This document discusses digital image processing concepts including:
- Image acquisition and representation, including sampling and quantization of images. CCD arrays are commonly used in digital cameras to capture images as arrays of pixels.
- A simple image formation model where the intensity of a pixel is a function of illumination and reflectance at that point. Typical ranges of illumination and reflectance are provided.
- Image interpolation techniques like nearest neighbor, bilinear, and bicubic interpolation which are used to increase or decrease the number of pixels in a digital image. Examples of applying these techniques are shown.
- Basic relationships between pixels including adjacency, paths, regions, boundaries, and distance measures like Euclidean, city block, and
its very useful for students.
Sharpening process in spatial domain
Direct Manipulation of image Pixels.
The objective of Sharpening is to highlight transitions in intensity
The image blurring is accomplished by pixel averaging in a neighborhood.
Since averaging is analogous to integration.
Prepared by
M. Sahaya Pretha
Department of Computer Science and Engineering,
MS University, Tirunelveli Dist, Tamilnadu.
Image Enhancement: Introduction to Spatial Filters, Low Pass Filter and High Pass Filters. Here Discussed Image Smoothing and Image Sharping, Gaussian Filters
its very useful for students.
Sharpening process in spatial domain
Direct Manipulation of image Pixels.
The objective of Sharpening is to highlight transitions in intensity
The image blurring is accomplished by pixel averaging in a neighborhood.
Since averaging is analogous to integration.
Prepared by
M. Sahaya Pretha
Department of Computer Science and Engineering,
MS University, Tirunelveli Dist, Tamilnadu.
Image Enhancement: Introduction to Spatial Filters, Low Pass Filter and High Pass Filters. Here Discussed Image Smoothing and Image Sharping, Gaussian Filters
Digital image processing is the use of computer algorithms to perform image processing on digital images. As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing.
Digital Image Processing denotes the process of digital images with the use of digital computer. Digital images are contains various types of noises which are reduces the quality of images. Noises can be removed by various enhancement techniques. Image smoothing is a key technology of image enhancement, which can remove noise in images.
Spatial filtering using image processingAnuj Arora
spatial filtering in image processing (explanation cocept of
mask),lapace filtering and filtering process of image for extract information and reduce noise
This presentation describes briefly about the image enhancement in spatial domain, basic gray level transformation, histogram processing, enhancement using arithmetic/ logical operation, basics of spatial filtering and local enhancements.
Digital image processing is the use of computer algorithms to perform image processing on digital images. As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing.
Digital Image Processing denotes the process of digital images with the use of digital computer. Digital images are contains various types of noises which are reduces the quality of images. Noises can be removed by various enhancement techniques. Image smoothing is a key technology of image enhancement, which can remove noise in images.
Spatial filtering using image processingAnuj Arora
spatial filtering in image processing (explanation cocept of
mask),lapace filtering and filtering process of image for extract information and reduce noise
This presentation describes briefly about the image enhancement in spatial domain, basic gray level transformation, histogram processing, enhancement using arithmetic/ logical operation, basics of spatial filtering and local enhancements.
Histogram Processing
Histogram Equalization
Histogram Matching
Local Histogram processing
Using histogram statistics for image enhancement
Uses for Histogram Processing
Histogram Equalization
Histogram Matching
Local Histogram Processing
Basics of Spatial Filtering
Adaptive Median Filters
Elements of visual perception
Representing Digital Images
Spatial and Intensity Resolution
cones and rods
Brightness Adaptation
Spatial and Intensity Resolution
Image Restoration And Reconstruction
Mean Filters
Order-Statistic Filters
Spatial Filtering: Mean Filters
Adaptive Filters
Adaptive Mean Filters
Adaptive Median Filters
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
Literature Review Basics and Understanding Reference Management.pptxDr Ramhari Poudyal
Three-day training on academic research focuses on analytical tools at United Technical College, supported by the University Grant Commission, Nepal. 24-26 May 2024
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
ACEP Magazine edition 4th launched on 05.06.2024Rahul
This document provides information about the third edition of the magazine "Sthapatya" published by the Association of Civil Engineers (Practicing) Aurangabad. It includes messages from current and past presidents of ACEP, memories and photos from past ACEP events, information on life time achievement awards given by ACEP, and a technical article on concrete maintenance, repairs and strengthening. The document highlights activities of ACEP and provides a technical educational article for members.
