digital image processing lecture 2 tariq mahmood khan
TRANSCRIPT
Digital Image ProcessingLecture 2
Tariq Mahmood Khan
Image Processing (Computer Vision) - Recap
“Inverse Photography”
Stages in Computer Vision
• Physics: Image Formation (Light, Reflectance)
• Physics: Cameras: Optics (Lens), Sensors (CCD, CMOS)
• Image Processing: Coding (Transmission, Compression)
• Image Processing: Enhancement (Noise Cleaning, Colors)
• IP-CV: Feature Detection (Objects, Actions, Motion)
• Computer Vision: Scene recovery (3D, Reflectance)
• Computer Vision: Object Recognition
• Human and Machine Vision: Visual Perception
• Robotics: Control Action (autonomous driving)
DIP Systems
All digital image processing systems consist of some means to
(1) digitise / acquire the images,
(2) process the images (computing capability),
(3) save the images
(4) produce human readable hardcopy, and
(5) communicate the images to other systems.
Image Acquisition
• Light is emitted by light source
• Light is reflected from objects
• Reflected light is sensed (captured) by eye or by camera
In general, any sensor which can produce spatially-distributed
intensity values of electromagnetic radiation is suited to
image capturing.
Types of Image capturing system
• In everyday life a number of image capturing systems
are used, depending on the application field. They
differ in the
– acquisition principle
– acquisition speed
– spatial resolution
– sensor system
Classification of Sensors
Sensors can be categorized into the following classes according to their sensitivity ranges:
• Electromagnetic sensors - sensitive to a certain range of electromagnetic radiation
– gamma radiation
– X-ray radiation
– the visual spectrum
– the infrared spectrum
– the radio wave range
• Non- Electromagnetic sensors
– ultrasonic sensors
04/19/23 8
Image Acquisition
04/19/23 9
Image description
f (x,y): intensity/brightness of the image at spatial coordinates (x,y)
0< f (x,y)<∞ and determined by 2 factors:
Illumination component i(x,y): amount of source light incident
Reflectance component r(x,y): amount of light reflected by objects
f (x,y) = i(x,y) r(x,y)
where
0< i(x,y)<∞: determined by the light source
0< r(x,y)<1: determined by the characteristics of objects
In case of X-rays, we would deal with a transmissivity instead of a
reflectivity
The Digital Image Formation
The digital image is a numerical computer
representation of the physical image. The physical
image is divided into small regions called picture
elements, or pixels. The number stored in each pixel
represents the brightness of the scene in the designated
region.
The Digital Image
The conversion process from physical to digital image is
called digitisation. At each pixel location, the
brightness of the physical image is quantized and
converted into an integer number, called the grey level.
04/19/23 12
Sampling and Quantization
Sampling and quantization
Digital line scan
quantization
The Digital Image
The image displayed is stored as an array of numbers in the computer memory.
Colour images are sampled 3 times, giving 3 digital images, 1 each for a primary colour variable (RGB, CMY or HSI).
Digital Image
Each pixel has an
address in the digital
image, i.e. row or line
number and column or
sample number.
Typically, the origin
(x,y)=(0,0) is at the top-left
corner of the image. A
digital image of 640
horizontal pixels and 400
vertical pixels will have
address values of x=0-639
and y=0-399.
The Digital Image
The digital image should
adequately resolve all spatial
and intensity details of the
original continuous tone
image. The Nyquist
(sampling) theorem
requires that the pixel size
should less than half the size
of the finest detail in the
original image. Likewise, the
gray level brightness
increments should be less
than half the smallest tonal
variation in the original
image.
The Digital Image
Undersampling
occurs when the
number of pixels in
a digital image is
too low to accurately
represent the fine
details present in the
original image.
The Digital Image
Undersampling results in
spatial aliasing. The example
shows this effect as Moire
patterns.
Digital Image: Spatial and Intensity Resolution•Spatial resolution refers to the number of pixels in the digital image. Typically, 256x256 is the minimum acceptable spatial resolution.
•Intensity resolution refers to the number of grey levels available in the digital image.
Spatial Resolution
Spatial Resolution
The Digital Image - Zooming
Although a digital image may appear smooth to the human eye, when zoomed up enough the individual pixels always become visible.
Intensity Resolution / Grey level Resolution
Intensity resolution refers to the number of grey levels available in the digital image.
(a) 256 grey levels
(b) 128 grey levels
(c) 64 grey levels
(d) 32 grey levels
Intensity Resolution / Grey level Resolution
For convenient computer storage, the number of grey levels is almost always 2N, N = number of bits.
(e) 16 grey levels
(f) 8 grey levels
(g) 4 grey levels
(h) 2 grey levels
Image (h) is a binary image.
Intensity Resolution / Grey level Resolution
Typically, the minimum
number of acceptable
grey levels is 16.
Note the introduction of
false contouring when
the brightness
resolution is too low.
The Digital Image
N : N2 = number of pixels, square digital image.
k: 2k = number of grey levels.
The memory requirements to store digital images is large. One typical high-resolution image requires 1 Megabyte of memory. Colour images require 3X the memory of monochrome images.
Image Interpolation
• It is a basic tool used extensively in tasks such as zooming,
shrinking, rotating, and geometric corrections.
• Fundamentally, Interpolation is a process of using known
data to estimate values at unknown locations.
