TheInfoList

Digital image processing is the use of a
digital computer A computer is a machine that can be programmed to Execution (computing), carry out sequences of arithmetic or logical operations automatically. Modern computers can perform generic sets of operations known as Computer program, programs. These ...
to process
digital image A digital image is an composed of s, also known as ''pixels'', each with ', ' of numeric representation for its or that is an output from its fed as input by its denoted with ''x'', ''y'' on the x-axis and y-axis, respectively. Depending on ...
s through an
algorithm In and , an algorithm () is a finite sequence of , computer-implementable instructions, typically to solve a class of problems or to perform a computation. Algorithms are always and are used as specifications for performing s, , , and other ...

. As a subcategory or field of
digital signal processing Digital signal processing (DSP) is the use of digital processing Digital data, in information theory and information systems, is information represented as a string of discrete symbols each of which can take on one of only a finite number of ...
, digital image processing has many advantages over
analog image processing Analog or analogue may refer to: Computing and electronics * Analog signal, in which information is encoded in a continuous variable ** Analog device, an apparatus that operates on analog signals *** Analog electronics, circuits which use analog s ...
. 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 Noise is unwanted sound In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and t ...
and
distortion Distortion is the alteration of the original shape (or other characteristic) of something. In communications Communication (from Latin ''communicare'', meaning "to share" or "to be in relation with") is "an apparent answer to the painful di ...

during processing. Since images are defined over two dimensions (perhaps more) digital image processing may be modeled in the form of
multidimensional systems In mathematical systems theory, a multidimensional system or m-D system is a system in which not only one independent variable exists (like time), but there are several independent variables. Important problems such as factorization and Stability t ...
. 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 A digital image is an composed of s, also known as ''pixels'', each with ', ' of numeric representation for its or that is an output from its fed as input by its denoted with ''x'', ''y'' on the x-axis and y-axis, respectively. Depending on ...
processing, or digital picture processing as it often was called, were developed in the 1960s, at
Bell Laboratories Nokia Bell Labs (formerly named Bell Labs Innovations (1996–2007), AT&T Bell Laboratories (1984–1996) and Bell Telephone Laboratories (1925–1984)) is an American industrial research and scientific development company A company, ab ...
, the
Jet Propulsion Laboratory The Jet Propulsion Laboratory (JPL) is a federally funded research and development center Federally funded research and development centers (FFRDCs) are public-private partnerships which conduct research and development Research is " c ...
,
Massachusetts Institute of Technology Massachusetts Institute of Technology (MIT) is a private Private or privates may refer to: Music * "In Private "In Private" was the third single in a row to be a charting success for United Kingdom, British singer Dusty Springfield, aft ...
,
University of Maryland The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public In public relations Public relations (PR) is the practice of managing and disseminating information from an individual or an org ...
, and a few other research facilities, with application to
satellite imagery Satellite images (also Earth observation imagery, spaceborne photography, or simply satellite photo) are images of Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. About 29% of Earth's su ...
, wire-photo standards conversion,
medical imaging Medical imaging is the technique and process of imaging Imaging is the representation or reproduction of an object's form; especially a visual representation (i.e., the formation of an image). Imaging technology is the application of materi ...
,
videophone Videotelephony, sometimes also referred to as video teleconference or videoconferencing, comprises the technologies for the reception and transmission of audio Audio most commonly refers to sound In physics Physics (from grc, φυ ...
,
character recognition Optical character recognition or optical character reader (OCR) is the electronic or mechanical conversion of image An SAR radar imaging, radar image acquired by the SIR-C/X-SAR radar on board the Space Shuttle Endeavour shows the Teide ...
, and photograph enhancement. The purpose of early image processing was to improve the quality of the image. It was aimed for human beings to improve the visual effect of people. In image processing, the input is a low-quality image, and the output is an image with improved quality. Common image processing include image enhancement, restoration, encoding, and compression. The first successful application was the American Jet Propulsion Laboratory (JPL). They used image processing techniques such as geometric correction, gradation transformation, noise removal, etc. on the thousands of lunar photos sent back by the Space Detector Ranger 7 in 1964, taking into account the position of the sun and the environment of the moon. The impact of the successful mapping of the moon's surface map by the computer has been a huge success. Later, more complex image processing was performed on the nearly 100,000 photos sent back by the spacecraft, so that the topographic map, color map and panoramic mosaic of the moon were obtained, which achieved extraordinary results and laid a solid foundation for human landing on the moon. The cost of processing was fairly high, however, with the computing equipment of that era. That changed in the 1970s, when digital image processing proliferated as cheaper computers and dedicated hardware became available. This led to images being processed in real-time, for some dedicated problems such as
television standards conversion Television standards conversion is the process of changing a television transmission or recording from one television Television, sometimes shortened to TV or telly, is a telecommunication Media (communication), medium used for transmitt ...
. As
general-purpose computer A computer is a machine A machine is a man-made device that uses power to apply forces and control movement to perform an action. Machines can be driven by animals and people A people is a plurality of person A person (plural ...
s became faster, they started to take over the role of dedicated hardware for all but the most specialized and computer-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.

