be any sequence of operations which can be performed by a Turing-complete system. Typically, when an algorithm is associated with processing information, data is read from an input source or device, written to an output sink or device, and/or stored for further use. Stored data is regarded as part of the internal state of the entity performing the algorithm. For any such computational process, the algorithm must be rigorously defined: specified in the way it applies in all possible circumstances that could arise. That is, any conditional steps must be systematically dealt with, case-by-case; the criteria for each case must be clear (and computable). Because an algorithm is a precise list of precise steps, the order of computation will almost always be critical to the functioning of the algorithm. Instructions are usually assumed to be listed explicitly, and are described as starting 'from the top' and going 'down to the bottom', an idea that is described more formally by flow of control. So far, this discussion of the formalisation of an algorithm has assumed the premises of imperative programming. This is the most common conception, and it attempts to describe a task in discrete, 'mechanical' means. Unique to this conception of formalized algorithms is the assignment operation, setting the value of a variable. It derives from the intuition of 'memory' as a scratchpad. There is an example below of such an assignment. See functional programming and logic programming for alternate conceptions of what constitutes an algorithm.

Implementation

Algorithms are not only implemented as computer programs, but often also by other means, such as in a biological neural network (for example, the human brain implementing arithmetic or an insect relocating food), or in electric circuits or in a mechanical device. The analysis and study of algorithms is one discipline of computer science, and is often practiced abstractly (without the use of a specific programming language or other implementation). In this sense, it resembles other mathematical disciplines in that the analysis focuses on the underlying principles of the algorithm, and not on any particular implementation. One way to embody (or sometimes codify) an algorithm is the writing of pseudocode. Some writers restrict the definition of algorithm to procedures that eventually finish. Others include procedures that could run forever without stopping, arguing that some entity may be required to carry out such permanent tasks. In the latter case, success can no longer be defined in terms of halting with a meaningful output. Instead, terms of success that allow for unbounded output sequences must be defined. For example, an algorithm that verifies if there are more zeros than ones in an infinite random binary sequence must run forever to be effective. If it is implemented correctly, however, the algorithm's output will be useful: for as long as it examines the sequence, the algorithm will give a positive response while the number of examined zeros outnumber the ones, and a negative response otherwise. Success for this algorithm could then be defined as eventually outputting only positive responses if there are actually more zeros than ones in the sequence, and in any other case outputting any mixture of positive and negative responses.

Example

One of the simplest algorithms is to find the largest number in an (unsorted) list of numbers. The solution necessarily requires looking at every number in the list, but only once at each. From this follows a simple algorithm: # Look at each item in the list. If it is larger than any that has been seen so far, make a note of it. # The latest noted item is the largest in the list when the process is complete. And here is a more formal coding of the algorithm in pseudocode: Algorithm LargestNumber Input: A non-empty list of numbers L. Output: The largest number in the list L. largest ← -∞ for each item in list L, do if the item > largest, then largest ← the item return largest Notes on notation:
- "←" is a loose shorthand for "changes to". For instance, with "largest ← the item", it means that the largest number found so far changes to this item.
- "return" terminates the algorithm and outputs the value listed behind it. As it happens, most people who implement algorithms want to know how much of a particular resource (such as time or storage) a given algorithm requires. Methods have been developed for the analysis of algorithms to obtain such quantitative answers; for example, the algorithm above has a time requirement of O(n), using the big O notation with n as the length of the list. At all times the algorithm only needs to remember a single value; the largest number found so far. Therefore this algorithm has a space requirement of O(1). (Note that the size of the inputs is not counted as space used by the algorithm.) For a more complex example see Euclid's algorithm.

History

Euclid's algorithm The word algorithm comes from the name of the 9th century Persian mathematician Abu Abdullah Muhammad bin Musa al-Khwarizmi. The word algorism originally referred only to the rules of performing arithmetic using Hindu-Arabic numerals but evolved into algorithm by the 18th century. The word has now evolved to include all definite procedures for solving problems or performing tasks. The first case of an algorithm written for a computer was Ada Byron's notes on the analytical engine written in 1842, for which she is considered by many to be the world's first programmer. However, since Charles Babbage never completed his analytical engine the algorithm was never implemented on it. The lack of mathematical rigor in the "well-defined procedure" definition of algorithms posed some difficulties for mathematicians and logicians of the 19th and early 20th centuries. This problem was largely solved with the description of the Turing machine, an abstract model of a computer formulated by Alan Turing, and the demonstration that every method yet found for describing "well-defined procedures" advanced by other mathematicians could be emulated on a Turing machine (a statement known as the Church-Turing thesis). Nowadays, a formal criterion for an algorithm is that it is a procedure that can be implemented on a completely-specified Turing machine or one of the equivalent formalisms. Turing's initial interest was in the halting problem: deciding when an algorithm describes a terminating procedure. In practical terms computational complexity theory matters more: it includes the problems called NP-complete, which are generally presumed to take more than polynomial time for any (deterministic) algorithm. NP denotes the class of decision problems that can be solved by a non-deterministic Turing machine in polynomial time.

