This document provides an overview of color image processing. It discusses that color is important for object identification and extraction. It describes the primary colors of light (red, green, blue) and pigments (cyan, magenta, yellow) and how they are used in different color models. The key color characteristics of brightness, hue, and saturation are defined. Common color models for image processing like RGB, CMY, and HSI are introduced. The RGB color model is described in more detail, representing colors as points in a color cube defined by normalized red, green, and blue values between 0 and 1.
Image Restoration UsingNonlocally Centralized Sparse Representation and histo...IJERA Editor
Due to the degradation of observed image the noisy, blurred, distorted image can be occurred .To restore the image informationby conventional modelsmay not be accurate enough for faithful reconstruction of the original image. I propose the sparse representations to improve the performance of based image restoration. In this method the sparse coding noise is added for image restoration, due to this image restoration the sparse coefficients of original image can be detected. The so-called nonlocally centralized sparse representation (NCSR) model is as simple as the standard sparse representation model, fordenoising the image here we use the histogram clipping method by using histogram based sparse representation to effectively reduce the noise and also implement the TMR filter for Quality image. Various types of image restoration problems, including denoising, deblurring and super-resolution, validate the generality and state-of-the-art performance of the proposed algorithm.
Image Restoration and Denoising By Using Nonlocally Centralized Sparse Repres...IJERA Editor
Due to the degradation of observed image the noisy, blurred, Distorted image can be occurred .for restoring image information we propose the sparse representations by conventional modelsmay not be accurate enough for a faithful reconstruction of the original image. To improve the performance of sparse representation-based image restoration,In this method the sparse coding noise is added for image restoration, due to this image restoration the sparse coefficients of original image can be detected. The so-called nonlocally centralized sparse representation (NCSR) model is as simple as the standard sparse representation model,for denoising the image here we use the Histogram clipping method by using histogram based sparse representation effectively reduce the noise.and also implement the TMR filter for Quality image.various types of image restoration problems, including denoising, deblurring and super-resolution, validate the generality and state-of-the-art performance of the proposed algorithm.
Perimetric Complexity of Binary Digital ImagesRSARANYADEVI
Perimetric complexity is a measure of the complexity of binary pictures. It is defined as the sum of inside and outside perimeters of the foreground, squared, divided by the foreground area, divided by . Difficulties arise when this definition is applied to digital images composed of binary pixels. In this article we identify these problems and propose solutions. Perimetric complexity is often used as a measure of visual complexity, in which case it should take into account the limited resolution of the visual system. We propose a measure of visual perimetric complexity that meets this requirement.
Image Restitution Using Non-Locally Centralized Sparse Representation ModelIJERA Editor
Sparse representation models uses a linear combination of a few atoms selected from an over-completed
dictionary to code an image patch which have given good results in different image restitution applications. The
reconstruction of the original image is not so accurate using traditional models of sparse representation to solve
degradation problems which are blurring, noisy, and down-sampled. The goal of image restitution is to suppress
the sparse coding noise and to improve the image quality by using the concept of sparse representation. To
obtain a good sparse coding coefficients of the original image we exploit the image non-local self similarity and
then by centralizing the sparse coding coefficients of the observation image to those estimates. This non-locally
centralized sparse representation model outperforms standard sparse representation models in all aspects of
image restitution problems including de-noising, de-blurring, and super-resolution.
Image Restoration UsingNonlocally Centralized Sparse Representation and histo...IJERA Editor
Due to the degradation of observed image the noisy, blurred, distorted image can be occurred .To restore the image informationby conventional modelsmay not be accurate enough for faithful reconstruction of the original image. I propose the sparse representations to improve the performance of based image restoration. In this method the sparse coding noise is added for image restoration, due to this image restoration the sparse coefficients of original image can be detected. The so-called nonlocally centralized sparse representation (NCSR) model is as simple as the standard sparse representation model, fordenoising the image here we use the histogram clipping method by using histogram based sparse representation to effectively reduce the noise and also implement the TMR filter for Quality image. Various types of image restoration problems, including denoising, deblurring and super-resolution, validate the generality and state-of-the-art performance of the proposed algorithm.
