Mathematics in Everyday Life by Gilad Lerman
Department of Mathematics
University of MinnesotaGilad Lerman
Department of Mathematics
University of Minnesota
1) Mathematics is useful for analyzing digital images which are composed of numbers representing brightness values.
2) Common image processing techniques like smoothing and sharpening images can be achieved through mathematical operations on the numeric values such as averaging pixels with neighbors or taking differences between pixels.
3) These techniques are applied in real-world problems to detect cracks in railroad tracks from millions of images collected, helping automate an important safety task.
1) Mathematics is useful for image processing and analyzing digital images which are composed of numbers representing color and brightness.
2) Common math techniques like averaging and differences can be used to smooth and sharpen images.
3) These techniques are applied in real-world problems like detecting cracks in railroad tracks from millions of images in order to identify defects and prevent accidents.
This document discusses the relationship between mathematics and imaging/image processing. It provides examples of how 6th grade students used math concepts like denoising and panorama recognition in their homework. The document then explains how digital images are composed of numbers and how basic math operations like averaging and differences can be used to smooth and sharpen images. It concludes by discussing a real-world application of using image processing to detect cracks in railroad tracks from pictures.
This document discusses magic squares, which are grids of numbers where the sums of each row, column and diagonal are equal. It provides examples of magic squares and asks the reader to determine which are magic squares and their magic totals. It also explains that a quick way to find the magic total is to multiply the center number by 3. The document covers identifying magic squares, completing magic squares, and using number sequences to make magic squares.
The document is a 9x9 multiplication table. It can be used to solve multiplication problems by finding the intersection of the row for the first number and the column for the second number.
This document defines two mathematical problems related to joining dots in a matrix without crossing lines. The first problem asks if it can be proven that at least one solution exists to join all dots in a matrix of size m x n, where m and n are greater than or equal to 3, under the conditions that adjacent dots on the same row cannot be joined and dots cannot be joined to their immediate neighbors. The second problem asks what the maximum matrix size is for which a solution exists, if the first problem can be proven. The document also provides example figures to illustrate the problem and notes an iPad game has been created to help understand the problem set.
This document discusses various measures of central tendency and dispersion used to summarize collected data. It defines mean, median and mode as measures of central tendency, and how to calculate each one. It also covers variance, standard deviation and coefficient of variation as measures of dispersion. The document provides examples of calculating and interpreting these statistical concepts, and explains when to use each measure to best summarize a data set.
1) Mathematics is useful for analyzing digital images which are composed of numbers representing brightness values.
2) Common image processing techniques like smoothing and sharpening images can be achieved through mathematical operations on the numeric values such as averaging pixels with neighbors or taking differences between pixels.
3) These techniques are applied in real-world problems to detect cracks in railroad tracks from millions of images collected, helping automate an important safety task.
1) Mathematics is useful for image processing and analyzing digital images which are composed of numbers representing color and brightness.
2) Common math techniques like averaging and differences can be used to smooth and sharpen images.
3) These techniques are applied in real-world problems like detecting cracks in railroad tracks from millions of images in order to identify defects and prevent accidents.
This document discusses the relationship between mathematics and imaging/image processing. It provides examples of how 6th grade students used math concepts like denoising and panorama recognition in their homework. The document then explains how digital images are composed of numbers and how basic math operations like averaging and differences can be used to smooth and sharpen images. It concludes by discussing a real-world application of using image processing to detect cracks in railroad tracks from pictures.
This document discusses magic squares, which are grids of numbers where the sums of each row, column and diagonal are equal. It provides examples of magic squares and asks the reader to determine which are magic squares and their magic totals. It also explains that a quick way to find the magic total is to multiply the center number by 3. The document covers identifying magic squares, completing magic squares, and using number sequences to make magic squares.
The document is a 9x9 multiplication table. It can be used to solve multiplication problems by finding the intersection of the row for the first number and the column for the second number.
This document defines two mathematical problems related to joining dots in a matrix without crossing lines. The first problem asks if it can be proven that at least one solution exists to join all dots in a matrix of size m x n, where m and n are greater than or equal to 3, under the conditions that adjacent dots on the same row cannot be joined and dots cannot be joined to their immediate neighbors. The second problem asks what the maximum matrix size is for which a solution exists, if the first problem can be proven. The document also provides example figures to illustrate the problem and notes an iPad game has been created to help understand the problem set.
