Digital Image Processing (AD-603 (B)) Unit 1 Notes

How unit 1 is examined

This unit covers what a digital image is, how it is sampled and quantized, pixel relationships, camera geometry, acquisition devices and image types; no past questions were asked recently, so every topic is short but complete.

Digital Image fundamentals, A simple image model

Not asked since 2022

Definition. A digital image is a two-dimensional function $f(x,y)$ whose spatial coordinates $x,y$ and amplitude values are all finite, discrete quantities.

Key points.

The simple image model is $f(x,y)=i(x,y)\,r(x,y)$, the product of illumination and reflectance.
Illumination satisfies $0<i(x,y)<\infty$ and reflectance satisfies $0<r(x,y)<1$, from total absorption to total reflection.
Each element of the $M\times N$ array is a pixel, and its value is the gray level at that point.
Storage needed is $b=M\times N\times k$ bits, so a $256\times256$, 8-bit image needs $65536$ bytes (64 KB).

Sampling and Quantization

Definition. Sampling digitizes the coordinate values $(x,y)$, and quantization digitizes the amplitude values.

Key points.

Sampling fixes the number of pixels ($M\times N$), so it sets the spatial resolution.
Quantization maps continuous intensity to $L=2^k$ gray levels, so it sets the gray-level resolution.
Too few samples give a checkerboard pattern, and too few gray levels give false contours.
More samples and more bits improve quality but increase storage $M N k$.

Relationship between pixels

Definition. Pixel relationships describe how a pixel $p$ at $(x,y)$ is related to its neighbours through neighbourhood, adjacency, connectivity and distance.

Key points.

The 4-neighbours $N_4(p)$ are $(x\pm1,y)$ and $(x,y\pm1)$, the diagonal neighbours $N_D(p)$ are $(x\pm1,y\pm1)$, and $N_8=N_4\cup N_D$.
Two pixels are 4-adjacent or 8-adjacent if both have values from the set $V$ and one lies in the other's $N_4$ or $N_8$.
m-adjacency (mixed) removes the ambiguity of multiple 8-paths between two pixels.
Distances: Euclidean $D_e=\sqrt{(x-s)^2+(y-t)^2}$, city-block $D_4=|x-s|+|y-t|$, chessboard $D_8=\max(|x-s|,|y-t|)$.

Imaging geometry

Definition. Imaging geometry is the mathematics of projecting a 3-D world point onto the 2-D image plane of a camera.

Key points.

In the pinhole (perspective) model with focal length $\lambda$, a point $(X,Y,Z)$ maps to $x=\dfrac{\lambda X}{\lambda-Z}$ and $y=\dfrac{\lambda Y}{\lambda-Z}$.
Perspective projection makes distant objects look smaller, and the mapping is many-to-one, so depth is lost.
Basic transformations (translation, scaling, rotation) are written as matrices in homogeneous coordinates so they can be combined by multiplication.

Image acquisition systems

Definition. Image acquisition is the process of converting illumination energy reflected from a scene into a digital image using a sensor and a digitizer.

Key points.

A single sensor is moved in both directions across the image to scan it, which is cheap but slow.
A line (strip) sensor scans one direction electronically while the object moves in the other, as in flatbed scanners and CT.
An array sensor (CCD or CMOS) captures the whole image at once, as in digital cameras.
Each sensor output is an analog voltage that the digitizer samples and quantizes into pixel values.

Different types of digital images

Definition. Digital images are classified by the number of bits per pixel and the kind of values stored: binary, grayscale, colour and indexed.

Key points.

A binary image has 1 bit per pixel, with only black (0) and white (1).
A grayscale image typically has 8 bits per pixel, giving 256 gray levels from 0 (black) to 255 (white).
A colour (RGB) image stores three planes, so it needs 24 bits per pixel, giving about 16.7 million colours.
An indexed image stores small integers that point into a colour map (palette), which saves memory.

Last-minute revision

Digital image: $f(x,y)$ with discrete coordinates and amplitude.
Image model: $f(x,y)=i(x,y)\,r(x,y)$, with $0<r<1$.
Sampling digitizes coordinates; quantization digitizes amplitude.
Gray levels $L=2^k$; storage $b=M N k$ bits.
$256\times256$ at 8 bits is 64 KB.
$N_4$ has 4 pixels, $N_8$ has 8 pixels.
$D_4=|x-s|+|y-t|$; $D_8=\max(|x-s|,|y-t|)$.
Pinhole projection: $x=\lambda X/(\lambda-Z)$.
Sensors: single, line, array (CCD/CMOS).
Binary 1 bit, gray 8 bits, RGB 24 bits.

Memory hooks

Sampling is Space (coordinates); quantization is Quantity (amplitude).
$D_4$ is the taxi (city-block) and $D_8$ is the king (chessboard) move.
Image = light times surface: illumination times reflectance.
1, 8, 24: binary, gray, RGB bits.

Coverage checklist

Digital Image fundamentals, A simple image model: definition, $i\cdot r$ model, storage; no past questions.
Sampling and Quantization: both defined, resolution effects; no past questions.
Relationship between pixels: neighbours, adjacency, distances; no past questions.
Imaging geometry: perspective projection; no past questions.
Image acquisition systems: single, line, array sensors; no past questions.
Different types of digital images: binary, gray, RGB, indexed; no past questions.

Account

Digital Image Processing (AD-603 (B)) - Unit 1 Short Notes

How unit 1 is examined

Digital Image fundamentals, A simple image model

Sampling and Quantization

Relationship between pixels

Imaging geometry

Image acquisition systems

Different types of digital images

Last-minute revision

Memory hooks

Coverage checklist