Classes

There are many ways to classify algorithms, and the merits of each classification have been the subject of ongoing debate. One way of classifying algorithms is by their design methodology or paradigm. There is a certain number of paradigms, each different from the other. Furthermore, each of these categories will include many different types of algorithms. Some commonly found paradigms include:
- Divide and conquer. A divide and conquer algorithm repeatedly reduces an instance of a problem to one or more smaller instances of the same problem (usually recursively), until the instances are small enough to solve easily.
- Dynamic programming. When a problem shows optimal substructure, meaning the optimal solution to a problem can be constructed from optimal solutions to subproblems, and overlapping subproblems, meaning the same subproblems are used to solve many different problem instances, we can often solve the problem quickly using dynamic programming, an approach that avoids recomputing solutions that have already been computed. For example, the shortest path to a goal from a vertex in a weighted graph can be found by using the shortest path to the goal from all adjacent vertices.
- The greedy method. A greedy algorithm is similar to a dynamic programming algorithm, but the difference is that solutions to the subproblems do not have to be known at each stage; instead a "greedy" choice can be made of what looks best for the moment.
- Linear programming. When solving a problem using linear programming, the program is put into a number of linear inequalities and then an attempt is made to maximize (or minimize) the inputs. Many problems (such as the maximum flow for directed graphs) can be stated in a linear programming way, and then be solved by a 'generic' algorithm such as the Simplex algorithm.
- Search and enumeration. Many problems (such as playing chess) can be modelled as problems on graphs. A graph exploration algorithm specifies rules for moving around a graph and is useful for such problems. This category also includes the search algorithms and backtracking.
- The probabilistic and heuristic paradigm. Algorithms belonging to this class fit the definition of an algorithm more loosely. # Probabilistic algorithms are those that make some choices randomly (or pseudo-randomly); for some problems, it can in fact be proved that the fastest solutions must involve some randomness. # Genetic algorithms attempt to find solutions to problems by mimicking biological evolutionary processes, with a cycle of random mutations yielding successive generations of 'solutions'. Thus, they emulate reproduction and "survival of the fittest". In genetic programming, this approach is extended to algorithms, by regarding the algorithm itself as a 'solution' to a problem. Also there are # Heuristic algorithms, whose general purpose is not to find a optimal solution, but an approximate solution where the time or resources to find a perfect solution are not practical. An example of this would be local search, taboo search, or simulated annealing algorithms, a class of heuristic probabilistic algorithms that vary the solution of a problem by a random amount. The name 'simulated annealing' alludes to the metallurgic term meaning the heating and cooling of metal to achieve freedom from defects. The purpose of the random variance is to find close to globally optimal solutions rather than simply locally optimal ones, the idea being that the random element will be decreased as the algorithm settles down to a solution. Another way to classify algorithms is by implementation. A recursive algorithm is one that invokes (makes reference to) itself repeatedly until a certain condition matches, which is a method common to functional programming. Algorithms are usually discussed with the assumption that computers execute one instruction of an algorithm at a time. Those computers are sometimes called serial computers. An algorithm designed for such an environment is called a serial algorithm, as opposed to parallel algorithms, which take advantage of computer architectures where several processors can work on a problem at the same time. The various heuristic algorithms would probably also fall into this category, as their name (e.g. a genetic algorithm) describes its implementation.

References

- Important algorithm-related publications

External links

-
- Algana.co.uk [http://www.algana.co.uk/ Algorithm analysis and puzzles.] Free source code for algorithm Java applets and C++ modules
- Gaston H. Gonnet and Ricardo Baeza-Yates: Example programs from [http://www.dcc.uchile.cl/~rbaeza/handbook/ Handbook of Algorithms and Data Structures.] Free source code for many important algorithms.
- [http://www.nist.gov/dads/ Dictionary of Algorithms and Data Structures]. "This is a dictionary of algorithms, algorithmic techniques, data structures, archetypical problems, and related definitions."
- [http://www.nr.com Numerical Recipes]
- [http://www.algosort.com/ Computer Programming Algorithms Directory]
- [http://dmoz.org/Computers/Algorithms/ Computers/Algorithms @ dmoz.org]
- [http://groups-beta.google.com/group/algogeeks "Algogeeks" Google Group] - Discuss ideas, algorithms, challenges related to programming. Also announcements about Online Programming Contests will be posted in this group.
- [http://musicalgorithms.ewu.edu/ Musicalgorithms] An interesting way of using algorithms to make music.
- [http://www.algorithmist.com/ The Algorithmist] is a resource dedicated to anything algorithms - from the practical realm, to the theoretical realm. There are also links and explanation to problem sets.
- [http://www.algogeeks.com/ AlgoGeeks] Community of algorithm enthusiastics actively involved in algorithm discussions, knowledge, problems and solutions, thus creating resource for algorithms, puzzles and problems
- Category:Discrete mathematics Category:Computer science Category:Mathematical logic Category:Arabic words ko:알고리즘 ja:アルゴリズム th:อัลกอริทึม

Digital image

A digital image is a representation of a two-dimensional image as a finite set of digital values, called picture elements or pixels. Typically, the pixels are stored in computer memory as a raster image or raster map, a two-dimensional array of small integers. These values are often transmitted or stored in a compressed form. Digital images can be created by a variety of input devices and techniques, such as digital cameras, scanners, coordinate-measuring machines, seismographic profiling, airborne radar, and more. They can also be synthetized from arbitrary non-image data, such as mathematical functions or three-dimensional geometric models; the latter being a major sub-area of computer graphics. The field of digital image processing is the study of algorithms for their transformation.

Image types

Each pixel of an image is typically associated to a specific 'position' in some 2D region, and has a value consisting of one or more quantities (samples) related to that position. Digital images can be classified according to the number and nature of those samples:
- binary (bilevel)
- grayscale
- color
- false-color
- multi-spectral
- thematic The term digital image is also applied to data associated to points scattered over a three-dimensional region, such as produced by tomographic equipment. In that case, each datum is called a voxel.

Image viewing

The user can utilize different program to see the image. The GIF, JPEG and PNG images can be seen simply using a web browser because they are the standard internet image formats. The SVG format is more and more used in the web and is a standard W3C format. The more advanced programs offer a slideshow utility, to see the images in a certain forlder one after the other automatically.

Image calibration

Proper use of a digital image usually requires knowledge of the relationship between it and the underlying phenomenon, which implies geometric and photometric (or sensor) calibration. One must also keep in mind the unavoidable errors that arise from the finite spatial resolution of the pixel array and the need to quantize each sample to a finite set of possible values.

Digital signal processing

Digital signal processing (DSP) is the study of signals in a digital representation and the processing methods of these signals. DSP and analog signal processing are subfields of signal processing. DSP has three major subfields: audio signal processing, digital image processing and speech processing. Since the goal of DSP is usually to measure or filter continuous real-world analog signals, the first step is usually to convert the signal from an analog to a digital form, by using an analog to digital converter. Often, the required output signal is another analog output signal, which requires a digital to analog converter. The algorithms required for DSP are sometimes performed using specialized computers, which make use of specialized microprocessors called digital signal processors (also abbreviated DSP). These process signals in real time and are generally purpose-designed ASICs.