This document discusses various measures of central tendency and dispersion used to summarize collected data. It defines mean, median and mode as measures of central tendency, and how to calculate each one. It also covers variance, standard deviation and coefficient of variation as measures of dispersion. The document provides examples of calculating and interpreting these statistical concepts, and explains when to use each measure to best summarize a data set.
Chapter 5 decision tree induction using frequency tables for attribute selectionKy Hong Le
This document discusses different methods for attribute selection in decision tree induction, including calculating entropy, the Gini index of diversity, and using gain ratio. It provides examples calculating these metrics on a sample training dataset to select the best attribute for splitting. The key points made are:
1) Entropy, Gini index, and gain ratio can be used to calculate the information gain of splitting on different attributes to select the optimal one.
2) Gain ratio reduces the bias of information gain by normalizing it by the split information.
3) On the example lens dataset, all three methods (entropy, Gini index, gain ratio) select the "tears" attribute as providing the greatest information gain.
The document defines percent as "of one hundred" and provides examples of converting between percentages, decimals, and fractions. It then outlines the steps to find the percent of a whole number: 1) recognize that "of" means to multiply, 2) change the percent to a decimal by moving the decimal point two places left, 3) multiply the whole number by the decimal, and 4) place the decimal in the answer two places from the right. Examples are provided to find 20%, 40%, and 60% of various whole numbers.
The document explains how to multiply two digit numbers. It shows that you multiply the ones place of the first number by the ones place of the second number. If there is a carry amount, you add it to the multiplication of the ones places. You then multiply the tens place of the first number by both digits of the second number and add the partial products together to get the total product.
This document provides instructions for using a number line to teach basic math operations like addition, subtraction, multiplication and comparisons of greater than and less than to students. It explains how to represent numbers on a number line and use curves and repetition to demonstrate addition, subtraction and multiplication visually. Examples are given for using the number line to solve problems involving these operations with numbers between 1-52.
- Scientific notation is a way of writing very large or small numbers as a product of a number between 1 and 10 and a power of 10.
- Prefixes are used to indicate the power of 10 being multiplied, with examples including mega (106) and micro (10-6).
- When measuring quantities, only a certain number of digits can be known with certainty based on the precision of the measuring instrument. Significant figures indicate the digits that are known precisely.
This document discusses graphing functions. It begins by introducing common functions like linear, quadratic, cubic, rational, absolute value, square root, and cube root functions. Examples of their graphs are shown. It then discusses using the vertical line test to determine if something is a function. Piecewise functions are introduced next along with steps for graphing them which include graphing each piece and indicating open and closed points. Examples of piecewise functions are given and discussed. The document concludes by noting T-tables can be used to graph but plotting each piece of piecewise functions is more accurate.
This document discusses significant figures in measurements and calculations. It makes three key points:
1. Significant figures in a measurement include all known digits plus one estimated digit and indicate the precision or uncertainty in the measurement.
2. Rules are provided for determining which digits are significant, depending on their position relative to other digits and the decimal point.
3. Calculations must be rounded according to whether addition/subtraction or multiplication/division was used, and based on the least precise term (fewest significant figures).
The document contains calculations to determine skewness using grouped data. It includes frequency distributions of grouped data with ranges of values for X, frequencies (f), deviations (d), d-squared (d2), and d-cubed (d3). Formulas are provided to calculate the second (m2) and third (m3) moments about the mean. The computations are presented in a table with columns for X, M, f, fM, d, d2, d3, fd2, and fd3.
The document defines variance as the average of the squared differences from the mean. It provides examples of calculating variance and standard deviation for different data sets involving heights of dogs, exam scores, and word counts per page. Variance is found by taking the difference of each value from the mean, squaring it, and averaging the results. Standard deviation is the square root of the variance.
This document discusses significant figures and how they are used to convey the precision and uncertainty of measurements. It provides examples of how to determine the number of significant figures in a measurement, as well as rules for performing calculations while maintaining the proper number of significant figures in the final answer based on the least precise term. Calculations include addition, subtraction, multiplication, and division. The key points are that non-zero digits and zeros between non-zero digits are always significant, and that the final answer should be rounded based on the number of decimal places in the least precise measurement used.