Image Restoration and Denoising By Using Nonlocally Centralized Sparse Repres...IJERA Editor
Due to the degradation of observed image the noisy, blurred, Distorted image can be occurred .for restoring image information we propose the sparse representations by conventional modelsmay not be accurate enough for a faithful reconstruction of the original image. To improve the performance of sparse representation-based image restoration,In this method the sparse coding noise is added for image restoration, due to this image restoration the sparse coefficients of original image can be detected. The so-called nonlocally centralized sparse representation (NCSR) model is as simple as the standard sparse representation model,for denoising the image here we use the Histogram clipping method by using histogram based sparse representation effectively reduce the noise.and also implement the TMR filter for Quality image.various types of image restoration problems, including denoising, deblurring and super-resolution, validate the generality and state-of-the-art performance of the proposed algorithm.
Perimetric Complexity of Binary Digital ImagesRSARANYADEVI
Perimetric complexity is a measure of the complexity of binary pictures. It is defined as the sum of inside and outside perimeters of the foreground, squared, divided by the foreground area, divided by . Difficulties arise when this definition is applied to digital images composed of binary pixels. In this article we identify these problems and propose solutions. Perimetric complexity is often used as a measure of visual complexity, in which case it should take into account the limited resolution of the visual system. We propose a measure of visual perimetric complexity that meets this requirement.
Image Restitution Using Non-Locally Centralized Sparse Representation ModelIJERA Editor
Sparse representation models uses a linear combination of a few atoms selected from an over-completed
dictionary to code an image patch which have given good results in different image restitution applications. The
reconstruction of the original image is not so accurate using traditional models of sparse representation to solve
degradation problems which are blurring, noisy, and down-sampled. The goal of image restitution is to suppress
the sparse coding noise and to improve the image quality by using the concept of sparse representation. To
obtain a good sparse coding coefficients of the original image we exploit the image non-local self similarity and
then by centralizing the sparse coding coefficients of the observation image to those estimates. This non-locally
centralized sparse representation model outperforms standard sparse representation models in all aspects of
image restitution problems including de-noising, de-blurring, and super-resolution.
Template matching is a technique in computer vision used for finding a sub-image of a target image which matches a template image. This technique is widely used in object detection fields such as vehicle tracking, robotics , medical imaging, and manufacturing .
Adaptive Median Filters
Elements of visual perception
Representing Digital Images
Spatial and Intensity Resolution
cones and rods
Brightness Adaptation
Spatial and Intensity Resolution
Chapter summary and solutions to end-of-chapter exercises for "Data Visualization: Principles and Practice" book by Alexandru C. Telea
Chapter provides an overview of a number of methods for visualizing tensor data. It explains principal component analysis as a technique used to process a tensor matrix and extract from it information that can directly be used in its visualization. It forms a fundamental part of many tensor data processing and visualization algorithms. Section 7.4 shows how the results of the principal component analysis can be visualized using the simple color-mapping techniques. Next parts of the chapter explain how same data can be visualized using tensor glyphs, and streamline-like visualization techniques.
In contrast to Slicer, which is a more general framework for analyzing and visualizing 3D slice-based data volumes, the Diffusion Toolkit focuses on DT-MRI datasets, and thus offers more extensive and easier to use options for fiber tracking.
GREY LEVEL CO-OCCURRENCE MATRICES: GENERALISATION AND SOME NEW FEATURESijcseit
Grey Level Co-occurrence Matrices (GLCM) are one of the earliest techniques used for image texture
analysis. In this paper we defined a new feature called trace extracted from the GLCM and its implications
in texture analysis are discussed in the context of Content Based Image Retrieval (CBIR). The theoretical
extension of GLCM to n-dimensional gray scale images are also discussed. The results indicate that trace
features outperform Haralick features when applied to CBIR.
Chapter summary and solutions to end-of-chapter exercises for "Data Visualization: Principles and Practice" book by Alexandru C. Telea
In this chapter author discusses a number of popular visualization methods for vector datasets: vector glyphs, vector color-coding, displacement plots, stream objects, texture-based vector visualization, and the simplified representation of vector fields.