DSP domains

In DSP, engineers usually study digital signals in one of the following domains: time domain (one-dimensional signals), spatial domain (multidimensional signals), frequency domain, autocorrelation domain, and wavelet domains. They choose the domain in which to process a signal by making an educated guess (or by trying different possibilities) as to which domain best represents the essential characteristics of the signal. A sequence of samples from a measuring device produces a time or spatial domain representation, whereas a discrete Fourier transform produces the frequency domain information, that is the frequency spectrum. Autocorrelation is defined as the cross-correlation of the signal with itself over varying intervals of time or space.

Signal sampling

Main article: Sampling (signal processing) With the increasing use of computers the usage and need of digital signal processing has increased. In order to use an analog signal on a computer it must be digitized with an analog to digital converter (ADC). Sampling is usually carried out in two stages, discretization and quantization. In the discretization stage, the space of signals is partioned into equivalence classes and discretization is carried out by replacing the signal with representative signal of the corresponding equivalence class. In the quantization stage the representative signal values are approximated by values from a finite set. In order to properly sample an analog signal the Nyquist-Shannon sampling theorem must be satisfied. In short, the sampling frequency must be greater than twice the bandwidth of the signal (provided it is filtered appropriately). A digital to analog converter (DAC) is used to convert the digital signal back to analog. The use of a digital computer is a key ingredient into digital control systems.

Time and space domains

The most common processing approach in the time or space domain is enhancement of the input signal through a method called filtering. Filtering generally consists of some transformation of a number of surrounding samples around the current sample of the input or output signal. There are various ways to characterize filters; for example:
- A "linear" filter is a linear transformation of input samples; other filters are "non-linear." Linear filters satisfy the superposition condition, i.e. if an input is a weighted linear combination of different signals, the output is an equally weighted linear combination of the corresponding output signals.
- A "causal" filter uses only previous samples of the input or output signals; while a "non-causal" filter uses future input samples. A non-causal filter can be changed into a causal filter by adding a delay to it.
- A "time-invariant" filter has constant properties over time; other filters such as adaptive filters change in time.
- Some filters are "stable", others are "unstable". A stable filter produces an output that converges to a constant value with time, or remains bounded within a finite interval. An unstable filter produces output which diverges.
- A "finite impulse response" (FIR) filter uses only the input signal, while an "infinite impulse response" filter (IIR) uses both the input signal and previous samples of the output signal. FIR filters are always stable, while IIR filters may be unstable. Most filters can be described in Z-domain (a superset of the frequency domain) by their transfer functions. A filter may also be described as a difference equation, a collection of zeroes and poles or, if it is an FIR filter, an impulse response or step response. The output of an FIR filter to any given input may be calculated by convolving the input signal with the impulse response. Filters can also be represented by block diagrams which can then be used to derive a sample processing algorithm to implement the filter using hardware instructions.

Frequency domain

Signals are converted from time or space domain to the frequency domain usually through the Fourier transform. The Fourier transform converts the signal information to a magnitude and phase component of each frequency. Often the Fourier transform is converted to the power spectrum, which is the magnitude of each frequency component squared. The most common purpose for analysis of signals in the frequency domain is analysis of signal properties. The engineer can study the spectrum to get information of which frequencies are present in the input signal and which are missing. There are some commonly used frequency domain transformations. For example, the cepstrum converts a signal to the frequency domain through Fourier transform, takes the logarithm, then applies another Fourier transform. This emphasises the frequency components with smaller magnitude while retaining the order of magnitudes of frequency components.

Applications

The main applications of DSP are audio signal processing, audio compression, digital image processing, video compression, speech processing, speech recognition and digital communications. Specific examples are speech compression and transmission in digital mobile phones, equalisation of sound in Hifi equipment, weather forecasting, economic forecasting, seismic data processing, analysis and control of industrial processes, computer-generated animations in movies, medical imaging such as CAT scans and MRI, image manipulation, and digital effects for use with electric guitar amplifiers. A further application is very low frequency (VLF) reception with a PC soundcard [http://www.vlf.it/harald/strangerec.htm].

Techniques

- Bilinear transform
- Discrete Fourier transform
- Discrete-time Fourier transform
- Filter design
- LTI system theory
- Minimum phase
- Transfer function
- Z-transform
- Goertzel algorithm

References

- Alan V. Oppenheim, Ronald W. Schafer, John R. Buck : Discrete-Time Signal Processing, Prentice Hall, ISBN 0-13-754920-2
- Richard G. Lyons: Understanding Digital Signal Processing, Prentice Hall, ISBN 0131089897
- Sen M. Kuo, Woon-Seng Gan: Digital Signal Processors: Architectures, Implementations, and Applications, Prentice Hall, ISBN 0130352144
- Bernard Mulgrew, Peter Grant, John Thompson: Digital Signal Processing - Concepts and Applications, Palgrave Macmillan, ISBN 0-333-96356-3
- Steven W. Smith: Digital Signal Processing - A Practical Guide for Engineers and Scientists, Newnes, ISBN 0-7506-7444-X
- Paul A. Lynn, Wolfgang Fuerst: Introductory Digital Signal Processing with Computer Applications, John Wiley & Sons, ISBN 0-471-97984-8
- James D. Broesch: Digital Signal Processing Demystified, Newnes, ISBN 1878707167
- John Proakis, Dimitris Manolakis: Digital Signal Processing - Principles, Algorithms and Applications, Pearson, ISBN 0133942899
- Hari Krishna Garg: Digital Signal Processing Algorithms, CRC Press, ISBN 0849371783
- P. Gaydecki: Foundations Of Digital Signal Processing: Theory, Algorithms And Hardware Design, Institution of Electrical Engineers, ISBN 0852964315
- Paul M. Embree, Damon Danieli: C++ Algorithms for Digital Signal Processing, Prentice Hall, ISBN 0131791443
- Anthony Zaknich: Neural Networks for Intelligent Signal Processing, World Scientific Pub Co Inc, ISBN 9812383050
- Vijay Madisetti, Douglas B. Williams: The Digital Signal Processing Handbook, CRC Press, ISBN 0849385725
- Stergios Stergiopoulos: Advanced Signal Processing Handbook: Theory and Implementation for Radar, Sonar, and Medical Imaging Real-Time Systems, CRC Press, ISBN 0849336910
- Joyce Van De Vegte: Fundamentals of Digital Signal Processing, Prentice Hall, ISBN 0130160776
- Ashfaq Khan: Digital Signal Processing Fundamentals, Charles River Media, ISBN 1584502819
- Jonathan M. Blackledge, Martin Turner: Digital Signal Processing: Mathematical and Computational Methods, Software Development and Applications, Horwood Publishing, ISBN 1898563489
- Bimal Krishna, K. Y. Lin, Hari C. Krishna: Computational Number Theory & Digital Signal Processing, CRC Press, ISBN 0849371775
- Doug Smith: Digital Signal Processing Technology: Essentials of the Communications Revolution, American Radio Relay League, ISBN 0872598195
- Henrique S. Malvar: Signal Processing with Lapped Transforms, Artech House Publishers, ISBN 0890064679
- Charles A. Schuler: Digital Signal Processing: A Hands-On Approach, McGraw-Hill, ISBN 0078297443
- James H. McClellan, Ronald Schafer, Mark A. Yoder: Signal Processing First, Prentice Hall, ISBN 0130909998
- Artur Krukowski, Izzet Kale: DSP System Design: Complexity Reduced Iir Filter Implementation for Practical Applications, Kluwer Academic Publishers, ISBN 1402075588
- John G. Proakis: A Self-Study Guide for Digital Signal Processing, Prentice Hall, ISBN 0131432397