The document discusses several math concepts including:
- A line graph showing temperature changes throughout the day, peaking at 70 degrees Fahrenheit at 4pm then decreasing.
- A student selling calendars and raffle tickets to raise funds, calculating their total earnings.
- Measures of central tendency (mean, median, mode) for a data set of heights, and how an outlier affects these values.
- Solving various math equations for unknown values.
- Identifying patterns in number sequences.
- Dividing snacks evenly between friends to calculate the maximum number of bags.
This document discusses the importance of mathematics in everyday life through several examples. It begins by addressing common misconceptions that mathematics is hard, boring, and irrelevant to real life. It then provides examples of how mathematics is used in crime detection, medicine, finding landmines, art, music, and predicting the future. The document goes on to discuss how the modern world would not exist without mathematics and provides scenarios of what life would be like without numbers. It then focuses on specific examples of how mathematics is used in crime detection using image processing techniques, medicine through medical imaging technologies like CAT scans and MRI, and finding hidden trip wires for landmines. It emphasizes that mathematics allows us to see inside the body and world without cutting them open
Identification of unknown parameters and prediction with hierarchical matrice...Alexander Litvinenko
We compare four numerical methods for the prediction of missing values in four different datasets.
These methods are 1) the hierarchical maximum likelihood estimation (H-MLE), and three machine learning (ML) methods, which include 2) k-nearest neighbors (kNN), 3) random forest, and 4) Deep Neural Network (DNN).
From the ML methods, the best results (for considered datasets) were obtained by the kNN method with three (or seven) neighbors.
On one dataset, the MLE method showed a smaller error than the kNN method, whereas, on another, the kNN method was better.
The MLE method requires a lot of linear algebra computations and works fine on almost all datasets. Its result can be improved by taking a smaller threshold and more accurate hierarchical matrix arithmetics. To our surprise, the well-known kNN method produces similar results as H-MLE and worked much faster.
Identification of unknown parameters and prediction of missing values. Compar...Alexander Litvinenko
H-matrix approximation of large Mat\'{e}rn covariance matrices, Gaussian log-likelihoods.
Identifying unknown parameters and making predictions
Comparison with machine learning methods.
kNN is easy to implement and shows promising results.
The document discusses the discrete cosine transform (DCT) and its applications in image compression. DCT transforms a signal or image into a combination of cosine functions arranged by frequency. This property allows for efficient compression by discarding high-frequency components with little visual impact. Specifically:
- DCT provides a basis to represent an image as a sum of cosine functions, with low frequencies more important visually.
- Applying DCT to blocks of an image separates information by importance, allowing lossy compression by discarding high frequencies.
- Quantization further compresses data by allocating fewer bits to store high-frequency DCT coefficients.
- Together DCT and quantization provide significant data compression with minimal visual
This document discusses techniques for solving simultaneous linear algebraic equations. It begins by introducing linear algebraic equations with n variables and describes graphical and algebraic manual solutions that can be used when n is less than or equal to 3. It then explains Gaussian elimination, a method for numerically solving systems of linear equations. The document discusses pivoting techniques like partial and full pivoting that can improve the stability and accuracy of the Gaussian elimination method by selecting larger pivot elements. It also notes potential pitfalls of elimination methods like division by zero, round-off errors, and ill-conditioned systems.
Solve Sudoku using Constraint Propagation- Search and Genetic AlgorithmAi Sha
The document compares two algorithms for solving Sudoku puzzles: a genetic algorithm (GA) and a constraint propagation-search algorithm. It tests both algorithms on 30 random Sudoku puzzles. The constraint propagation-search algorithm solved all puzzles in an average of 0.01 seconds, while the GA took an average of 3.94 seconds to solve each puzzle, demonstrating that the constraint propagation-search algorithm is much more efficient for solving Sudoku puzzles.
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
help.mbaassignments@gmail.com
or
call us at : 08263069601
Este taller vamos a ver una rama de las matemáticas que se ocupa del estudio de las propiedades de las figuras en el plano o el espacio, incluyendo: puntos, rectas, planos etc
Museum Paper Rubric50 pointsRubric below is a chart form of .docxgilpinleeanna
Museum Paper Rubric
50 points
Rubric below is a chart form of the instructions on the Museum Paper assignment sheet.
