This document contains questions and answers about image processing concepts such as linear indexing, converting between m-paths and 4-paths, adjacency in image subsets, shortest path lengths between pixels using different adjacency types, and inverse affine transformations including scaling, translation, shearing, and rotation. Equations and examples are provided to derive the inverse transformations from the original transformations.
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.
After an image has been segmented into regions ; the resulting pixels is usually is represented and described in suitable form for further computer 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.
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.
After an image has been segmented into regions ; the resulting pixels is usually is represented and described in suitable form for further computer 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.
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Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Image Acquisition and Representation
A Simple Image Formation Model
Image Sampling and Quantization
Image Interpolation
Image quantization
Nearest Neighbor Interpolation
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
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The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
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A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
The Digital Image Processing Q@A
1. DIP Homework: 3
Q- 5 You are preparing a report and have to install in it an image of size 2048 * 2048 pixels?
a- Assuming on limitations on the printer, what would the resolution in line pairs mm
have to be for the image to fit in a space of size 5*5cm?
Answer: the resolution of the fitting in the space size of 5*5 can be calculated
2048 𝐿𝑖𝑛𝑒𝑠
50 𝑚𝑚
≅ 41 lines / min
≅ 20 lines / min
b- What would the resolution have to be in dpi for the image to fit in 2*2 inches?
Answer: the image resolution for fitting 2*2 inch will be calculated as
2048 𝑑𝑜𝑡𝑠
2 𝑖𝑛𝑐ℎ
= 1024 dots per inch
Q- 11 When discussing linear indexing in section 2.4, we arrived at the linear index in Eq.
(2.14) by inspection. The same argument used there can be extended to a 3-D array with
coordinates x,y and z, and corresponding dimensions M, N and P. The linear index for any
(x,y,z) is S = x + M (y + Nz) = x + Mg + Myz
Start with expression and
a- *Drive Eq. (2.15)
b- Drive Eq. (2.16)
Answer:
For 2D array to 1D array (leaner)
∝ = 𝑀𝑦 + 𝑥
𝑥 = ∝ +𝑥
⟹ 𝑦 =
𝑎−𝑥
𝑀
For 3D case we have
( 𝑥, 𝑦, 𝑧) ⟶ 𝑠
M
N
y
x
m-1
0
2. 𝑠 = 𝑥 + 𝑚 ( 𝑦 + 𝑁𝑧) ⟹ 𝑥 = 𝑠 𝑚𝑜𝑑 𝑚
𝑠 − 𝑥 = 𝑚 (𝑦 + 𝑁𝑧)
𝑦 + 𝑁𝑧 =
𝑠−𝑥
𝑀
⟹ 𝑦 = (
𝑠−𝑥
𝑀
) 𝑚𝑜𝑑 𝑀
Since the (
𝑠−𝑥
𝑀
) < 𝑀 , (
𝑠−𝑥
𝑀
) 𝑚𝑜𝑑 𝑁 =
𝑠−𝑥
𝑀
. The maximum value of S is MN - 1 and, the
maximum of x is 0.
Q- 16 Develop an algorithm for converting a one-pixel-thick m-path to a 4-paths?
Answer: Any pixel p (x, y) has two vertical and two horizontal neighbors, given by (x+1,
y), (x-1, y), (x, y+1), (x, y-1) and This set of pixels are called the 4-neighbors of P, and is
denoted by N4 (P) and each of them are at a unit distance from P. We assume that (x,y) is
spatial location of the starting of 4-path. and in image path is represented by 1's and
remaining values are 0's.
1- we assign (p,q) is the m-connected neighborhood of (x,y) which is not processed yet
2- For each pixel is unit distance from (x,y)
3- Check whether the common 4-neighborhood pixel position of (x,y) and (p,q) is part of
existing path, if not make any one of the common 4-neighborhood to be 1, else no need
to do anything(because it is already 4-connected).
4- We assign (x,y )= (p,q)
5- 4-neighbors of p, denoted by N4(p): (x-1, y), (x+1, y), (x, y-1), and (x, y+1).
The solution to this problem consists of defining all possible neighborhood shapes to go from a
diagonal segment to a corresponding 4-connected segment, as shown in fig bellow. The algorithm
then simply looks for the appropriate match every time a diagonal segment is encountered in the
3. boundary for converting from an m-connected path to a 4-connected path simply involves
detecting diagonal segments and converting them to the appropriate 4-connected segment.