## Image sensors

The basis for modern
image sensors An image sensor or imager is a sensor that detects and conveys information used to make an image. It does so by converting the variable attenuation of light waves (as they refraction, pass through or reflection (physics), reflect off objects) int ...
is metal-oxide-semiconductor (MOS) technology, which originates from the invention of the
MOSFET The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET), also known as the metal–oxide–silicon transistor (MOS transistor, or MOS), is a type of insulated-gate field-effect transistor that is fabricated by th ...

(MOS field-effect transistor) by
Mohamed M. Atalla Mohamed M. Atalla ( ar, محمد عطاالله; August 4, 1924 – December 30, 2009) was an Egyptian-American engineer, physical chemist Physical chemistry is the study of macroscopic The macroscopic scale is the length scale on which ...

and
Dawon Kahng Dawon Kahng ( ko, 강대원; May 4, 1931 – May 13, 1992) was a Korean-American electrical engineer and inventor, known for his work in solid-state electronics Solid-state electronics means semiconductor A semiconductor material has an el ...

at
Bell Labs Nokia Bell Labs (formerly named Bell Labs Innovations (1996–2007), AT&T Bell Laboratories (1984–1996) and Bell Telephone Laboratories (1925–1984)) is an American industrial research and scientific development company A company, ab ...
in 1959. This led to the development of digital
semiconductor A semiconductor material has an electrical conductivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric curre ...
image sensors, including the
charge-coupled device A charge-coupled device (CCD) is an integrated circuit containing an array of linked, or coupled, capacitors. Under the control of an external circuit, each capacitor can transfer its electric charge to a neighboring capacitor. CCD sensors are a ...
(CCD) and later the
CMOS sensor An active-pixel sensor (APS) is an image sensor An image sensor or imager is a that detects and conveys information used to make an . It does so by converting the variable of light s (as they or objects) into , small bursts of that convey t ...
. The charge-coupled device was invented by
Willard S. Boyle Willard Sterling Boyle, (August 19, 1924May 7, 2011) was a Canadian Canadians (french: Canadiens) are people identified with the country of Canada. This connection may be residential, legal, historical or cultural. For most Canadians, many ...
and at Bell Labs in 1969. While researching MOS technology, they realized that an electric charge was the analogy of the magnetic bubble and that it could be stored on a tiny
MOS capacitor The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET), also known as the metal–oxide–silicon transistor (MOS transistor, or MOS), is a type of insulated-gate field-effect transistor The field-effect trans ...
. As it was fairly straightforward to fabricate a series of MOS capacitors in a row, they connected a suitable voltage to them so that the charge could be stepped along from one to the next. The CCD is a semiconductor circuit that was later used in the first
digital video camera A video camera is a camera A camera is an optical Optics is the branch of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior ...

s for
television broadcasting A television network or broadcaster is a telecommunications network for distribution of television program content, where a central operation provides programming to many television stations or multichannel video programming distributor, pay tel ...

. The NMOS
active-pixel sensorAn active-pixel sensor (APS) is an image sensor where each pixel sensor unit cell has a photodetector Photodetectors, also called photosensors, are sensors of light Light or visible light is electromagnetic radiation within the portion o ...
(APS) was invented by Olympus in Japan during the mid-1980s. This was enabled by advances in MOS
semiconductor device fabrication Semiconductor device fabrication is the process used to manufacture semiconductor devices A semiconductor A semiconductor material has an Electrical resistivity and conductivity, electrical conductivity value falling between that of a El ...
, with
MOSFET scaling The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET), also known as the metal–oxide–silicon transistor (MOS transistor, or MOS), is a type of insulated-gate field-effect transistor The field-effect tran ...
reaching smaller micron and then sub-micron levels. The NMOS APS was fabricated by Tsutomu Nakamura's team at Olympus in 1985. The
CMOS Complementary metal–oxide–semiconductor (CMOS, pronounced "see-moss"), also known as complementary-symmetry metal–oxide–semiconductor (COS-MOS), is a type of metal–oxide–semiconductor field-effect transistor The metal–oxide–se ...
active-pixel sensor (CMOS sensor) was later developed by
Eric Fossum Eric R. Fossum (born October 17, 1957) is an American physicist and engineer known for developing the CMOS sensor, CMOS image sensor. He is currently a professor at Thayer School of Engineering in Dartmouth College. Early years and education Fo ...
's team at the
NASA The National Aeronautics and Space Administration (NASA; ) is an independent agency A regulatory agency or regulatory authority, is a Public benefit corporation Public-benefit corporation is a term that has different meanings in differen ...