Category
Description
Points
First Step
10 points
Selfie with image (5)
5
Evocative, detailed description and comparisons (5)
3
Second Step
6 points
3 scholarly sources (6)
6
Third Step
26 points
Clear statement with individual analysis (10)
7
Selective and objective detail that supports statement (10)
8
Writing: flow, readability (6)
6
Format
8 points
Length 3-4 pages (3)
3
Illustration/image included at end (2)
2
Chicago style end note citations (3)
3
Total
50 points
Comments
Good research about Shiva and iconography. Your particular thesis - your personal analysis - should be the core of the essay rather than a historical overview, and the research content would revolve around your thesis statement. For example, your descriptions include descriptions of iconography showing his power, so that could be a direction for your thesis statement. Shiva is a Hindu deity, so it is unlikely that this would be "Shiva Buddha" (since Buddha is part of Buddhism). To avoid generalizations such as the third eye and red mark (page 2 middle) , it would be stronger to explain what that third eye meant.
43
MATH 220 - CT Scan Project
(in class)
Directions This project is due Thursday April 26 at the beginning of class. There are two
parts to this project - the first is an introduction to computed tomography scan, or CT scan, and
works through a sample project while explaining how CT scan images are produced. If there is
time, this will be worked through in class. The second part is an individual project, in which you
are given the output of a two-dimensional CT scan and you are to determine what the picture is.
For this project, we do not ask that you summarize the statement of each problem, nor do
we want you to turn in this paper. Please turn in one sheet of paper with the answers to each
question clearly written. Answer each question using complete sentences. Answers that
simply indicate a single number, a single equation, etc, will be given no credit. Although you may
work in groups or even as a class, your responses should be in your own words. Any indication
of plagiarism, such as duplicate sentences, will be treated as a violation of academic integrity,
resulting in a zero on this project and the dishonesty reported to the Office of Academic Integrity.
This project will be worth 3% of your course grade. Technology allowed. The data is given in a
file that assumes you are using MatLab.
CT Scan Project
The radiation x-ray was discovered by a German physicist, Wilhelm Roentgen, who did not
know what it was, so he simply called it “X-radiation”. A single x-ray passing through a body is
absorbed at rates depending upon the material it goes through. Thus if an x-ray is passed through
bone, a certain amount of intensity units is absorbed, while if it passes through soft material, a
different amount of intensity u ...
Chapter 5 decision tree induction using frequency tables for attribute selectionKy Hong Le
This document discusses different methods for attribute selection in decision tree induction, including calculating entropy, the Gini index of diversity, and using gain ratio. It provides examples calculating these metrics on a sample training dataset to select the best attribute for splitting. The key points made are:
1) Entropy, Gini index, and gain ratio can be used to calculate the information gain of splitting on different attributes to select the optimal one.
2) Gain ratio reduces the bias of information gain by normalizing it by the split information.
3) On the example lens dataset, all three methods (entropy, Gini index, gain ratio) select the "tears" attribute as providing the greatest information gain.
The document defines percent as "of one hundred" and provides examples of converting between percentages, decimals, and fractions. It then outlines the steps to find the percent of a whole number: 1) recognize that "of" means to multiply, 2) change the percent to a decimal by moving the decimal point two places left, 3) multiply the whole number by the decimal, and 4) place the decimal in the answer two places from the right. Examples are provided to find 20%, 40%, and 60% of various whole numbers.
The document explains how to multiply two digit numbers. It shows that you multiply the ones place of the first number by the ones place of the second number. If there is a carry amount, you add it to the multiplication of the ones places. You then multiply the tens place of the first number by both digits of the second number and add the partial products together to get the total product.
This document provides instructions for using a number line to teach basic math operations like addition, subtraction, multiplication and comparisons of greater than and less than to students. It explains how to represent numbers on a number line and use curves and repetition to demonstrate addition, subtraction and multiplication visually. Examples are given for using the number line to solve problems involving these operations with numbers between 1-52.
- Scientific notation is a way of writing very large or small numbers as a product of a number between 1 and 10 and a power of 10.
- Prefixes are used to indicate the power of 10 being multiplied, with examples including mega (106) and micro (10-6).
- When measuring quantities, only a certain number of digits can be known with certainty based on the precision of the measuring instrument. Significant figures indicate the digits that are known precisely.
