Chapter 1: Digital image processing
To put it simply, digital image processing is the algorithmic manipulation of digital pictures on a digital computer. Digital image processing, a subfield of digital signal processing, offers many benefits over its analog predecessor. It enables the use of more algorithms on the input data and helps prevent issues like noise and distortion from accumulating. Digital image processing may be described as multidimensional systems due to the fact that pictures are specified across two (or more) dimensions. The advancement of computing technology, the growth of mathematics (particularly the development and improvement of discrete mathematics theory), and the rising demand for digital image processing in a variety of fields, including the environment, agriculture, the military, industry, and medicine, are the primary influences on its creation and growth.
Digital image processing, or digital picture processing as it was formerly known, was pioneered in the 1960s by a number of research institutions including Bell Laboratories, the Jet Propulsion Laboratory, MIT, the University of Maryland, and others for use in fields such as satellite imaging, wire-photo standards conversion, medical imaging, videophone, character recognition, and photograph enhancement.
However, given the technology available at the time, the processing cost was rather expensive. In the 1970s, however, digital image processing exploded as low-cost computers and specialized gear became widely accessible. As a result, challenges like converting television standards might be tackled in real time using image processing. General-purpose computers began to replace specialist hardware for all but the most computationally expensive tasks as their processing speeds increased. With the advent of powerful computers and signal processors in the 2000s, digital image processing quickly replaced analog techniques as the gold standard in the industry.
Metal-oxide-semiconductor (MOS) technology is the foundation of current image sensors, The discrete cosine transform (DCT) was a key innovation in digital image compression technology that was initially presented by Nasir Ahmed in 1972.
In the 1970s, the widespread use of MOS technology radically altered the field of electronic signal processing.
The X-ray computed tomography (often known as CT) gadget for head diagnostics was created in 1972 by British business EMI Housfield's engineer (computer tomography). The CT nucleus technique relies on a projection of a cross-section of a human head, which is then processed digitally to recreate the cross-sectional picture. Tomographic images of different sections of the human body were produced clearly when EMI created a whole-body CT device in 1975. This method of diagnosis was awarded the Nobel Prize in 1979.
As a result of the employment of more complicated algorithms, digital image processing may provide both improved performance on basic jobs and the introduction of techniques that would be difficult to do with analog equipment.
Digital image processing, in particular, is both a useful application and technology that relies on:
Classification
Feature extraction
Signal analysis on several scales
Pattern recognition
Projection
Examples of methods used by digital image processing:
Anisotropic diffusion
Hidden Markov models
Image editing
Image restoration
Independent component analysis
Linear filtering
Neural networks
Partial differential equations
Pixelation
Point feature matching
Principal components analysis
Maps that organize themselves
Wavelets
To soften or sharpen digital photos, just apply a suitable filter. It is possible to filter data by:
convolution in the spatial domain using a set of well crafted kernels (filters).
frequency (Fourier) domain masking to hide certain frequencies
The two approaches are seen below:
Before being translated into the Fourier space, pictures are often padded; the highpass filtered images below show the effects of various padding methods:
When compared to repeated edge padding, zero padding causes the highpass filter to display an additional set of edges.
High-pass filtering in the spatial domain: a MATLAB demonstration.
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')
Examples of how affine transformations may be used to perform fundamental picture manipulations including scaling, rotation, translation, reflection, and shearing are shown below:
The affine matrix is applied to a picture by first transforming it into a matrix where each entry represents the intensity of a single pixel. Once the row and column of a pixel in the image matrix are known, the position of a pixel may be represented as a vector showing the coordinates of that pixel in the picture, [x, y]. This makes it possible to multiply the coordinate by an affine-transformation matrix, which in turn yields the output image's pixel value at the desired location.
However, 3D homogeneous coordinates are required for transformations that include translation transformations. The new coordinate system looks like this: [x, y, 1], with the third dimension assigned to a non-zero constant (typically 1). This permits translational shifts by multiplying the coordinate vector by a 3 by 3 matrix. So, because 1 is a constant, the third dimension permits translation.
Since matrix multiplication is associative, if many affine transformations are performed in sequence, they may be collapsed into a single affine transformation by multiplying their respective matrices. When applied to a point vector, the resulting matrix has the same effect as applying the individual transformations [x, y, 1] in order. This means that a list of affine transformation matrices may be simplified to a single one.
Two-dimensional coordinates, for instance, may only be rotated relative to the zero-point (0, 0). Any point, however, may be brought to the origin (0, 0) in 3D homogeneous coordinates, rotated, and then brought back to its original position (the opposite of the first translation). By combining these three affine transformations into a single matrix, we may rotate the picture around any given point.
Denoising photographs is a task well suited to mathematical morphology. Mathematical morphology relies heavily on structural elements.
Structural components are discussed in the following instances. Below and in table form, we see the denoise function, the picture as I, and the structural element as B.
e.g.
What is the meaning of the term "dilation"?, B)(i,j) =
.
Allow Dilation(I,B) = D. (I,B)
D(I', B)(1,1) =
Clarify the meaning of the term "erosion", B)(i,j) =
.
Assume Erosion(I,B) = E. (I,B)
E(I', B)(1,1) =
After dilation
After erosion
While opening, erosion occurs first, followed by dilation, and when closing, dilation comes first, followed by erosion. In practice, Convolution may be used to implement both the D(I,B) and the E(I,B).
Denoising is a technique used to remove noise from images, The picture has been grayscaled.
A mask with denoising method is logical matrix with
.
Denoising techniques use a center-half-height approach, Partial width, Then stop at the row number where the picture ends, column number.
It's a picture block whose border is [the point below center: the point above center]; this is a neighbor, [The left-of-center point: the right-of-center point.].
Convolution Replace the core with a small group of neighbors and a structural element.
Consider the Closing technique.
Dilation first
Matlab is used to read the picture and grayscale it.
Find out how big a picture is. We will take the row and column numbers from the returned result as our boundaries.
The dilation and erosion functions determine the structural components. A pixel's erosion technique is determined by its neighbors' minimum, whereas a pixel's dilation method is determined by its neighbors' maximum.
Decide when to open, shrink, and close.
Make a zero matrix that's the same size as the source picture.
The window of structural dilation is used initially.
The 33 matrices and convolution used for windowing and structuring
In a for loop, choose the rows in the range [2 image height - 1] and take the minimum value using a window. columns [2 picture width - 1] in width.
Create a new picture by bringing the minimum value in the matrix to zero.
The border still has room for development. Because this approach disregards the border. To cope with edges, padding may be used.
Next Erosion Assume the picture of the dilated pupil as input.
Make a zero matrix that's the same size as the source picture.
Framing-window erosion.
The 33 matrices and convolution used for windowing and structuring
Maximum from row range [2 image height - 1] using a for loop to extract a window. columns [2 picture width - 1] in width.
A fresh picture will be saved once the maximum value is filled into the zero matrix.
The border still has room for development. Given that in this approach, boundaries are disregarded. To cope with edges,...