Section 6.5 presents stream objects, which use integral techniques to construct paths in vector fields. Section 6.7 discusses a number of strategies for simplified representation of vector datasets. Section 6.8 presents a number of illustrative visualization techniques for vector fields, which offer an alternative mechanism for simplified representation to the techniques discussed in Section 6.7 Chapter presents also feature detection methods, algorithm for computing separatrices on field’s topology, and top-down and bottom-up field decomposition methods.
After an image has been segmented into regions ; the resulting pixels is usually is represented and described in suitable form for further computer processing.
Comparison of Distance Transform Based FeaturesIJERA Editor
The distance transform based features are widely used in pattern recognition applications. A distance transform
assigns to each background pixel in a binary image a value equal to its distance to the nearest foreground pixel
according to a defined metric. Among these metrics the Chessboard, Euclidean, Chamfer and City-block are
popular. The role of a feature extraction method is quite important in pattern recognition applications. Before
applying a feature, it is essential to judge its performance on the given applications. In this research work, a
study on the performance of above mentioned distance transform based features is made. We have conducted
experiments with 500 hand-printed characters/class and the study has been performed on 43 classes. The
classifiers used are k-NN, MLP, SVM and PNN.
Template matching is a technique in computer vision used for finding a sub-image of a target image which matches a template image. This technique is widely used in object detection fields such as vehicle tracking, robotics , medical imaging, and manufacturing .
Adaptive Median Filters
Elements of visual perception
Representing Digital Images
Spatial and Intensity Resolution
cones and rods
Brightness Adaptation
Spatial and Intensity Resolution
Chapter summary and solutions to end-of-chapter exercises for "Data Visualization: Principles and Practice" book by Alexandru C. Telea
Chapter provides an overview of a number of methods for visualizing tensor data. It explains principal component analysis as a technique used to process a tensor matrix and extract from it information that can directly be used in its visualization. It forms a fundamental part of many tensor data processing and visualization algorithms. Section 7.4 shows how the results of the principal component analysis can be visualized using the simple color-mapping techniques. Next parts of the chapter explain how same data can be visualized using tensor glyphs, and streamline-like visualization techniques.
In contrast to Slicer, which is a more general framework for analyzing and visualizing 3D slice-based data volumes, the Diffusion Toolkit focuses on DT-MRI datasets, and thus offers more extensive and easier to use options for fiber tracking.
GREY LEVEL CO-OCCURRENCE MATRICES: GENERALISATION AND SOME NEW FEATURESijcseit
Grey Level Co-occurrence Matrices (GLCM) are one of the earliest techniques used for image texture
analysis. In this paper we defined a new feature called trace extracted from the GLCM and its implications
in texture analysis are discussed in the context of Content Based Image Retrieval (CBIR). The theoretical
extension of GLCM to n-dimensional gray scale images are also discussed. The results indicate that trace
features outperform Haralick features when applied to CBIR.
Chapter summary and solutions to end-of-chapter exercises for "Data Visualization: Principles and Practice" book by Alexandru C. Telea
In this chapter author discusses a number of popular visualization methods for vector datasets: vector glyphs, vector color-coding, displacement plots, stream objects, texture-based vector visualization, and the simplified representation of vector fields.
Section 6.5 presents stream objects, which use integral techniques to construct paths in vector fields. Section 6.7 discusses a number of strategies for simplified representation of vector datasets. Section 6.8 presents a number of illustrative visualization techniques for vector fields, which offer an alternative mechanism for simplified representation to the techniques discussed in Section 6.7 Chapter presents also feature detection methods, algorithm for computing separatrices on field’s topology, and top-down and bottom-up field decomposition methods.
After an image has been segmented into regions ; the resulting pixels is usually is represented and described in suitable form for further computer processing.
Comparison of Distance Transform Based FeaturesIJERA Editor
The distance transform based features are widely used in pattern recognition applications. A distance transform
assigns to each background pixel in a binary image a value equal to its distance to the nearest foreground pixel
according to a defined metric. Among these metrics the Chessboard, Euclidean, Chamfer and City-block are
popular. The role of a feature extraction method is quite important in pattern recognition applications. Before
applying a feature, it is essential to judge its performance on the given applications. In this research work, a
study on the performance of above mentioned distance transform based features is made. We have conducted
experiments with 500 hand-printed characters/class and the study has been performed on 43 classes. The
classifiers used are k-NN, MLP, SVM and PNN.