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
Low power architecture of logic gates using adiabatic techniquesnooriasukmaningtyas
The growing significance of portable systems to limit power consumption in ultra-large-scale-integration chips of very high density, has recently led to rapid and inventive progresses in low-power design. The most effective technique is adiabatic logic circuit design in energy-efficient hardware. This paper presents two adiabatic approaches for the design of low power circuits, modified positive feedback adiabatic logic (modified PFAL) and the other is direct current diode based positive feedback adiabatic logic (DC-DB PFAL). Logic gates are the preliminary components in any digital circuit design. By improving the performance of basic gates, one can improvise the whole system performance. In this paper proposed circuit design of the low power architecture of OR/NOR, AND/NAND, and XOR/XNOR gates are presented using the said approaches and their results are analyzed for powerdissipation, delay, power-delay-product and rise time and compared with the other adiabatic techniques along with the conventional complementary metal oxide semiconductor (CMOS) designs reported in the literature. It has been found that the designs with DC-DB PFAL technique outperform with the percentage improvement of 65% for NOR gate and 7% for NAND gate and 34% for XNOR gate over the modified PFAL techniques at 10 MHz respectively.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
2. Contents
Image Acquisition and Representation
A Simple Image Formation Model
Image Sampling and Quantization
Image Interpolation
Homework
3. Light and EM spectrum
Monochromatic light
Intensity is the only attribute, from black to white
Monochromatic images are referred to as gray-
scale images
Chromatic light bands: 0.43 to 0.79 um
The quality of a chromatic light source:
Radiance (W)
Luminance (lm)
Brightness
12. 12
A Simple Image Formation Model
0 < ( , ) <
( , ) ( , ) ( , )
where
0 < ( , ) <
and
0 < ( , ) < 1
f x y
f x y i x y r x y
i x y
r x y
( , ) : intensity at the point ( , )
( , ) : illumination at the point ( , )
(the amount of source illumination incident on the scene)
( , ) : reflectance/transmissivity at the point ( , )
(t
f x y x y
i x y x y
r x y x y
he amount of illumination reflected/transmitted by the object)
13. 13
Some Typical Ranges of illumination
Illumination
Lumen — A unit of light flow or luminous flux
Lumen per square meter (lm/m2) — The metric unit of measure for
illuminance of a surface
On a clear day, the sun may produce in excess of 90,000 lm/m2 of illumination
on the surface of the Earth
On a cloudy day, the sun may produce less than 10,000 lm/m2 of illumination
on the surface of the Earth
On a clear evening, the moon yields about 0.1 lm/m2 of illumination
The typical illumination level in a commercial office is about 1000 lm/m2
14. 14
Some Typical Ranges of Reflectance
Reflectance
0.01 for black velvet
0.65 for stainless steel
0.80 for flat-white wall paint
0.90 for silver-plated metal
0.93 for snow
15. Digital vs. Analog Images
Analog:
Function v = f(x,y): v,x,y are REAL
Digital:
Function v = f(x,y): v,x,y are INTEGER
16. Sampling means measuring the value of an
image at a finite number of points.
Quantization is the representation of the
measured value at the sampled point by an
integer.
24. Color images can be represented by
3D Arrays (e.g. 320 x 240 x 3)
25. But for the time being we’ll handle 2D
grayvalue images
26. 26
Image Interpolation
Interpolation — Process of using known data to
estimate unknown values
e.g., zooming, shrinking, rotating, and geometric correction
Interpolation (sometimes called resampling) — an
imaging method to increase (or decrease) the number of pixels
in a digital image.
Some digital cameras use interpolation to produce a larger image than the
sensor captured or to create digital zoom
29. 29
Image Interpolation:
Bilinear Interpolation
(x,y)
The output pixel value is a weighted average of pixels in the nearest 2-by-2
neighborhood
Considers the closest 2x2 neighborhood of known pixel values surrounding the
unknown pixel
It then takes a weighted average of these 4 pixels to arrive at its final interpolated
value
This results in much smoother looking images than nearest neighbor
31. 31
Image Interpolation:
Bicubic Interpolation
3 3
3
0 0
( , ) i j
ij
i j
f x y a x y
The intensity value assigned to point (x,y) is obtained by the
following equation
The sixteen coefficients are determined by using the sixteen
nearest neighbors.
42. 42
Basic Relationships Between Pixels
Neighbors of a pixel p at coordinates (x,y)
4-neighbors of p, denoted by N4(p):
(x-1, y), (x+1, y), (x,y-1), and (x, y+1).
4 diagonal neighbors of p, denoted by ND(p):
(x-1, y-1), (x+1, y+1), (x+1,y-1), and (x-1, y+1).
8 neighbors of p, denoted N8(p)
N8(p) = N4(p) U ND(p)
43. Weeks 1 & 2 43
Basic Relationships Between Pixels
Adjacency
Let V be the set of intensity values
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).
44. 44
Basic Relationships Between Pixels
Adjacency
Let V be the set of intensity values
m-adjacency: Two pixels p and q with values from V are m-
adjacent if
(i) q is in the set N4(p), or
(ii) q is in the set ND(p) and the set N4(p) ∩ N4(p) has no pixels whose values
are from V.
45. Weeks 1 & 2 45
Basic Relationships Between Pixels
Path
A (digital) path (or curve) from pixel p with coordinates (x0, y0) to pixel q with
coordinates (xn, yn) is a sequence of distinct pixels with coordinates
(x0, y0), (x1, y1), …, (xn, yn)
Where (xi, yi) and (xi-1, yi-1) are adjacent for 1 ≤ i ≤ n.
Here n is the length of the path.
If (x0, y0) = (xn, yn), the path is closed path.
We can define 4-, 8-, and m-paths based on the type of adjacency used.