Original resampling shrinking zooming
Image Interpolation
Image Interpolation
Many methods exist in literature for interpolation such as:
• Pixel Replication / Nearest Neighbor
• Bilinear Interpolation
• Bicubic Interpolation
Image Interpolation: Nearest Neighbor
• Unknown pixel is assigned a value of its nearest neighbor
Image Interpolation: Nearest Neighbor
• Unknown pixel is assigned a value of its nearest neighbor
Image Interpolation: Bilinear Interpolation
f(x, y) = ax + by + cxy + d
coefficients that need to be estimated
• Unknown pixel is estimated using values of four neighbors.
Known pixels
Unknown pixels
Image Interpolation: Bilinear Interpolation
f(x, y) = ax + by + cxy + d
coefficients that need to be estimated
• Unknown pixel is estimated using values of four neighbors.
? Known pixels
Unknown pixels
Image Interpolation: Bilinear Interpolation
f(x, y) = ax + by + cxy + d
coefficients that need to be estimated
• Unknown pixel is estimated using values of four neighbors.
? Known pixels
Unknown pixels
Nearest Neighbor pixels
Image Interpolation: Bilinear Interpolation
f(x, y) = ax + by + cxy + d
coefficients that need to be estimated
• Unknown pixel is estimated using values of four neighbors.
?
ax1 + by1 + cx1y1 + d = f(x1, y1)ax2 + by2 + cx2y2 + d = f(x2, y2)ax3 + by3 + cx3y3 + d = f(x3, y3)ax4 + by4 + cx4y4 + d = f(x4, y4)
1 2
43
a, b, c, d
Image Interpolation: Bilinear Interpolation
• Unknown pixel is estimated using values of sixteen
neighbors.
Image Interpolation
Basic relationships between pixels
Neighbours of a pixel – 4-neighbors
A pixel p at coordinates (x, y) has four horizontal and vertical neighbors whose coordinates are given by
(x+1,y), (x-1,y), (x,y+1), (x,y-1)
This set of pixels, called the 4-neighbors of p, is denoted by N4(p).
Each pixel is a unit distance from (x, y), and some of the neighbors of p lie outside the digital image if (x, y) is on the border of the image.
Neighbours of a pixel – 8-neighbors
The four diagonal neighbors of p have coordinates(x+1,y+1),(x+1,y-1),(x-1,y+1),(x-1,y-1)
and are denoted by ND(p).
These points, together with the 4-neighbors, are called the 8-neighbors of p, denoted by N8(p).
As before, some of the points in ND(p) and N8(p) fall outside the image if (x, y) is on the border of the image.
Some Definitions
• Two pixels are said to connected if they are neighbors and if
their gray levels satisfy a specified criterion of similarity (say, if
their gray levels are equal)
• 4-adjacency. Two pixels p and q with values from V are 4-
adjacent if q is in the set N4(p).
• 8-adjacency. Two pixels p and q with values from V are 8-
adjacent if q is in the set N8(p).
• m-adjacency (mixed adjacency). Two pixels p and q with values
from V are m-adjacent if
– q is in N4(p), or
– q is in ND(p) and the set N4(p) N4(q) has no pixels whose
values are from V.
Basic relationships between pixels
Arrangement of pixels: 0 1 10 1 00 0 1
4 neighbors N4(p): 1 0 1 0 0
Diagonal neighbors ND(p): 0 1 1 0 1
8 neighbors N8 (p) = ND(p) U N4(p) : 0 1 1 0 1 0 0 0 1
Basic relationships between pixels
Mixed Connectivity:
Note: Mixed connectivity can eliminate the multiple path connections that often occurs in 8-connectivity
Pixel arrangement
8-adjacent to the center pixel
m-adjacency
Basic relationships between pixels
Path
Let coordinates of pixel p: (x, y), and of pixel q: (s, t)
A path from p to q is a sequence of distinct pixels with
coordinates: (x0, y0), (x1, y1), ......, (xn, yn) where
(x0, y0) = (x, y) & (xn, yn) = (s, t),
and (xi, yi) is adjacent to (xi-1, yi-1) 1 i n
Regions
A set of pixels in an image where all component pixels are
connected
Boundary of a region
A set of pixels of a region R that have one of more
neighbors that are not in R
Distance Measures
Given coordinates of pixels p, q, and z: (x,y), (s,t), and (u,v)
Euclidean distance between p and q:
• City-block distance between p and q:
• Chessboard distance between p and q:
22 )()(),( tysxqpDe
tysxqpD ),(4
|)||,max(|),(8 tysxqpD
Image Operation on a Pixel Basis
• when we refer to an operation like “dividing one image by
another,” we mean specifically that the division is carried
out between corresponding pixels in the two images
• Other arithmetic and logic operations are similarly defined
between corresponding pixels in the images involved.
Liner and Nonlinear Operations
• Let H be an operator whose input and output are images. H
is said to be a linear operator if, for any two images f and g
and any two scalars a and b,
H(af + bg) = aH(f) + bH(g).
• An operator that fails the test of above equation by
definition is nonlinear.
Reading Assignment
• Chapter 2 (2.3-2.6) of “Digital Image Processing” by
Gonzalez.
Assignment
1. Interpolate the following image of size 4x4 to size 8x8 by using:
Nearest Neighbor Interpolation
Bilinear Interpolation
3 1 2 1
2 2 0 2
1 2 1 1
1 0 1 2
2. Prob # 2.11 and 2.15 of textbook
Due Date 17/09/2012