Jet Propulsion Laboratory The Jet Propulsion Laboratory (JPL) is a federally funded research and development center Federally funded research and development centers (FFRDCs) are public-private partnerships which conduct research and development Research is " c ...
in 1993. By 2007, sales of CMOS sensors had surpassed CCD sensors.

## Image compression

An important development in digital
image compression Image compression is a type of data compression In signal processing Signal processing is an electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, ...
technology was the
discrete cosine transform A discrete cosine transform (DCT) expresses a finite sequence of data points In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are ...
(DCT), a
lossy compression In information technology, lossy compression or irreversible compression is the class of data compression, data encoding methods that uses inexact approximations and partial data discarding to represent the content. These techniques are used to r ...
technique first proposed by Nasir Ahmed in 1972. DCT compression became the basis for
JPEG JPEG ( ) is a commonly used method of lossy compression In information technology, lossy compression or irreversible compression is the class of data encoding methods that uses inexact approximations and partial data discarding to represe ...

, which was introduced by the
Joint Photographic Experts Group The Joint Photographic Experts Group (JPEG) is the joint committee between ISO The International Organization for Standardization (ISO ) is an international standard An international standard is a technical standard A technical standard is an ...
in 1992. JPEG compresses images down to much smaller file sizes, and has become the most widely used
image file format Image file formats are standardized means of organizing and storing digital image A digital image is an composed of s, also known as ''pixels'', each with ', ' of numeric representation for its or that is an output from its fed as input ...
on the
Internet The Internet (or internet) is the global system of interconnected computer networks that uses the Internet protocol suite (TCP/IP) to communicate between networks and devices. It is a ''internetworking, network of networks'' that consist ...

. Its highly efficient DCT compression algorithm was largely responsible for the wide proliferation of
digital images Digital usually refers to something using digits, particularly binary digits. Technology and computing Hardware *Digital electronics Digital electronics is a field of electronics Electronics comprises the physics, engineering, technology a ...
and
digital photo Digital photography uses cameras A camera is an optical Optics is the branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the ...
s, with several billion JPEG images produced every day as of 2015.

## Digital signal processor (DSP)

Electronic
signal processing Signal processing is an electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetis ...

was revolutionized by the wide adoption of
MOS technology MOS Technology, Inc. ("MOS" being short for Metal Oxide Semiconductor The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET), also known as the metal–oxide–silicon transistor (MOS transistor, or MOS), i ...
in the 1970s.
MOS integrated circuit file:MOSFET Structure.png, upright=1.6, MOSFET, showing metal gate, gate (G), body (B), source (S) and drain (D) terminals. The gate is separated from the body by an gate oxide, insulating layer (pink). The metal–oxide–semiconductor field-eff ...
technology was the basis for the first single-chip
microprocessors A microprocessor is a computer processor where the data processing logic and control is included on a single integrated circuit An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchi ...
and
microcontrollers A microcontroller (MCU for ''microcontroller unit'') is a small computer on a single MOSFET, metal-oxide-semiconductor (MOS) integrated circuit (IC) chip. A microcontroller contains one or more Central processing unit, CPUs (processor cores) alo ...
in the early 1970s, and then the first single-chip
digital signal processor A digital signal processor (DSP) is a specialized microprocessor A microprocessor is a computer processor where the data processing logic and control is included on a single integrated circuit An integrated circuit or monolithic i ...
(DSP) chips in the late 1970s. DSP chips have since been widely used in digital image processing. The
discrete cosine transform A discrete cosine transform (DCT) expresses a finite sequence of data points In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are ...
(DCT)
image compression Image compression is a type of data compression In signal processing Signal processing is an electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, ...
algorithm has been widely implemented in DSP chips, with many companies developing DSP chips based on DCT technology. DCTs are widely used for
encoding In communication Communication (from Latin Latin (, or , ) is a classical language A classical language is a language A language is a structured system of communication Communication (from Latin ''communicare'', mean ...