External links

- [http://Microcontroller.com Microcontroller.com]
- [http://www.dspguide.com The Scientist and Engineer's Guide to Digital Signal Processing]
- [http://www.dsprelated.com DSP related discussion groups ]
- [http://www.altera.com/technology/dsp/dsp-index.jsp FPGA based DSP dev kit]
- [http://www.dsptutor.freeuk.com/ Digital Signal Processing Tutorial]
- [http://www.bdti.com/faq/dsp_faq.htm FAQ on Digital Signal Processing]
- [http://www.tapr.org/tapr/html/dspf.html Introduction to Digital Signal Processing]
- [http://www.cdsp.neu.edu/ CDSP - Center for Digital Signal Processing]
- [http://www.musicdsp.org Music DSP Source Code Archive]
- [http://users.aber.ac.uk/dgw/dsp.htm DSP links]
- [http://www.bores.com/courses/intro/ Yet another good DSP tutorial (bores) ]
- [http://www.spectrum-analyzer.info Spectrum Analysis Tutorials]
- [http://www.k9spud.com/traxmod/ TRAXMOD dsPIC MOD music player]
- [http://www.devicetools.com DeviceTools] - Tools and silicon for embedded device developers
- [http://www.digitalfilterdesign.com Free digital filter design software] Category:Digital electronics
- ja:デジタル信号処理 th:การประมวลผลสัญญาณดิจิทัล

1970

1970 (MCMLXX) was a common year starting on Thursday. 1970 is the Unix epoch time.

Events

January-February

- January 1 - Construction begins on Arcosanti, by Paolo Soleri, in Mayer, Arizona, located 65 miles north of Phoenix, Arizona.
- January 1 - Unix epoch at 00:00:00 UTC.
- January 12 - Biafra capitulates, ending the Nigerian civil war.
- January 15 - After a 32-month fight for independence from Nigeria, Biafran forces under General Effiong formally surrender to General Yakubu Gowon.
- January 15 - Muammar al-Qaddafi is proclaimed premier of Libya.
- January 16 - Buckminster Fuller receives the Gold Medal award from the American Institute of Architects.
- February 11 - Launch of Japan's first satellite Osumi with a Lamba-4 Rocket.
- February 17 - MacDonald family massacre at Fort Bragg, North Carolina - Jeffrey MacDonald kills his wife and children and tries to claim that "hippies" did it

March

- March 1 - Rhodesia severs its last tie with the British crown and declares itself a racially segregated republic.
- March 4 - Nigerian Francis Okechukwu Ohanyido, Poet/Philosopher born in Jos.
- March 5 - A nuclear non-proliferation treaty goes into effect after ratification by 43 nations.
- March 11 - Henry "Dickie" Marrow is murdered in a violent hate crime in Oxford, N.C..
- March 16 - The Expo '70 world's fair opens in Suita, Osaka, Japan.
- March 16 - Publication of complete New English Bible.
- March 16 - Birth of Stephen Martin.
- March 17 - My Lai massacre: The United States Army charges 14 officers with suppressing information related to the incident.
- March 18 - Lon Nol ousts Prince Norodom Sihanouk of Cambodia.
- March 18 - Post Office strike in USA - 210,000 out of 750,000 US postal employees walk out. President Nixon assigns military units to New York City post offices. Strike lasts two weeks.
- March 21 The first Earth Day proclamation is issued by San Francisco Mayor Joseph Alioto.
- March 25 - The Concorde makes its 1st supersonic flight (700 mph /1,127 km/h).
- March 31 - Explorer I spacefract re-enters atmosphere, after twelve years in orbit.

April

- April 1 - President Richard Nixon signs the Public Health Cigarette Smoking Act into law banning cigarette television advertisements in the United States starting on January 1, 1971.
- April 1 - American Motors introduces the Gremlin.
- April 10 - Paul McCartney announces that the Beatles have disbanded.
- April 11 - US spaceflight Apollo 13 launches for the moon, carrying James Lovell, Fred Haise, and Jack Swigert. On April 13, an oxygen tank in the spacecraft explodes, forcing the crew to abort the mission. The crew returns to earth safely on April 17
- April 22 - First Earth Day celebrated.
- April 29 - U.S. invades Cambodia to hunt out Viet Cong. Massive protests against the war continue in the U.S.