Image Acquisition and Representation
A Simple Image Formation Model
Image Sampling and Quantization
Image Interpolation
Image quantization
Nearest Neighbor Interpolation
Performance Improvement of Vector Quantization with Bit-parallelism HardwareCSCJournals
Vector quantization is an elementary technique for image compression; however, searching for the nearest codeword in a codebook is time-consuming. In this work, we propose a hardware-based scheme by adopting bit-parallelism to prune unnecessary codewords. The new scheme uses a “Bit-mapped Look-up Table” to represent the positional information of the codewords. The lookup procedure can simply refer to the bitmaps to find the candidate codewords. Our simulation results further confirm the effectiveness of the proposed scheme.
Content Based Image Retrieval Using Gray Level Co-Occurance Matrix with SVD a...ijcisjournal
In this paper, gray level co-occurrence matrix, gray level co-occurrence matrix with singular value
decomposition and local binary pattern are presented for content based image retrieval. Based upon the
feature vector parameters of energy, contrast, entropy and distance metrics such as Euclidean distance,
Canberra distance, Manhattan distance the retrieval efficiency, precision, and recall of the images are
calculated. The retrieval results of the proposed method are tested on Corel-1k database. The results after
being investigated shows a significant improvement in terms of average retrieval rate, average retrieval
precision and recall of different algorithms such as GLCM, GLCM & SVD, LBP with radius one and LBP
with radius two based on different distance metrics.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
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Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
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Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
Contact with Dawood Bhai Just call on +92322-6382012 and we'll help you. We'll solve all your problems within 12 to 24 hours and with 101% guarantee and with astrology systematic. If you want to take any personal or professional advice then also you can call us on +92322-6382012 , ONLINE LOVE PROBLEM & Other all types of Daily Life Problem's.Then CALL or WHATSAPP us on +92322-6382012 and Get all these problems solutions here by Amil Baba DAWOOD BANGALI
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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.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Student information management system project report ii.pdf
Ip unit 1
1. Image Processing (KCS-062):
Fundamentals of Digital Image Processing
Dr. Radhey Shyam
Professor
Department of Computer Science and Engineering
BIET Lucknow
(Affiliated to Dr. A.P.J. Abdul Kalam Technical University (APJAKTU) Lucknow)
Unit-1 has been written/prepared by Dr. Radhey Shyam, with grateful acknowledgement of others who
made their course contents freely available. Feel free to use this manual for your own academic purposes.
For any query, the communication can be made through my mail shyam0058@gmail.com.
Course Outcome of Unit-1, the students will be able to explain the basic concepts of two-dimensional signal
acquisition, sampling, quantization and color model.
Date: May 03, 2021
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29. 66 Chapter 2 ■ Digital Image Fundamentals
64*64 cases.The 32*32 to 1024*1024 image is blurry,but keep in mind that
this image was zoomed by a factor of 32. In spite of this, the result of bilinear
interpolation shown in Fig. 2.25(f) is a reasonably good rendition of the origi-
nal image shape, something that is lost in Fig. 2.25(c). ■
Some Basic Relationships Between Pixels
In this section, we consider several important relationships between pixels in a
digital image.As mentioned before,an image is denoted by f(x, y).When refer-
ring in this section to a particular pixel,we use lowercase letters,such as p and q.
2.5.1 Neighbors of a Pixel
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.
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.
2.5.2 Adjacency, Connectivity, Regions, and Boundaries
Connectivity between pixels is a fundamental concept that simplifies the defini-
tion of numerous digital image concepts, such as regions and boundaries.To es-
tablish if two pixels are connected,it must be determined if they are neighbors and
if their gray levels satisfy a specified criterion of similarity (say, if their gray lev-
els are equal).For instance,in a binary image with values 0 and 1,two pixels may
be 4-neighbors,but they are said to be connected only if they have the same value.