49. Weeks 1 & 2 49
Examples: Adjacency and Path
01,1 11,2 11,3 0 1 1 0 1 1
02,1 22,2 02,3 0 2 0 0 2 0
03,1 03,2 13,3 0 0 1 0 0 1
V = {1, 2}
8-adjacent m-adjacent
The 8-path from (1,3) to (3,3):
(i) (1,3), (1,2), (2,2), (3,3)
(ii) (1,3), (2,2), (3,3)
The m-path from (1,3) to (3,3):
(1,3), (1,2), (2,2), (3,3)
50. Weeks 1 & 2 50
Basic Relationships Between Pixels
Connected in S
Let S represent a subset of pixels in an image. Two pixels p with
coordinates (x0, y0) and q with coordinates (xn, yn) are said to be
connected in S if there exists a path
(x0, y0), (x1, y1), …, (xn, yn)
Where ,0 ,( , )i ii i n x y S
51. Weeks 1 & 2 51
Basic Relationships Between Pixels
Let S represent a subset of pixels in an image
For every pixel p in S, the set of pixels in S that are connected to p is called a
connected component of S.
If S has only one connected component, then S is called Connected Set.
We call R a region of the image if R is a connected set
Two regions, Ri and Rj are said to be adjacent if their union forms a connected
set.
Regions that are not to be adjacent are said to be disjoint.
52. Weeks 1 & 2 52
Basic Relationships Between Pixels
Boundary (or border)
The boundary of the region R is the set of pixels in the region that have one
or more neighbors that are not in R.
If R happens to be an entire image, then its boundary is defined as the set of
pixels in the first and last rows and columns of the image.
Foreground and background
An image contains K disjoint regions, Rk, k = 1, 2, …, K. Let Ru denote the
union of all the K regions, and let (Ru)c denote its complement.
All the points in Ru is called foreground;
All the points in (Ru)c is called background.
53. 53
Question
In the following arrangement of pixels, are the two regions (of
1s) adjacent? (if 8-adjacency is used)
1 1 1
1 0 1
0 1 0
0 0 1
1 1 1
1 1 1
Region 1
Region 2
54. 54
Question
In the following arrangement of pixels, are the two parts (of 1s)
adjacent? (if 4-adjacency is used)
1 1 1
1 0 1
0 1 0
0 0 1
1 1 1
1 1 1
Part 1
Part 2
55. Weeks 1 & 2 55
In the following arrangement of pixels, the two regions (of 1s)
are disjoint (if 4-adjacency is used)
1 1 1
1 0 1
0 1 0
0 0 1
1 1 1
1 1 1
Region 1
Region 2
56. Weeks 1 & 2 56
In the following arrangement of pixels, the two regions (of 1s)
are disjoint (if 4-adjacency is used)
1 1 1
1 0 1
0 1 0
0 0 1
1 1 1
1 1 1
foreground
background
57. 57
Question
In the following arrangement of pixels, the circled point is part
of the boundary of the 1-valued pixels if 8-adjacency is used,
true or false?
0 0 0 0 0
0 1 1 0 0
0 1 1 0 0
0 1 1 1 0
0 1 1 1 0
0 0 0 0 0
58. 58
Homework: Question 1
In the following arrangement of pixels, the circled point is part
of the boundary of the 1-valued pixels if 4-adjacency is used,
true or false?
0 0 0 0 0
0 1 1 0 0
0 1 1 0 0
0 1 1 1 0
0 1 1 1 0
0 0 0 0 0
59. 59
Distance Measures
Given pixels p, q and z with coordinates (x, y), (s, t), (u, v)
respectively, the distance function D has following
properties:
a. D(p, q) ≥ 0 [D(p, q) = 0, iff p = q]
b. D(p, q) = D(q, p)
c. D(p, z) ≤ D(p, q) + D(q, z)
60. 60
Distance Measures
The following are the different Distance measures:
a. Euclidean Distance :
De(p, q) = [(x-s)2 + (y-t)2]1/2
b. City Block Distance:
D4(p, q) = |x-s| + |y-t|
c. Chess Board Distance:
D8(p, q) = max(|x-s|, |y-t|)
61. 61
Question
In the following arrangement of pixels, what’s the value of the
chessboard distance between the circled two points?
0 0 0 0 0
0 0 1 1 0
0 1 1 0 0
0 1 0 0 0
0 0 0 0 0
0 0 0 0 0
62. 62
Homework: Question 2
In the following arrangement of pixels, what’s the value of the
city-block distance between the circled two points?
0 0 0 0 0
0 0 1 1 0
0 1 1 0 0
0 1 0 0 0
0 0 0 0 0
0 0 0 0 0
63. 63
Homework: Question 3
In the following arrangement of pixels, what’s the value of the
length of the m-path between the circled two points?
0 0 0 0 0
0 0 1 1 0
0 1 1 0 0
0 1 0 0 0
0 0 0 0 0
0 0 0 0 0
64. 64
Homework: Question 4
In the following arrangement of pixels, what’s the value of the
length of the m-path between the circled two points?
0 0 0 0 0
0 0 1 1 0
0 0 1 0 0
0 1 0 0 0
0 0 0 0 0
0 0 0 0 0