This document discusses graphing functions. It begins by introducing common functions like linear, quadratic, cubic, rational, absolute value, square root, and cube root functions. Examples of their graphs are shown. It then discusses using the vertical line test to determine if something is a function. Piecewise functions are introduced next along with steps for graphing them which include graphing each piece and indicating open and closed points. Examples of piecewise functions are given and discussed. The document concludes by noting T-tables can be used to graph but plotting each piece of piecewise functions is more accurate.
This document discusses significant figures in measurements and calculations. It makes three key points:
1. Significant figures in a measurement include all known digits plus one estimated digit and indicate the precision or uncertainty in the measurement.
2. Rules are provided for determining which digits are significant, depending on their position relative to other digits and the decimal point.
3. Calculations must be rounded according to whether addition/subtraction or multiplication/division was used, and based on the least precise term (fewest significant figures).
The document contains calculations to determine skewness using grouped data. It includes frequency distributions of grouped data with ranges of values for X, frequencies (f), deviations (d), d-squared (d2), and d-cubed (d3). Formulas are provided to calculate the second (m2) and third (m3) moments about the mean. The computations are presented in a table with columns for X, M, f, fM, d, d2, d3, fd2, and fd3.
The document defines variance as the average of the squared differences from the mean. It provides examples of calculating variance and standard deviation for different data sets involving heights of dogs, exam scores, and word counts per page. Variance is found by taking the difference of each value from the mean, squaring it, and averaging the results. Standard deviation is the square root of the variance.
This document discusses significant figures and how they are used to convey the precision and uncertainty of measurements. It provides examples of how to determine the number of significant figures in a measurement, as well as rules for performing calculations while maintaining the proper number of significant figures in the final answer based on the least precise term. Calculations include addition, subtraction, multiplication, and division. The key points are that non-zero digits and zeros between non-zero digits are always significant, and that the final answer should be rounded based on the number of decimal places in the least precise measurement used.
The document discusses several math concepts including:
- A line graph showing temperature changes throughout the day, peaking at 70 degrees Fahrenheit at 4pm then decreasing.
- A student selling calendars and raffle tickets to raise funds, calculating their total earnings.
- Measures of central tendency (mean, median, mode) for a data set of heights, and how an outlier affects these values.
- Solving various math equations for unknown values.
- Identifying patterns in number sequences.
- Dividing snacks evenly between friends to calculate the maximum number of bags.
This document discusses the importance of mathematics in everyday life through several examples. It begins by addressing common misconceptions that mathematics is hard, boring, and irrelevant to real life. It then provides examples of how mathematics is used in crime detection, medicine, finding landmines, art, music, and predicting the future. The document goes on to discuss how the modern world would not exist without mathematics and provides scenarios of what life would be like without numbers. It then focuses on specific examples of how mathematics is used in crime detection using image processing techniques, medicine through medical imaging technologies like CAT scans and MRI, and finding hidden trip wires for landmines. It emphasizes that mathematics allows us to see inside the body and world without cutting them open
Identification of unknown parameters and prediction with hierarchical matrice...Alexander Litvinenko
We compare four numerical methods for the prediction of missing values in four different datasets.
These methods are 1) the hierarchical maximum likelihood estimation (H-MLE), and three machine learning (ML) methods, which include 2) k-nearest neighbors (kNN), 3) random forest, and 4) Deep Neural Network (DNN).
From the ML methods, the best results (for considered datasets) were obtained by the kNN method with three (or seven) neighbors.
On one dataset, the MLE method showed a smaller error than the kNN method, whereas, on another, the kNN method was better.
The MLE method requires a lot of linear algebra computations and works fine on almost all datasets. Its result can be improved by taking a smaller threshold and more accurate hierarchical matrix arithmetics. To our surprise, the well-known kNN method produces similar results as H-MLE and worked much faster.
Identification of unknown parameters and prediction of missing values. Compar...Alexander Litvinenko
H-matrix approximation of large Mat\'{e}rn covariance matrices, Gaussian log-likelihoods.
Identifying unknown parameters and making predictions
Comparison with machine learning methods.
kNN is easy to implement and shows promising results.
The document discusses the discrete cosine transform (DCT) and its applications in image compression. DCT transforms a signal or image into a combination of cosine functions arranged by frequency. This property allows for efficient compression by discarding high-frequency components with little visual impact. Specifically:
- DCT provides a basis to represent an image as a sum of cosine functions, with low frequencies more important visually.