, decoding,
video coding A video coding format (or sometimes video compression format) is a content representation format for storage or transmission of digital Digital usually refers to something using digits, particularly binary digits. Technology and computing Ha ...
,
audio coding An audio coding format (or sometimes audio compression format) is a content representation format for storage or transmission of digital audio Digital audio is a representation of sound recorded in, or converted into, Digital signal (signal ...
,
multiplexing In telecommunications Telecommunication is the transmission of information by various types of technologies over , radio, , or other systems. It has its origin in the desire of humans for communication over a distance greater than that ...
, control signals,
signaling In signal processing Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as audio signal processing, sound, image processing, images, and scientific measurements. Sig ...
, analog-to-digital conversion, formatting
luminance Luminance is a photometricPhotometry can refer to: * Photometry (optics), the science of measurement of visible light in terms of its perceived brightness to human vision * Photometry (astronomy), the measurement of the flux or intensity of an ...

and color differences, and color formats such as YUV444 and YUV411. DCTs are also used for encoding operations such as
motion estimation Motion estimation is the process of determining ''motion vector In video compression In signal processing Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as a ...
,
motion compensation Motion compensation is an algorithmic technique used to predict a frame in a video, given the previous and/or future frames by accounting for motion of the camera and/or objects in the video. It is employed in the encoding of video data for video ...
,
inter-frame An inter frame is a frame in a video compression In signal processing, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression i ...
prediction, quantization, perceptual weighting,
entropy encoding In information theory, an entropy coding (or entropy encoding) is a lossless compression , lossless data compression scheme that is independent of the specific characteristics of the medium. One of the main types of entropy coding creates and assi ...
, variable encoding, and
motion vector In video compression In signal processing Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as audio signal processing, sound, image processing, images, and scienti ...
s, and decoding operations such as the inverse operation between different color formats (
YIQ An image along with its Y, I, and Q components. YIQ is the color space A color space is a specific organization of colors. In combination with color profiling supported by various physical devices, it supports reproducible representations of co ...
,
YUV YUV is a color encoding system typically used as part of a color image pipelineAn image pipeline or video pipeline is the set of components commonly used between an image source (such as a camera, a scanner, or the rendering engine in a compute ...
and
RGB s The RGB color model is an additive color, additive color model A color model is an abstract mathematical model describing the way colors can be represented as tuples of numbers, typically as three or four values or color components. When ...

) for display purposes. DCTs are also commonly used for
high-definition television High-definition television (HD or HDTV) describes a television system providing a substantially higher image resolution Image resolution is the detail an holds. The term applies to s, film images, and other types of images. Higher resolution m ...
(HDTV) encoder/decoder chips.

## Medical imaging

In 1972, the engineer from British company EMI Housfield invented the X-ray computed tomography device for head diagnosis, which is what is usually called CT (computer tomography). The CT nucleus method is based on the projection of the human head section and is processed by computer to reconstruct the cross-sectional image, which is called image reconstruction. In 1975, EMI successfully developed a CT device for the whole body, which obtained a clear tomographic image of various parts of the human body. In 1979, this diagnostic technique won the Nobel Prize. Digital image processing technology for medical applications was inducted into the
Space Foundation Space Foundation is an American nonprofit organization that space advocacy, advocates for all sectors of the global space industry through space awareness activities, educational programs and major industry events. Founded in 1983. Locations Loc ...
Space Technology Hall of Fame in 1994.

Digital image processing allows the use of much more complex algorithms, and hence, can offer both more sophisticated performance at simple tasks, and the implementation of methods which would be impossible by analogue means. In particular, digital image processing is a concrete application of, and a practical technology based on: *
Classification Classification is a process related to categorization Categorization is the human ability and activity of recognizing shared features or similarities between the elements of the experience Experience refers to conscious , an English Paracels ...
*
Feature extractionIn machine learning, pattern recognition, and image processing, feature extraction starts from an initial set of measured data and builds derived values (Feature (machine learning), features) intended to be informative and non-redundant, facilitatin ...
* Multi-scale signal analysis *
Pattern recognition Pattern recognition is the automated recognition of pattern A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of ...
* Projection Some techniques which are used in digital image processing include: *
Anisotropic diffusion In image processing and computer vision, anisotropic diffusion, also called Perona–Malik diffusion, is a technique aiming at reducing image noise without removing significant parts of the image content, typically edges, lines or other details tha ...
*
Hidden Markov model Hidden Markov Model (HMM) is a statistical Markov model in which the system being mathematical model, modeled is assumed to be a Markov processcall it Xwith unobservable ("''hidden''") states. HMM assumes that there is another process Y whose beh ...
s *
Image editing Image editing encompasses the processes of altering images, whether they are Digital photography, digital photographs, traditional Photographic processing, photo-chemical photographs, or illustrations. Traditional analog image editing is kno ...
*
Image restoration Image restoration is the operation of taking a corrupt/noisy image and estimating the clean, original image. Corruption may come in many forms such as motion blur Motion blur is the apparent streaking of moving objects in a photograph or a sequen ...
*
Independent component analysis In signal processing Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as audio signal processing, sound, image processing, images, and scientific measurements. Signal p ...
*
Linear filter Linearity is the property of a mathematical relationship (''function (mathematics), function'') that can be graph of a function, graphically represented as a straight Line (geometry), line. Linearity is closely related to Proportionality (mathema ...
ing *
Neural networks#REDIRECT Artificial neural network Artificial neural networks (ANNs), usually simply called neural networks (NNs), are computing systems vaguely inspired by the biological neural networks that constitute animal brain A brain is an organ ( ...
*
Partial differential equations In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...
*
Pixelation In computer graphics, pixelation (or pixellation in British English) is caused by displaying a bitmap or a section of a bitmap at such a large size that individual pixels, small single-colored square display elements that comprise the bitmap, ar ...
* Point feature matching * Principal components analysis *
Self-organizing map A self-organizing map (SOM) or self-organizing feature map (SOFM) is an unsupervised machine learning Machine learning (ML) is the study of computer algorithms that can improve automatically through experience and by the use of data. It is ...
s *
Wavelet A wavelet is a wave In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other wor ...

