Digital image processing

The basis for modern image sensors is metal-oxide-semiconductor (MOS) technology,[5] which originates from the invention of the MOSFET (MOS field-effect transistor) by Mohamed M. Atalla and Dawon Kahng at Bell Labs in 1959.[6] This led to the development of digital semiconductor image sensors, including the charge-coupled device (CCD) and later the CMOS sensor.[5]

The charge-coupled device was invented by Willard S. Boyle and George E. Smith at Bell Labs in 1969.[7] 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. 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.[5] The CCD is a semiconductor circuit that was later used in the first digital video cameras for television broadcasting.[8]

The NMOS active-pixel sensor (APS) was invented by Olympus in Japan during the mid-1980s. This was enabled by advances in MOS semiconductor device fabrication, with MOSFET scaling reaching smaller micron and then sub-micron levels.[9][10] The NMOS APS was fabricated by Tsutomu Nakamura's team at Olympus in 1985.[11] The CMOS active-pixel sensor (CMOS sensor) was later developed by Eric Fossum's team at the NASA Jet Propulsion Laboratory in 1993.[12] By 2007, sales of CMOS sensors had surpassed CCD sensors.[13]

An important development in digital image compression technology was the discrete cosine transform (DCT), a lossy compression technique first proposed by Nasir Ahmed in 1972.[14] DCT compression became the basis for JPEG, which was introduced by the Joint Photographic Experts Group in 1992.[15] JPEG compresses images down to much smaller file sizes, and has become the most widely used image file format on the Internet.[16] Its highly efficient DCT compression algorithm was largely responsible for the wide proliferation of digital images and digital photos,[17] with several billion JPEG images produced every day as of 2015.[18]

Electronic signal processing was revolutionized by the wide adoption of MOS technology in the 1970s.[19] MOS integrated circuit technology was the basis for the first single-chip microprocessors and microcontrollers in the early 1970s,[20] and then the first single-chip digital signal processor (DSP) chips in the late 1970s.[21][22] DSP chips have since been widely used in digital image processing.[21]

The discrete cosine transform (DCT) image compression algorithm has been widely implemented in DSP chips, with many companies developing DSP chips based on DCT technology. DCTs are widely used for encoding, decoding, video coding, audio coding, multiplexing, control signals, signaling, analog-to-digital conversion, formatting luminance and color differences, and color formats such as YUV444 and YUV411. DCTs are also used for encoding operations such as motion estimation, motion compensation, inter-frame prediction, quantization, perceptual weighting, entropy encoding, variable encoding, and motion vectors, and decoding operations such as the inverse operation between different color formats (YIQ, YUV and RGB) for display purposes. DCTs are also commonly used for high-definition television (HDTV) encoder/decoder chips.[23]

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.[4] Digital image processing technology for medical applications was inducted into the Space Foundation Space Technology Hall of Fame in 1994.[24]

Digital filters are used to blur and sharpen digital images. Filtering can be performed by:

• convolution with specifically designed kernels (filter array) in the spatial domain[25]
• masking specific frequency regions in the frequency (Fourier) domain

The following examples show both methods:[26]

Filter type	Kernel or mask	Example
Original Image	${\displaystyle {\begin{bmatrix}0&0&0\\0&1&0\\0&0&0\end{bmatrix}}}$
Spatial Lowpass	${\displaystyle {\frac {1}{9}}\times {\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}}}$
Spatial Highpass	${\displaystyle {\begin{bmatrix}0&-1&0\\-1&4&-1\\0&-1&0\end{bmatrix}}}$
Fourier Representation	Pseudo-code: image = checkerboard F = Fourier Transform of image Show Image: log(1+Absolute Value(F))
Fourier Lowpass
Fourier Highpass

Images are typically padded before being transformed to the Fourier space, the highpass filtered images below illustrate the consequences of different padding techniques:

Zero padded	Repeated edge padded

Notice that the highpass filter shows extra edges when zero padded compared to the repeated edge padding.

MATLAB example for spatial domain highpass filtering.

img=checkerboard(20);                           % generate checkerboard
% **************************  SPATIAL DOMAIN  ***************************
klaplace=[0 -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 enable basic image transformations including scale, rotate, translate, mirror and shear as is shown in the following examples:[26]

Transformation Name	Affine Matrix	Example
Identity	${\displaystyle {\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}}}$
Reflection	${\displaystyle {\begin{bmatrix}-1&0&0\\0&1&0\\0&0&1\end{bmatrix}}}$
Scale	${\displaystyle {\begin{bmatrix}c_{x}=2&0&0\\0&c_{y}=1&0\\0&0&1\end{bmatrix}}}$
Rotate	${\displaystyle {\begin{bmatrix}\cos(\theta )&\sin(\theta )&0\\-\sin(\theta )&\cos(\theta )&0\\0&0&1\end{bmatrix}}}$	where θ = π/6 =30°
Shear	${\displaystyle {\begin{bmatrix}1&c_{x}=0.5&0\\c_{y}=0&1&0\\0&0&1\end{bmatrix}}}$

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, [x, y], 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 are needed. The third dimension is usually set to a non-zero constant, usually 1, so that the new coordinate is [x, 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 [x, y, 1] in 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.[27]

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 into a color-corrected image in a standard image file format.

Westworld (1973) was the first feature film to use the digital image processing to pixellate photography to simulate an android's point of view.[28]