May-June

Viet Cong
- May 4 - The Kent State shootings: Four students at Kent State University in Ohio are killed and 9 wounded by National Guardsmen at a demonstration protesting against the incursion into Cambodia.
- May 5 - Earthquake in Yungay, Peru below Hauscaran Mountain buries the city
- May 6 - Charles Haughey and Neil Blaney are dismissed as members of the Irish Government due to accusations of their involvement in a plot to import arms for use in Northern Ireland.
- May 9 - 100,000 people demonstrate in Washington DC against the Vietnam War.
- May 14 - Ulrike Meinhof helps Andreas Baader escape.
- May 17 - Thor Heyerdahl sets sail from Morocco on the papyrus boat Ra II to sail the Atlantic Ocean.
- May 26 - The Soviet Tupolev Tu-144 becomes the first commercial transport to exceed Mach 2.
- May 27 - British expedition climbs south face of Annapurna I.
- May 31 - The Ancash earthquake causes a landslide that buries the town of Yungay, Peru; more than 47,000 people are killed.
- June 2 - Norway announces that it has rich oil deposits off its North Sea coast.
- June 4 - Tonga gains independence from the United Kingdom.
- June 10 - President Nixon signed a measure lowering the voting age to 18.
- June 11 - The United States gets its first female Generals: Anna Mae Hays and Elizabeth P. Hoisington.
- June 18 - Edward Heath is elected Prime Minister of United Kingdom.
- June 21 - Brazil defeats Italy 4-1 to win the Football World Cup 1970
- June 24 - The United States Senate repeals the Gulf of Tonkin Resolution.
- June 28 - US ground troops withdraw from Cambodia.

July-August

- July 4 - Chartered Dan-Air Comet crashes into mountains north of Barcelona - at least 112 dead.
- July 11 - The first tunnel under the Pyrenees links the Basque towns of Aranoutes and Biesma.
- July 21 - Aswan High Dam in Egypt completed.
- July 30 - Damages awarded to Thalidomide victims,
- August 7 - Harold Haley, Marin County Superior Court Judge taken hostage and murdered in an effort to free George Jackson from police custody.
- August 17-18 - US sinks 418 containers of nerve gas into the Gulf Stream near the Bahamas
- August 17 - Venera program: Venera 7 is launched. It will later becomes the first spacecraft to successfully transmit data from another planet.
- August 26- The Women's Strike For Equality takes place down Fifth Avenue in New York City.
- August 26- August 30- The Isle of Wight Festival 1970 takes place on East Afton Farm off the coast of England. 600,000 people attend the largest rock festival of all time. Artists include Jimi Hendrix, The Who, The Doors, Chicago, Richie Havens, John Sebastian, Joan Baez, Ten Years After, Emerson Lake & Palmer and Jethro Tull.

September

- September 1 - Assassination attempt against king Hussein of Jordan
- September 3-6 - Israeli forces fight Palestinian guerillas in southern Lebanon.
- September 5 - Vietnam War: Operation Jefferson Glenn begins - The United States 101st Airborne Division and the South Vietnamese 1st Infantry Division initiate a new operation in Thua Thien Province (operation ends in October 1971).
- September 7 - An anti-war rally is held at Valley Forge, Pennsylvania, attended by John Kerry, Jane Fonda and Donald Sutherland.
- September 7 - Fighting between Arabic guerillas and government forces in Amman, Jordan
- September 8-10 - Jordanian government and Palestinian guerillas make truces that keep breaking.
- September 9 – Guinea recognizes East Germany.
- September 10 – Cambodian government forces break the blockage around Kompong Tho after a 3-month siege.
- September 11 - The Ford Pinto is introduced.
- September 13 - First running of the New York City Marathon.
- September 15 - King Hussein of Jordan forms a military government with Muhammad Daoud as the prime minister.
- September 18 - Jimi Hendrix dies of barbiturate overdose in London
- September 20 - End of term for Ismail Nasiruddin Shah ibni Almarhum Sultan Zainal Abidin III as the 4th Yang di-Pertuan Agong of Malaysia.
- September 20 - Syrian armored forces cross Jordanian border.
- September 20-21 - Luna 16 lands on the Moon and lifts off the day later with samples. Lands on Earth September 24.
- September 21 - Palestinian armored forces reinforce Palestinian guerillas in Irbidi, Jordan.
- September 21 - Tuanku Al-Mutassimu Billahi Muhibbudin Sultan Abdul Halim Al-Muadzam Shah ibni Almarhum Sultan Badlishah, Sultan of Kedah becomes the 5th Yang di-Pertuan Agong of Malaysia.
- September 26 - Laguna Fire starts in San Diego County burning 175,425 acres (710 km²).
- September 27 - Richard Nixon begins a tour in Europe and visits Italy, Yugoslavia, Spain, United Kingdom and Ireland.
- September 28 - Gamal Abdal Nasser dies - vice president Anwar Sadat is named temporary president of Egypt.
- September 29 - US Congress gives president Richard Nixon authority to sell arms to Israel.
- September 29 - In Berlin, Baader-Meinhof Gang members rob three banks, loot totaling over DM200.000.