Let V be the set of gray-level values used to define adjacency. In a binary
image, V={1} if we are referring to adjacency of pixels with value 1. In a gray-
scale image, the idea is the same, but set V typically contains more elements. For
example, in the adjacency of pixels with a range of possible gray-level values 0
to 255, set V could be any subset of these 256 values. We consider three types
of adjacency:
(a) 4-adjacency. Two pixels p and q with values from V are 4-adjacent if q is
in the set N4(p).
(b) 8-adjacency. Two pixels p and q with values from V are 8-adjacent if q is
in the set N8(p).
2.5
GONZ02-034-074.II 29-08-2001 13:36 Page 66
30. 2.5 ■ Some Basic Relationships Between Pixels 67
(c) m-adjacency (mixed adjacency).Two pixels p and q with values from V are
m-adjacent if
(i) q is in N4(p), or
(ii) q is in ND(p) and the set has no pixels whose values
are from V.
Mixed adjacency is a modification of 8-adjacency. It is introduced to eliminate
the ambiguities that often arise when 8-adjacency is used. For example, consid-
er the pixel arrangement shown in Fig. 2.26(a) for V={1}.The three pixels at
the top of Fig. 2.26(b) show multiple (ambiguous) 8-adjacency, as indicated by
the dashed lines.This ambiguity is removed by using m-adjacency, as shown in
Fig. 2.26(c). Two image subsets S1 and S2 are adjacent if some pixel in S1 is ad-
jacent to some pixel in S2. It is understood here and in the following definitions
that adjacent means 4-, 8-, or m-adjacent.
A (digital) path (or curve) from pixel p with coordinates (x, y) to pixel q
with coordinates (s, t) is a sequence of distinct pixels with coordinates
where and pixels and are
adjacent for 1 i n. In this case, n is the length of the path. If
the path is a closed path.We can define 4-, 8-, or m-paths de-
pending on the type of adjacency specified. For example, the paths shown in
Fig. 2.26(b) between the northeast and southeast points are 8-paths, and the
path in Fig. 2.26(c) is an m-path. Note the absence of ambiguity in the m-path.
Let S represent a subset of pixels in an image.Two pixels p and q are said to
be connected in S if there exists a path between them consisting entirely of pix-
els in S. For any pixel p in S, the set of pixels that are connected to it in S is
called a connected component of S. If it only has one connected component,
then set S is called a connected set.
Let R be a subset of pixels in an image.We call R a region of the image if R
is a connected set. The boundary (also called border or contour) of a 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 (which we recall is a rectangular set of
pixels), then its boundary is defined as the set of pixels in the first and last rows
and columns of the image.This extra definition is required because an image has
no neighbors beyond its border. Normally, when we refer to a region, we are
Ax0, y0B = (xn, yn),
Axi-1, yi-1B
Axi, yiB
Axn, ynB = (s, t),
Ax0, y0B = (x, y),
Ax0, y0B, Ax1, y1B, p , Axn, ynB
N4(p) ¨ N4(q)
0 1 1
0 1 0
0 0 1
0 1 1
0 1 0
0 0 1
0 1 1
0 1 0
0 0 1
FIGURE 2.26 (a) Arrangement of pixels; (b) pixels that are 8-adjacent (shown dashed)
to the center pixel; (c) m-adjacency.
a b c
GONZ02-034-074.II 29-08-2001 13:36 Page 67
31. 68 Chapter 2 ■ Digital Image Fundamentals
referring to a subset of an image, and any pixels in the boundary of the region
that happen to coincide with the border of the image are included implicitly as
part of the region boundary.
The concept of an edge is found frequently in discussions dealing with re-
gions and boundaries. There is a key difference between these concepts, how-
ever.The boundary of a finite region forms a closed path (Problem 2.14) and is
thus a “global” concept.As discussed in detail in Chapter 10, edges are formed
from pixels with derivative values that exceed a preset threshold.Thus, the idea
of an edge is a “local” concept that is based on a measure of gray-level discon-
tinuity at a point.It is possible to link edge points into edge segments,and some-
times these segments are linked in such a way that correspond to boundaries,
but this is not always the case.The one exception in which edges and boundaries
correspond is in binary images. Depending on the type of connectivity and edge
operators used (we discuss these in Chapter 10), the edge extracted from a bi-
nary region will be the same as the region boundary. This is intuitive. Concep-
tually, until we arrive at Chapter 10, it is helpful to think of edges as intensity
discontinuities and boundaries as closed paths.