s

# Digital image transformations

## Filtering

Digital filters are used to blur and sharpen digital images. Filtering can be performed by: *
convolution In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities a ...
with specifically designed kernels (filter array) in the spatial domain * masking specific frequency regions in the frequency (Fourier) domain The following examples show both methods:

### Image padding in Fourier domain filtering

Images are typically padded before being transformed to the Fourier space, the highpass filtered images below illustrate the consequences of different padding techniques: Notice that the highpass filter shows extra edges when zero padded compared to the repeated edge padding.

### Filtering code examples

MATLAB example for spatial domain highpass filtering. img=checkerboard(20); % generate checkerboard % ************************** SPATIAL DOMAIN *************************** klaplace= -1 0; -1 5 -1; 0 -1 0 % Laplacian filter kernel X=conv2(img,klaplace); % convolve test img with % 3x3 Laplacian kernel figure() imshow(X,[]) % show Laplacian filtered title('Laplacian Edge Detection')

## Affine transformations

Affine transformations enable basic image transformations including scale, rotate, translate, mirror and shear as is shown in the following examples: To apply the affine matrix to an image, the image is converted to matrix in which each entry corresponds to the pixel intensity at that location. Then each pixel's location can be represented as a vector indicating the coordinates of that pixel in the image,
, y The comma is a punctuation Punctuation (or sometimes interpunction) is the use of spacing, conventional signs (called punctuation marks), and certain typographical devices as aids to the understanding and correct reading of written text, ...
where x and y are the row and column of a pixel in the image matrix. This allows the coordinate to be multiplied by an affine-transformation matrix, which gives the position that the pixel value will be copied to in the output image. However, to allow transformations that require translation transformations, 3 dimensional
homogeneous coordinates In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It h ...
are needed. The third dimension is usually set to a non-zero constant, usually 1, so that the new coordinate is , y, 1 This allows the coordinate vector to be multiplied by a 3 by 3 matrix, enabling translation shifts. So the third dimension, which is the constant 1, allows translation. Because matrix multiplication is associative, multiple affine transformations can be combined into a single affine transformation by multiplying the matrix of each individual transformation in the order that the transformations are done. This results in a single matrix that, when applied to a point vector, gives the same result as all the individual transformations performed on the vector , y, 1in sequence. Thus a sequence of affine transformation matrices can be reduced to a single affine transformation matrix. For example, 2 dimensional coordinates only allow rotation about the origin (0, 0). But 3 dimensional homogeneous coordinates can be used to first translate any point to (0, 0), then perform the rotation, and lastly translate the origin (0, 0) back to the original point (the opposite of the first translation). These 3 affine transformations can be combined into a single matrix, thus allowing rotation around any point in the image.