- Applying DCT to blocks of an image separates information by importance, allowing lossy compression by discarding high frequencies.
- Quantization further compresses data by allocating fewer bits to store high-frequency DCT coefficients.
- Together DCT and quantization provide significant data compression with minimal visual
This document discusses techniques for solving simultaneous linear algebraic equations. It begins by introducing linear algebraic equations with n variables and describes graphical and algebraic manual solutions that can be used when n is less than or equal to 3. It then explains Gaussian elimination, a method for numerically solving systems of linear equations. The document discusses pivoting techniques like partial and full pivoting that can improve the stability and accuracy of the Gaussian elimination method by selecting larger pivot elements. It also notes potential pitfalls of elimination methods like division by zero, round-off errors, and ill-conditioned systems.
Solve Sudoku using Constraint Propagation- Search and Genetic AlgorithmAi Sha
The document compares two algorithms for solving Sudoku puzzles: a genetic algorithm (GA) and a constraint propagation-search algorithm. It tests both algorithms on 30 random Sudoku puzzles. The constraint propagation-search algorithm solved all puzzles in an average of 0.01 seconds, while the GA took an average of 3.94 seconds to solve each puzzle, demonstrating that the constraint propagation-search algorithm is much more efficient for solving Sudoku puzzles.
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
help.mbaassignments@gmail.com
or
call us at : 08263069601
Este taller vamos a ver una rama de las matemáticas que se ocupa del estudio de las propiedades de las figuras en el plano o el espacio, incluyendo: puntos, rectas, planos etc
Museum Paper Rubric50 pointsRubric below is a chart form of .docxgilpinleeanna
Museum Paper Rubric
50 points
Rubric below is a chart form of the instructions on the Museum Paper assignment sheet.
Category
Description
Points
First Step
10 points
Selfie with image (5)
5
Evocative, detailed description and comparisons (5)
3
Second Step
6 points
3 scholarly sources (6)
6
Third Step
26 points
Clear statement with individual analysis (10)
7
Selective and objective detail that supports statement (10)
8
Writing: flow, readability (6)
6
Format
8 points
Length 3-4 pages (3)
3
Illustration/image included at end (2)
2
Chicago style end note citations (3)
3
Total
50 points
Comments
Good research about Shiva and iconography. Your particular thesis - your personal analysis - should be the core of the essay rather than a historical overview, and the research content would revolve around your thesis statement. For example, your descriptions include descriptions of iconography showing his power, so that could be a direction for your thesis statement. Shiva is a Hindu deity, so it is unlikely that this would be "Shiva Buddha" (since Buddha is part of Buddhism). To avoid generalizations such as the third eye and red mark (page 2 middle) , it would be stronger to explain what that third eye meant.
43
MATH 220 - CT Scan Project
(in class)
Directions This project is due Thursday April 26 at the beginning of class. There are two
parts to this project - the first is an introduction to computed tomography scan, or CT scan, and
works through a sample project while explaining how CT scan images are produced. If there is
time, this will be worked through in class. The second part is an individual project, in which you
are given the output of a two-dimensional CT scan and you are to determine what the picture is.
For this project, we do not ask that you summarize the statement of each problem, nor do
we want you to turn in this paper. Please turn in one sheet of paper with the answers to each
question clearly written. Answer each question using complete sentences. Answers that
simply indicate a single number, a single equation, etc, will be given no credit. Although you may
work in groups or even as a class, your responses should be in your own words. Any indication
of plagiarism, such as duplicate sentences, will be treated as a violation of academic integrity,
resulting in a zero on this project and the dishonesty reported to the Office of Academic Integrity.
This project will be worth 3% of your course grade. Technology allowed. The data is given in a
file that assumes you are using MatLab.
CT Scan Project
The radiation x-ray was discovered by a German physicist, Wilhelm Roentgen, who did not
know what it was, so he simply called it “X-radiation”. A single x-ray passing through a body is
absorbed at rates depending upon the material it goes through. Thus if an x-ray is passed through
bone, a certain amount of intensity units is absorbed, while if it passes through soft material, a
different amount of intensity u ...
Operations in Digital Image Processing + Convolution by ExampleAhmed Gad
Digital image processing operations can be either point or group.
This presentation explains both operations (point and group) and shows how convolution works by a numerical example.