2.5.3 Distance Measures
For pixels p, q, and z, with coordinates (x, y), (s, t), and (v, w), respectively, D
is a distance function or metric if
(a) D(p, q) 0 AD(p, q)=0 iff p=qB,
(b) D(p, q)=D(q, p), and
(c) D(p, z) D(p, q)+D(q, z).
The Euclidean distance between p and q is defined as
(2.5-1)
For this distance measure,the pixels having a distance less than or equal to some
value r from (x, y) are the points contained in a disk of radius r centered at (x, y).
The D4 distance (also called city-block distance) between p and q is defined as
(2.5-2)
In this case, the pixels having a D4 distance from (x, y) less than or equal to
some value r form a diamond centered at (x, y). For example, the pixels with
D4 distance 2 from (x, y) (the center point) form the following contours of
constant distance:
The pixels with D4=1 are the 4-neighbors of (x, y).
2
2
1
2
2
1
0
1
2
2
1
2
2
D4(p, q) = ∑x - s∑ + ∑y - t∑.
De(p, q) = C(x - s)2
+ (y - t)2
D
1
2.
GONZ02-034-074.II 29-08-2001 13:36 Page 68
32. 2.5 ■ Some Basic Relationships Between Pixels 69
The D8 distance (also called chessboard distance) between p and q is defined as
(2.5-3)
In this case,the pixels with D8 distance from (x, y) less than or equal to some value
r form a square centered at (x, y). For example, the pixels with D8 distance 2
from (x, y) (the center point) form the following contours of constant distance:
The pixels with D8=1 are the 8-neighbors of (x, y).
Note that the D4 and D8 distances between p and q are independent of any
paths that might exist between the points because these distances involve only
the coordinates of the points. If we elect to consider m-adjacency, however, the
Dm distance between two points is defined as the shortest m-path between the
points. In this case, the distance between two pixels will depend on the values
of the pixels along the path, as well as the values of their neighbors. For in-
stance, consider the following arrangement of pixels and assume that p, p2, and
p4 have value 1 and that p1 and p3 can have a value of 0 or 1:
Suppose that we consider adjacency of pixels valued 1 (i.e., V={1}). If p1 and
p3 are 0, the length of the shortest m-path (the Dm distance) between p and p4
is 2. If p1 is 1, then p2 and p will no longer be m-adjacent (see the definition of
m-adjacency) and the length of the shortest m-path becomes 3 (the path goes
through the points ). Similar comments apply if p3 is 1 (and p1 is 0); in
this case, the length of the shortest m-path also is 3. Finally, if both p1 and p3 are
1 the length of the shortest m-path between p and p4 is 4. In this case, the path
goes through the sequence of points
2.5.4 Image Operations on a Pixel Basis
Numerous references are made in the following chapters to operations between
images, such as dividing one image by another. In Eq. (2.4-2), images were rep-
resented in the form of matrices. As we know, matrix division is not defined.
However, when we refer to an operation like “dividing one image by another,”
we mean specifically that the division is carried out between corresponding pix-
els in the two images.Thus, for example, if f and g are images, the first element
of the image formed by “dividing” f by g is simply the first pixel in f divided
by the first pixel in g; of course, the assumption is that none of the pixels in g
have value 0. Other arithmetic and logic operations are similarly defined be-
tween corresponding pixels in the images involved.
pp1p2p3p4.
pp1p2p4
p1
p
p3
p2
p4
2
2
2
2
2
2
1
1
1
2
2
1
0
1
2
2
1
1
1
2
2
2
2
2
2
D8(p, q) = maxA∑x - s∑, ∑y - t∑B.
GONZ02-034-074.II 29-08-2001 13:36 Page 69
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