## Image denoising with Morphology

Mathematical morphology Mathematical morphology (MM) is a theory and technique for the analysis and processing of Geometry, geometrical structures, based on set theory, lattice theory, topology, and random functions. MM is most commonly applied to digital images, but it ca ...
is suitable for denoising images. Structuring element are important in
Mathematical morphology Mathematical morphology (MM) is a theory and technique for the analysis and processing of Geometry, geometrical structures, based on set theory, lattice theory, topology, and random functions. MM is most commonly applied to digital images, but it ca ...
. The following examples are about Structuring elements. The denoise function, image as I, and structuring element as B are shown as below and table. e.g. $\left(I\text{'}\right) = \begin 45 & 50 & 65 \\ 40 & 60 & 55 \\ 25 & 15 & 5 \end B = \begin 1 & 2 & 1 \\ 2 & 1 & 1 \\ 1 & 0 & 3 \end$ Define Dilation(I, B)(i,j) = $max\$. Let Dilation(I,B) = D(I,B) D(I', B)(1,1) = $max\left(45+1,50+2,65+1,40+2,60+1,55+1,25+1,15+0,5+3\right) = 66$ Define Erosion(I, B)(i,j) = $min\$. Let Erosion(I,B) = E(I,B) E(I', B)(1,1) = $min\left(45-1,50-2,65-1,40-2,60-1,55-1,25-1,15-0,5-3\right) = 2$ After dilation $\left(I\text{'}\right) = \begin 45 & 50 & 65 \\ 40 & 66 & 55 \\ 25 & 15 & 5 \end$ After erosion $\left(I\text{'}\right) = \begin 45 & 50 & 65 \\ 40 & 2 & 55 \\ 25 & 15 & 5 \end$ An opening method is just simply erosion first, and then dilation while the closing method is vice versa. In reality, the D(I,B) and E(I,B) can implemented by
Convolution In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities a ...
In order to apply the denoising method to an image, the image is converted into grayscale. A mask with denoising method is logical matrix with
Convolution In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities a ...
Neighbor and structuring element and then replace the center with a minimum of neighbor. Take the Closing method for example. Dilation first # Read the image and convert it into grayscale with Matlab. ## Get the size of an image. The return value row numbers and column numbers are the boundaries we are going to use later. ## structuring elements depend on your dilation or erosion function. The minimum of the neighbor of a pixel leads to an erosion method and the maximum of neighbor leads to a dilation method. ## Set the time for dilation, erosion, and closing. # Create a zero matrix of the same size as the original image. # Dilation first with structuring window. ## structuring window is 3*3 matrix and convolution ## For loop extract the minimum with window from row range ~ image height - 1with column range ~ image width - 1# Fill the minimum value to the zero matrix and save a new image ## For the boundary, it can still be improved. Since in the method, a boundary is ignored. Padding elements can be applied to deal with boundaries. Then Erosion (Take the dilation image as input) # Create a zero matrix of the same size as the original image. # Erosion with structuring window. ## structuring window is 3*3 matrix and convolution ## For loop extract the maximum with window from row range ~ image height - 1with column range ~ image width - 1# Fill the maximum value to the zero matrix and save a new image ## For the boundary, it can still be improved. Since in the method, boundary is ignored. Padding elements can be applied to deal with boundaries. # Results are as above table shown

# Applications

## Digital camera images

Digital cameras generally include specialized digital image processing hardware – either dedicated chips or added circuitry on other chips – to convert the raw data from their
image sensor An image sensor or imager is a sensor A sensor is a device that produces an output signal for the purpose of sensing of a physical phenomenon. In the broadest definition, a sensor is a device, module, machine, or subsystem that detects e ...
into a color-corrected image in a standard
image file format Image file formats are standardized means of organizing and storing digital image A digital image is an composed of s, also known as ''pixels'', each with ', ' of numeric representation for its or that is an output from its fed as input ...
. Additional post processing techniques increase edge sharpness or color saturation to create more naturally looking images.

## Film

''
Westworld ''Westworld'' is an American science fiction-thriller (genre), thriller media franchise that began with the Westworld (film), 1973 film ''Westworld'', written and directed by Michael Crichton. The film depicts a technologically advanced Wild Wes ...
'' (1973) was the first feature film to use the digital image processing to
pixellate In computer graphics, pixelation (or pixellation in British English) is caused by displaying a bitmap or a section of a bitmap at such a large size that individual pixels, small single-colored square display elements that comprise the bitmap, ar ...
photography to simulate an android's point of view. Image processing is also vastly used to produce the
chroma key Chroma key compositing, or chroma keying, is a visual-effects and post-production 275px, A video editing suite Post-production is part of the process of filmmaking, video production, audio production Sound design is the art and practi ...

effect that replaces the background of actors with natural or artistic scenery.

## Face detection

Face detection Face detection is a computer technology being used in a variety of applications that identifies human faces in digital images. Face detection also refers to the psychological process by which humans locate and attend to faces in a visual scene. ...