Q- 14 Consider the two image subsets, S1 and S2, shown in the following figure. For V = {1},
determine whether these two subsets are (a) 4-adjacent, (b) 8-adjacent, or (c) m-adjacent.
A- Let p and q be as shown in Fig. Then:
(a) S1 and S2 are not 4-connected because q is not in the set N4(p);
(b) S1 and S2 are 8-connected because q is in the set N8(p);
(c) S1 and S2 are m-connected because
(i) q is in ND(p), and
(ii) the set N4(p) ∩ N4(q) is empty
B- Paths
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
4. (x0, y0), (x1,y1), ……., (xn, yn)
where (x0, y0) = (x, y), (xn, yn) = (s, t),
and pixels (xi, yi) and (xi-1, yi-1) are adjacent for 1≤ i ≤ n.
In this case, n is the length of the path.
If (x0, y0) = (xn, yn) the path is a closed path.
The path can be defined 4-,8-m-paths depending on adjacency type.
Let S be 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 pixels
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.
Q- 18 Consider the image segment show in the figure that follows
a- As in section 2.5, let V= {0,1} be the set of intensity values to defined adjacency.
Compute the lengths of the shortest 4-, 8- and m-path between p and q in the following
image. If a particular path does not exist between these points, explain why?
Answer- (a) When V = {0,1}, 4-path does not exist between p and q because it is impossible to get
from p to q by traveling along points that are both 4-adjacent and also have values from V. Figure
P2.15(a) shows this condition; it is not possible to get to q. The shortest 8-path is shown in Fig.
P2.15(b); its length is 4. The length of the shortest m- path (shown dashed) is 5. Both of these
shortest paths are unique in this case.
b- Repeat (a) by using V= {1,2}
Answer- (b) One possibility for the shortest 4-path when V = {1, 2}is shown in Fig.
P2.15(c); its length is 6. It is easily verified that another 4-path of the same length exists
5. between p and q. One possibility for the shortest 8-path (it is not unique) is shown in Fig.
P2.15(d); its length is 4. The length of a shortest m-path (shown dashed) is 6. This path is
not unique.
Q- 30 Give Venn diagram for the following expression?
a- *(𝑨 ∩ 𝑪) - (A ∩ B ∩ 𝑪 )
b- (𝑨 ∩ 𝑪) ∪ (𝑩 ∩ 𝑪)
c- B - [(𝑨 ∩ 𝑩)- (A ∩ B ∩ 𝑪 )]
d- B-B ∩ ( A ∪ C); Give that ( 𝑨 ∩ 𝑪)= ∅
Q- 37 We know from the E.q (2-45) that an offline transformation of coordinators given by
6. Where (x’,y’) are the transformed coordinators (x,y) are the original coordinator, and the
element of A are given in the table 2.3. for the various type of transformation. The inverse
transformation, A-1, to go from transformed back to the original coordinators in just as
important for performing inverse mappings.
a- Find the inverse scaling transformation?
b- Find the inverse translation transformation?
c- Find the inverse vertical and horizontal shearing transformation?
d- Find the inverse rotation transformation?
e- Show a composite inverse translate/rotation transformation?
Answer for the former of matrix
1 0 0
0 1 0
0 0 1
x = v and y = w
𝑐 𝑥 0 0
0 𝑐 𝑦 0
0 0 1
x’ = cx v and y’ = cy w
For the inverse translation transformation
1 0 𝑡 𝑥
0 1 𝑡 𝑦
𝑡 𝑥 𝑡 𝑦 1
x’ = v + tx and y’ = w + ty
For the inverse vertical and horizontal shearing transformation
1 𝑠 𝑥 0
0 1 0
0 0 1
x’ = v +sx w and y’ = w
1 0 0
𝑠 𝑘 1 0
0 0 1
x’ = v and y’ = sk x + w
7. For the inverse rotation transformation
−
𝑐𝑜𝑠 𝜃 𝑠𝑖𝑛 𝜃 0
𝑠𝑖𝑛 𝜃 𝑐𝑜𝑠 𝜃 0
0 0 1
x’ = v cos 𝜃 - w sin 𝜃 and y’ = v sin 𝜃 + w cos 𝜃
Note:
The above diagram used of OpenCV3 operates on images. Image operations are mainly based on
various coordinate transformations of images, such as scale transformation, rotation
transformation, translation transformation and offset transformation (horizontal or vertical). These
transformations are all directed at the coordinates of images, not the pixels of images. They can be
collectively called affine transformation. The above description is for several transformations in
Gonzalez's Digital Image Processing.