October

- October 2 - Wichita State University loses most of its football team in a plane crash.
- October 3 - In Lebanon, government of the prime minister Rashid Karami resigns.
- October 4 - In Bolivia, army commander general Rogelio Miranda and group of officers rebel and demand resignation of the president Alfredo Ovando Candía – president fires him.
- October 4 - Janis Joplin dies of a heroin overdose inside her hotel room in Los Angeles, California
- October 5 - Nixon's European tour ends.
- October 5 - The Front de Libération du Québec (FLQ) kidnap James Cross in Montreal and demands release of all its imprisoned members. The next day the Canadian government announces it won't accept the demand - first stirrings of Quebec's October Crisis.
- October 6 - Bolivian president Alfredo Ovando Candía resigns – general Rogelio Miranda takes over but resigns soon after.
- October 6 - French president Georges Pompidou visits Soviet Union.
- October 7 - General Juan José Torres becomes the new president of Bolivia.
- October 7 - Anwar Sadat accepted as Egyptian president.
- October 8 - US foreign office announces that it renews its arms sales to Pakistan.
- October 8 - Soviet author Alexander Solzhenitsyn is awarded Nobel Prize for Literature.
- October 8 - Vietnam War: In Paris, a Communist delegation rejects US President Richard Nixon's October 7 peace proposal as "a maneuver to deceive world opinion."
- October 9 - The Khmer Republic is proclaimed in Cambodia.
- October 9 - Divorce law in Italy.
- October 10 - Fiji becomes independent.
- October 10 - October Crisis: In Montreal, Quebec, a national crisis hits Canada when Quebec Vice-Premier and Minister of Labour Pierre Laporte becomes the second statesman kidnapped by members of the FLQ terrorist group.
- October 11 - 11 French soldiers are killed in a shootout with rebels in Chad.
- October 12 - Vietnam War: US President Richard Nixon announces that the United States will withdraw 40,000 more troops before Christmas.
- October 13 - Canada and the People's Republic of China established diplomatic relations.
- October 13 - Saeb Salam's government forms in Lebanon.
- October 14 - Chinese nuclear test in Lop Nor.
- October 15 - In Egypt, referendum supports Anwar Sadat 90.04%.
- October 15 - 35 construction workers are killed when a section of the new West Gate Bridge in Melbourne collapses into the river below.
- October 16 - Canadian government declares state of emergency and outlaws Quebec Liberation Front.
- October 17 - Pierre Laporte is found killed in south of Montreal.
- October 17 - Cholera epidemic in Istanbul.
- October 17 - Anwar Sadat becomes officially president of Egypt.
- October 20 - Soviet Union launches Zond 8 lunar probe.
- October 20 - Algerian ex-minister Krim Belkacem is found strangled in his hotel room in Frankfurt.
- October 20 - Egyptian president Anwar Sadat names Mahmoud Fawzi as his prime minister.
- October 21 - US Air Force plane makes an emergency landing near Leninakan, Soviet Union. Soviets release the American officers, including two generals, November 10.
- October 22 - Chilean army commander Rene Schneider is shot in Santiago – government declares state of emergency. Schneider dies October 25.
- October 24 - Salvador Allende is elected President of Chile.
- October 26 - US and Soviet space researchers meet in Moscow.
- October 26 - Garry Trudeau's comic strip Doonesbury, debuts in approximately two dozen newspapers in the United States.
- October 28 - In Jordan, government of Ahmed Toukan resigns – next prime minister is Wasfi Al-Tal.
- October 28 - Cholera outbreak in eastern Slovakia – Hungary closes its border with Czechoslovakia.
- October 28 - Gary Gabelich drives the rocket-powered Blue Flame to an official world land speed record of 622.287 mph (1,001.452863 km/h) on the dry lake bed of the Bonneville Salt Flats in Utah. The record, the first above 1,000 km/h, stands for nearly 13 years.
- October 30 - In Vietnam, the worst monsoon to hit the area in six years causes large floods, kills 293, leaves 200,000 homeless and virtually halts the Vietnam War.

November

- November 1 - Fire destroys Le Cinq Sept dance hall in St. Laurent Du Pont, France – 144 dead.
- November 4 - Vietnam War: Vietnamization - The United States turns control of the air base in the Mekong Delta to South Vietnam. Genie "the Wild Child" discovered in her house at the age of 13 after being in complete isolation for 10 years with no language skills.
- November 4 - Social authorities in California, USA, take custody of Genie, a girl who had been kept in solitary confinement since her birth
- November 5 - Vietnam War: United States Military Assistance Command in Vietnam reports the lowest weekly American soldier death toll in five years (24 soldiers died that week, which was the fifth consecutive week the death toll was below 50; 431 were reported wounded that week, however).
- November 8 - Egypt, Sudan and Libya announce their intentions to form a federation.
- November 9 - Charles de Gaulle dies – he is buried November 13.
- November 9 - Soviet Union launches Luna 17.
- November 9 - Vietnam War: The Supreme Court of the United States votes 6 to 3 to not hear a case by the state of Massachusetts asking to allow the state the ability to enforce its law granting Massachusetts residents the right to refuse military service in an undeclared war.
- November 10 - Vietnam War: Vietnamization - For the first time in five years, an entire week ended with no reports of American combat fatalities in Southeast Asia.
- November 12 - Soviet author Andrei Amalrik sentenced for three years for anti-Soviet writings.
- November 12 - The Oregon Highway Division (now known as the Oregon Department of Transportation) is given the task of removing a rotting beached Grey whale, leading to the now infamous exploding whale incident.
- November 13 - Military coup in Syria – Hafez al-Assad takes the power.
- November 13 - 1970 Bhola cyclone: A 120-mph tropical cyclone hits the densely populated Ganges Delta region of East Pakistan (now Bangladesh), killing an estimated 500,000 people (this is regarded as the 20th century's worst cyclone disaster).
- November 14 - fatal airplane accident in Wayne County, West Virginia, claims the lives of the entire Marshall University football team.
- November 17 - Vietnam War: Lieutenant William Calley goes on trial for the My Lai massacre.
- November 17 - Luna program: The Soviet Union lands Lunokhod 1 on Mare Imbrium (Sea of Rains) on the Moon. This is the first roving remote-controlled robot to land on another world and was released by the orbiting Luna 17 spacecraft.
- November 18 - US President Richard Nixon asks the U.S. Congress for US$155 million in supplemental aid for the Cambodian government (US$85 million was for military assistance in order to help prevent the overthrow of the government of Premier Lon Nol by the Khmer Rouge and North Vietnam).
- November 18 - United Nations Security Council demands that no government should recognize Rhodesia.
- November 19 - EEC prime minister meeting in Munich.
- November 21 - Syrian Prime Minister Hafez al-Assad forms a new government but retains the post of defense minister.
- November 21 - in Ethiopia, Eritrea Liberation Front kills an Ethiopian general.
- November 21 - Vietnam War: Operation Ivory Coast - A joint Air Force and Army team raids the Son Tay prison camp in an attempt to free American POWs thought to be held there (there were zero Americans killed, but the prisoners had already moved to another camp; All US POWs were moved to a handful of central prison complexes as a result of this raid).
- November 22 - Guinean president Sekou Toure accuses Portugal of an attack when hundreds of mercenaries land near capital Conakry. Guinean army repels the landing attempts in November 23-24. November 25-29 UN delegation arrives to investigate the situation. In December 4 UN announces that Portuguese navy and army units are responsible.
- November 25 - In Japan, world-famous author and Tatenokai militia leader Yukio Mishima and his followers take over Inchigaya HQ of the Japan Self-Defense Forces and take general Kanetoshi Mashita hostage. When Mishima's speech fails to sway public opinion towards his right-wing political beliefs, he commits seppuku.
- November 26 - East Pakistan leader sheik Mujibur Rahman accuses central government of negligence in catastrophe relief.
- November 26 - Pope Paul VI begins an Asian tour.
- November 27 - Bolivian artist Benjamin Mendoza tries to assassinate Paul VI during pope's visit in Manila.