can be implemented with
Mathematical morphology Mathematical morphology (MM) is a theory and technique for the analysis and processing of Geometry, geometrical structures, based on set theory, lattice theory, topology, and random functions. MM is most commonly applied to digital images, but it ca ...
,
Discrete cosine transform A discrete cosine transform (DCT) expresses a finite sequence of data points In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are ...
which is usually called DCT, and horizontal
Projection (mathematics) In mathematics, a projection is a function (mathematics), mapping of a set (mathematics), set (or other mathematical structure) into a subset (or sub-structure), which is equal to its square for function composition, mapping composition, i.e., wh ...
. General method with feature-based method The feature-based method of face detection is using skin tone, edge detection, face shape, and feature of a face (like eyes, mouth, etc.) to achieve face detection. The skin tone, face shape, and all the unique elements that only the human face have can be described as features. Process explanation # Given a batch of face images, first, extract the skin tone range by sampling face images. The skin tone range is just a skin filter. ##
Structural similarity The structural similarity index measure (SSIM) is a method for predicting the perceived quality of digital television and cinematic pictures, as well as other kinds of digital images and videos. SSIM is used for measuring the similarity between t ...
index measure (SSIM) can be applied to compare images in terms of extracting the skin tone. ## Normally, HSV or RGB color spaces are suitable for the skin filter. E.g. HSV mode, the skin tone range is ,48,50~ 0,255,255# After filtering images with skin tone, to get the face edge, morphology and DCT are used to remove noise and fill up missing skin areas. ## Opening method or closing method can be used to achieve filling up missing skin. ## DCT is to avoid the object with tone-like skin. Since human faces always have higher texture. ## Sobel operator or other operators can be applied to detect face edge. # To position human features like eyes, using the projection and find the peak of the histogram of projection help to get the detail feature like mouse, hair, and lip. ## Projection is just projecting the image to see the high frequency which is usually the feature position.

## Improvement of image quality method

Image quality can be influenced by camera vibration, over-exposure, gray level distribution too centralized, and noise, etc. For example, noise problem can be solved by
Smoothing In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with ...

method while gray level distribution problem can be improved by
Histogram Equalization Histogram equalization is a method in image processing of contrast (vision), contrast adjustment using the image's Image histogram, histogram. Image:Histogrammeinebnung.png, 300px, alt=A histogram which is zero apart from a central area contain ...

.
Smoothing In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with ...

method In drawing, if there is some dissatisfied color, taking some color around dissatisfied color and averaging them. This is an easy way to think of Smoothing method. Smoothing method can be implemented with mask and
Convolution In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities a ...
. Take the small image and mask for instance as below. image is $\begin 2 & 5 & 6 & 5\\ 3 & 1 & 4 & 6 \\ 1 & 28 & 30 & 2 \\ 7 & 3 & 2 & 2 \end$ mask is $\begin 1/9 & 1/9 & 1/9 \\ 1/9 & 1/9 & 1/9 \\ 1/9 & 1/9 & 1/9 \end$ After
Convolution In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities a ...
and smoothing, image is $\begin 2 & 5 & 6 & 5\\ 3 & 9 & 10 & 6 \\ 1 & 9 & 9 & 2 \\ 7 & 3 & 2 & 2 \end$ Oberseving image
, 1 The comma is a punctuation Punctuation (or sometimes interpunction) is the use of spacing, conventional signs (called punctuation marks), and certain typographical devices as aids to the understanding and correct reading of written text, ...
image
, 2 The comma is a punctuation Punctuation (or sometimes interpunction) is the use of spacing, conventional signs (called punctuation marks), and certain typographical devices as aids to the understanding and correct reading of written text, ...
image
, 1 The comma is a punctuation Punctuation (or sometimes interpunction) is the use of spacing, conventional signs (called punctuation marks), and certain typographical devices as aids to the understanding and correct reading of written text, ...
and image
, 2 The comma is a punctuation Punctuation (or sometimes interpunction) is the use of spacing, conventional signs (called punctuation marks), and certain typographical devices as aids to the understanding and correct reading of written text, ...
The original image pixel is 1, 4, 28, 30. After smoothing mask, the pixel becomes 9, 10, 9, 9 respectively. new image
, 1 The comma is a punctuation Punctuation (or sometimes interpunction) is the use of spacing, conventional signs (called punctuation marks), and certain typographical devices as aids to the understanding and correct reading of written text, ...
= $\tfrac$ * (image ,0image ,1image ,2image ,0image ,1image ,2image ,0image ,1image ,2 new image
, 1 The comma is a punctuation Punctuation (or sometimes interpunction) is the use of spacing, conventional signs (called punctuation marks), and certain typographical devices as aids to the understanding and correct reading of written text, ...
= floor($\tfrac$ * (2+5+6+3+1+4+1+28+30)) = 9 new image
, 2 The comma is a punctuation Punctuation (or sometimes interpunction) is the use of spacing, conventional signs (called punctuation marks), and certain typographical devices as aids to the understanding and correct reading of written text, ...
= floor({$\tfrac\left\{1\right\}\left\{9\right\}$ * (5+6+5+1+4+6+28+30+2)) = 10 new image
, 1 The comma is a punctuation Punctuation (or sometimes interpunction) is the use of spacing, conventional signs (called punctuation marks), and certain typographical devices as aids to the understanding and correct reading of written text, ...
= floor($\tfrac\left\{1\right\}\left\{9\right\}$ * (3+1+4+1+28+30+73+3+2)) = 9 new image
, 2 The comma is a punctuation Punctuation (or sometimes interpunction) is the use of spacing, conventional signs (called punctuation marks), and certain typographical devices as aids to the understanding and correct reading of written text, ...
= floor($\tfrac\left\{1\right\}\left\{9\right\}$ * (1+4+6+28+30+2+3+2+2)) = 9 Gray Level Histogram method Generally, given a gray level histogram from an image as below. Changing the histogram to uniform distribution from an image is usually what we called
Histogram equalization Histogram equalization is a method in image processing of contrast (vision), contrast adjustment using the image's Image histogram, histogram. Image:Histogrammeinebnung.png, 300px, alt=A histogram which is zero apart from a central area contain ...