December

- December 1 - Italian House of Representatives accepts the divorce law.
- December 1 - Ethiopia recognizes People's Republic of China.
- December 1 - Basque ETA kidnaps West German Eugen Beihl in San Sebastian.
- December 1 - Luis Echeverría Álvarez becomes president of Mexico.
- December 2 - The United States Environmental Protection Agency begins operations.
- December 3 - October Crisis: In Montreal, Quebec, kidnapped British Trade Commissioner James Cross is released by the Front de Libération du Québec terrorist group after being held hostage for 60 days. Police negotiate his release and in return the Government of Canada grants five terrorists from the FLQ's Chenier Cell their request for safe passage to Cuba.
- December 3 - Burgos Trial - In Burgos, Spain, begins a trial against 16 Basques accused of terrorism.
- December 4 - Spanish government declares a three-month martial law in Basque county of Guipuzco due to strikes and demonstrations.
- December 5 - Asian and Australian tour of Paul VI ends.
- December 7 - Giovanni Enrico Bucher, Swiss ambassador to Brazil, is kidnapped in Rio de Janeiro; kidnappers demand release of 70 political prisoners.
- December 7 - UN general assembly supports the isolation of South Africa due to its apartheid policies.
- December 7 - During his visit to the Polish capital, German chancellor Willy Brandt goes down on his knees in front of a monument for the victims in the ghetto of Warsaw.
- December 12 - Landslide in western Colombia – over 200 dead.
- December 13 - Government of Poland announces increases in the prize of food. Riots and looting erupt until a bloody confrontation between the rioters against army and the police in December 15. Martial law December 17-22. December 23 the government will freeze the food prizes for two years.
- December 15 - The USSR's Venera 7 becomes the first spacecraft to land successfully on Venus and transmit data back to earth
- December 16 - Ethiopian government declares state of emergency in the county of Eritrea due to activities of Eritrea Liberation Front.
- December 20 - General secretary of the communist part of Poland, Wladyslaw Gomulka, resigns – Edward Gierek takes his place.
- December 20 - Egyptian delegation leaves for Moscow to ask for economic and military aid.
- December 21 - Elvis Presley pays an unscheduled call on Richard Nixon in the Oval Office, volunteering to help with law enforcement problems.
- December 22 - Libyan revolutionary council declares that it will nationalize all foreign banks in the country.
- December 22 - Franz Stangl, the ex-commander of Treblinka is sentenced to life imprisonment.
- December 23 - Bolivian government releases Regis Debray.
- December 25 - ETA releases Eugen Beihl.
- December 27 - Indian president declares new elections.
- December 28 - Burgos Trial – three Basques are sentenced to death (three twice), others sentenced for 12-62 years and one released. December 30 Franco commutes the death sentences to 30 years in prison.
- December 28 - Suspects of killing Pierre Laporte, Jacques & Paul Rose and Francis Sunard, are arrested near Montreal.
- December 30 - In Viscaya Basque county 15.000 goes to strike to protest Burgos trial death sentences.

Unknown date

- The first Regional Technical Colleges open in Ireland.
- Disappearance of Sada Abe, Japanese former prostitute and later actress.
- Discovery in England of the Sweet Track, the World's oldest engineered roadway.

Births

January-March

- January 6 - Gabrielle Reece, American volleyball player and model
- January 13 - Keith Coogan, American actor
- January 13 - Marco Pantani, Italian cyclist (d. 2004)
- January 15 - Shane McMahon, American Wrestler
- January 17 - Jeremy Roenick, American hockey player
- January 17 - Genndy Tartakovsky Russian animator
- January 22 - Alex Ross, American comic artist
- January 29 - Heather Graham, American actress
- January 29 - Rajyavardhan Singh Rathore, Indian shooter
- January 31 - Minnie Driver, English actress
- February 24 - Jeff Garcia, American football player
- March 8 - Jason Elam, American football player
- March 18 - Queen Latifah, American rapper, record producer, and actress
- March 22 - Leontien van Moorsel, Dutch cyclist
- March 24 - Lara Flynn Boyle, American actress
- March 24 - Sharon Corr, Irish musician (The Corrs)
- March 27 - Mariah Carey, American singer
- March 27 - Leila Pahlavi, Iranian princess (d. 2001)
- March 28 - Vince Vaughn, American actor, writer, and producer

April-May

- April 4 - Barry Pepper, Canadian actor
- April 12 - Nick Hexum, American singer and guitarist
- April 13 - Rick Schroeder, American actor
- April 18 - Greg Eklund, American drummer (Everclear)
- April 21 - Nicole Sullivan, American actress, comedienne, and writer
- April 22 - Regine Velasquez, Filipina singer, actress, model, record producer, and entrepreneur
- April 25 - Jason Lee, American skateboarder and actor
- April 27 - Kylie Travis, English-born actress and model
- April 29 - Andre Agassi, American tennis player
- April 29 - Uma Thurman, American actress
- May 12 - Mike Weir, Canadian golfer
- May 15 - Rod Smith, American football player
- May 16 - Gabriela Sabatini, Argentine tennis player
- May 18 - Tina Fey, American writer, comedienne, and actress
- May 22 - Naomi Campbell, English model and actress
- May 24 - Jeff Zgonina, American football player
- May 25 - Jamie Kennedy, American actor and comedian
- May 26 - Nobuhiro Watsuki, Japanese cartoonist
- May 27 - Joseph Fiennes, English actor

June-July

- June 6 - Anthony Norris, American professional wrestler
- June 8 - Kelli Williams, American actress
- June 13 - Mikael Ljungberg, Swedish wrestler (d. 2004)
- June 16 - Phil Mickelson, American golfer
- June 19 - Quincy Watts, American athlete
- June 20 - Russell Garcia, British field hockey player
- June 20 - Moulay Rachid, Prince of Morocco
- June 25 - Lucy Benjamin, British actress
- June 26 - Patrick Norton, American writer and television host
- June 26 - Chris O'Donnell, American actor
- June 27 - Jim Edmonds, baseball player
- June 27 - Vitamin C, American singer
- July 3 - Teemu Selanne, Finnish hockey player
- July 3 - Shawnee Smith, American actress
- July 3 - Yona Kosashvili, chess player
- July 5 - Mac Dre, American rapper (d. 2004)
- July 8 - Beck, American singer
- July 11 - Saj Karim, British politician
- July 23 - Charisma Carpenter, American actress
- July 23 - Thea Dorn, German writer

August-September

- August 2 - Tony Amonte, American hockey player
- August 6 - M. Night Shyamalan, Indian film director, writer, producer, and actor
- August 13 - Alan Shearer, English footballer
- August 17 - Jim Courier, American tennis player
- August 18 - Malcolm-Jamal Warner, American actor
- August 20 - John Carmack, American computer game programmer
- August 21 - Erik Dekker, Dutch professional cyclist
- August 23 - Jay Mohr, American actor and comedian
- August 25 - Claudia Schiffer, German model
- August 27 - Jim Thome, baseball player
- August 29 - Jacco Eltingh, Dutch tennis player
- August 31 - Deborah Gibson, American singer
- September 4 - Daisy Dee, Dutch singer and actress
- September 8 - Latrell Sprewell, American basketball player
- September 9 - Macy Gray, American singer
- September 10 - Phaswane Mpe, South African writer (d. 2004)
- September 14 - Craig Montoya, American musician (Everclear)
- September 18 - Darren Gough, English cricketer
- September 19 - Takanori Nishikawa, Japanese singer
- September 22 - Mike Matheny, baseball player
- September 23 - Ani DiFranco, American mus

Classification

Classification may refer to:
- Taxonomic classification
- See also class (philosophy)
- Statistical classification
- Security classification Hint: Language use may refer to a taxonomic classification that is used for statistical purposes also as a "statistical classification" (like International Statistical Classification of Diseases and Related Health Problems). Information about such classifications can be found in Taxonomic classification. ja:分類

Pattern recognition

:For the William Gibson novel, see: Pattern Recognition (novel). Pattern recognition is a field within the area of machine learning. Alternatively, it can be defined as "the act of taking in raw data and taking an action based on the category of the data" [1]. As such, it is a collection of methods for supervised learning. Pattern recognition aims to classify data (patterns) based on either a priori knowledge or on statistical information extracted from the patterns. The patterns to be classified are usually groups of measurements or observations, defining points in an appropriate multidimensional space. A complete pattern recognition system consists of a sensor that gathers the observations to be classified or described; a feature extraction mechanism that computes numeric or symbolic information from the observations; and a classification or description scheme that does the actual job of classifying or describing observations, relying on the extracted features. The classification or description scheme is usually based on the availability of a set of patterns that have already been classified or described. This set of patterns is termed the training set and the resulting learning strategy is characterised as supervised learning. Learning can also be unsupervised, in the sense that the system is not given an a priori labelling of patterns, instead it establishes the classes itself based on the statistical regularities of the patterns. The classification or description scheme usually uses one of the following approaches: statistical (or decision theoretic), syntactic (or structural). Statistical pattern recognition is based on statistical characterisations of patterns, assuming that the patterns are generated by a probabilistic system. Structural pattern recognition is based on the structural interrelationships of features. Typical applications are automatic speech recognition, classification of text into several categories (e.g. spam/non-spam email messages), the automatic recognition of handwritten postal codes on postal envelopes, or the automatic recognition of images of human faces. The last three examples form the subtopic image analysis of pattern recognition that deals with digital images as input to pattern recognition systems.

External Links

- [http://cgm.cs.mcgill.ca/~godfried/teaching/pr-web.html List of Pattern Recognition web sites]

References

- Richard O. Duda, Peter E. Hart, David G. Stork (2001) Pattern classification (2nd edition), Wiley, New York, ISBN 0471056693.
- Dietrich Paulus and Joachim Hornegger (1998) Applied Pattern Recognition (2nd edition), Vieweg. ISBN 3-528-15558-2
- J. Schuermann: Pattern Classification: A Unified View of Statistical and Neural Approaches, Wiley&Sons, 1996, ISBN 0471135348
- Sholom Weiss and Casimir Kulikowski (1991) Computer Systems That Learn, Morgan Kaufmann. ISBN 1-55860-065-5 Category:Classification algorithms Category:Machine learning ms:Pengecaman pola ja:パターン認識 th:การรู้จำแบบ

Projection

The word projection has several uses.
- In digital identity, a transaction. See also link contracts
- In chemistry:
- Fischer projection
- Haworth projection
- Newman projection
- stereochemical projection
- In dentistry, enamel projection: focal apical extensions of the coronal enamel beyond the normally smooth cervical margin and on to the root of the tooth.
- In cartography, a map projection
- In psychology, psychological projection
- In neuroscience, the outputs from a neuron to other neurons.
- 3D projection, orthographic projection, oblique projection, and isometric projection are ways of representing 3D scenes in 2D; see graphical projection.
- In mathematics a projection is a linear transformation which remains unchanged if applied twice (p(u) = p(p(u))) (in other words, it is idempotent), such as that taking (x, y, z) in three dimensions to (x, y, 0) in the plane or generalisations of this in other dimensions. See orthogonal projection, projection (linear algebra), projection operator.
- In mathematics a projection is also a mapping that takes an element to the equivalence class it is in, and

Digital image processing

History

Digital processing of camera images

Uses

See also

External link

Algorithm

Formalized algorithms

Implementation

Example

History

Classes

See also

References

External links

Digital image

Image types

Image viewing

Image calibration

See also

Digital signal processing

DSP domains

Signal sampling

Time and space domains

Frequency domain

Applications

Techniques

Related fields

References

External links

1970

Events

January-February

March

April

May-June

July-August

September

October

November

December

Unknown date

Births

January-March

April-May

June-July

August-September

Classification

Pattern recognition

External Links

References

Projection