. In discrete time, the area of gray level histogram is $\sum_\left\{i=0\right\}^\left\{k\right\}H\left(p_i\right)$(see figure 1) while the area of uniform distribution is $\sum_\left\{i=0\right\}^\left\{k\right\}G\left(q_i\right)$(see figure 2). It's clear that the area won't change, so $\sum_\left\{i=0\right\}^\left\{k\right\}H\left(p_i\right) = \sum_\left\{i=0\right\}^\left\{k\right\}G\left(q_i\right)$. From the uniform distribution, the probability of $q_i$ is $\tfrac\left\{N^2\right\}\left\{q_k - q_0\right\}$ while the $0 < i < k$ In continuous time, the equation is $\displaystyle \int_\left\{q_0\right\}^\left\{q\right\} \tfrac\left\{N^2\right\}\left\{q_k - q_0\right\}ds = \displaystyle \int_\left\{p_0\right\}^\left\{p\right\}H\left(s\right)ds$. Moreover, based on the definition of a function, the Gray level histogram method is like finding a function $f$ that satisfies f(p)=q. {, class="wikitable" , - ! Improvement method ! Issue ! Before improvement ! Process ! After improvement , - , - , Smoothing method , noise with Matlab, salt & pepper with 0.01 parameter is added
to the original image in order to create a noisy image. , , # read image and convert image into grayscale # convolution the graysale image with the mask $\begin\left\{bmatrix\right\} 1/9 & 1/9 & 1/9 \\ 1/9 & 1/9 & 1/9 \\ 1/9 & 1/9 & 1/9 \end\left\{bmatrix\right\}$ # denoisy image will be the result of step 2. , , - , - , Histogram Equalization , Gray level distribution too centralized , , Refer to the
Histogram equalization Histogram equalization is a method in image processing of contrast (vision), contrast adjustment using the image's Image histogram, histogram. Image:Histogrammeinebnung.png, 300px, alt=A histogram which is zero apart from a central area contain ...

, , -

# Fatigue detection and monitoring technologies

There were significant advancements in fatigue monitoring technology the past decade. These innovative technology solutions are now commercially available and offer real safety benefits to drivers, operators and other shift workers across all industries. Software developers, engineers and scientists develop
fatigue detection softwareFatigue detection software is intended to reduce fatigue related fatalities and incidents. Several companies are working on a technology for use in industries such as mining, road- and rail haulage and aviation. The technology may soon find wider app ...
using various physiological cues to determine the state of fatigue or drowsiness. The measurement of brain activity (electroencephalogram) is widely accepted as the standard in fatigue monitoring. Other technology used to determine fatigue related impairment include behavioural symptom measurements such as; eye behaviour, gaze direction, micro-corrections in steering and throttle use as well as heart rate variability.

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Digital imaging Digital imaging or digital image acquisition is the creation of a digital Digital usually refers to something using discrete digits, often binary digits. Technology and computing Hardware *Digital electronics Digital electronics is a fie ...
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Computer graphics Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great dea ...

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Computer vision Computer vision is an interdisciplinary scientific field that deals with how computer A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations automatically. Modern computers can perform ge ...
* CVIPtools *
Digitizing DigitizationDefinition of digitization
at WhatIs.com
is the process of converting ...
* Free boundary condition *
GPGPU General-purpose computing on graphics processing units (GPGPU, or less often GPGP) is the use of a graphics processing unit A graphics processing unit (GPU) is a specialized designed to rapidly manipulate and alter to accelerate the creatio ...
* Homomorphic filtering *
Image analysis Image analysis or imagery analysis is the extraction of meaningful information from image File:TEIDE.JPG, An Synthetic aperture radar, SAR radar imaging, radar image acquired by the SIR-C/X-SAR radar on board the Space Shuttle Endeavour sho ...
* IEEE Intelligent Transportation Systems Society *
Multidimensional systems In mathematical systems theory, a multidimensional system or m-D system is a system in which not only one independent variable exists (like time), but there are several independent variables. Important problems such as factorization and Stability t ...
* Remote sensing software * Standard test image * Superresolution * Total variation denoising * Machine Vision * Bounded variation * Radiomics