Ahmed Fawzy Gad
ahmed.fawzy@ci.menofia.edu.eg
Information Technology Department
Faculty of Computers and Information (FCI)
Menoufia University
Egypt
Find me on:
AFCIT
http://www.afcit.xyz
YouTube
https://www.youtube.com/channel/UCuewOYbBXH5gwhfOrQOZOdw
Google Plus
https://plus.google.com/u/0/+AhmedGadIT
SlideShare
https://www.slideshare.net/AhmedGadFCIT
LinkedIn
https://www.linkedin.com/in/ahmedfgad/
ResearchGate
https://www.researchgate.net/profile/Ahmed_Gad13
Academia
https://www.academia.edu/
Google Scholar
https://scholar.google.com.eg/citations?user=r07tjocAAAAJ&hl=en
Mendelay
https://www.mendeley.com/profiles/ahmed-gad12/
ORCID
https://orcid.org/0000-0003-1978-8574
StackOverFlow
http://stackoverflow.com/users/5426539/ahmed-gad
Twitter
https://twitter.com/ahmedfgad
Facebook
https://www.facebook.com/ahmed.f.gadd
Pinterest
https://www.pinterest.com/ahmedfgad/
Application of Parallel Hierarchical Matrices in Spatial Statistics and Param...Alexander Litvinenko
Part 1: Parallel H-matrices in spatial statistics
1. Motivation: improve statistical model
2. Tools: Hierarchical matrices [Hackbusch 1999]
3. Matern covariance function and joint Gaussian likelihood
4. Identification of unknown parameters via maximizing Gaussian
log-likelihood
5. Implementation with HLIBPro.
1. The document discusses image formation, cameras, and digital image acquisition and representation. It describes how images are formed through light projection and sampling, and how analog and digital cameras work to capture images.
2. Digital images are represented as matrices, with each element corresponding to a pixel value. Grayscale images have a single value per pixel while color images have multiple values representing channels like red, green, and blue.
3. Pixels in digital images are quantized to a finite set of numeric values like 8-bit integers from 0 to 255 for storage and processing in computer systems. This affects qualities like radiometric resolution of the encoded image.
Simultaneous equations in two variables. Finding solution to systems of linear equations by graphing. Solving systems of linear equations by elimination and substitution method.
Disclaimer: Some parts of the presentation are obtained from various sources. Credit to the rightful owners.
The document discusses composition and impact in photography. It covers three main points: 1) Get in close to simplify the photo and focus attention on the subject. 2) Use compositional techniques like the rule of thirds, leading lines, framing, and negative space. 3) Experiment with different points of view like walking around the subject or changing angles. The goal is to eliminate distractions and guide the viewer's eye in a way that effectively communicates the photographer's intended message.
This document discusses dos and don'ts of using t-SNE to understand vision models. It explains how t-SNE works by computing pairwise similarities between high-dimensional data points and minimizing the divergence between the high-D and low-D distributions. The document recommends being creative in how t-SNE is applied and visualized, but warns against overinterpreting results and forgetting that t-SNE has limitations like local minima and an inability to capture all similarities.
This document discusses key concepts related to image formation in computer vision. It covers geometric primitives like points, lines, and planes and how they are projected from 3D to 2D. It also discusses image formation in the human eye and digital cameras. The process of capturing digital images involves sampling and quantizing the continuous image function. Factors like spatial resolution, intensity resolution, and image representations like RGB images are also summarized.
The document describes various computer graphics output primitives and algorithms for drawing them, including lines, circles, and filled areas. It discusses line drawing algorithms like DDA, Bresenham's, and midpoint circle algorithms. These algorithms use incremental integer calculations to efficiently rasterize primitives by determining the next pixel coordinates without performing floating point calculations at each step. The midpoint circle algorithm in particular uses a "circle function" and incremental updates to its value to determine whether the next pixel is inside or outside the circle boundary.
Vision systems_Image processing tool box in MATLABHinna Nayab
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إضغ بين إيديكم من أقوى الملازم التي صممتها
ملزمة تشريح الجهاز الهيكلي (نظري 3)
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تتميز هذهِ الملزمة بعِدة مُميزات :
1- مُترجمة ترجمة تُناسب جميع المستويات
2- تحتوي على 78 رسم توضيحي لكل كلمة موجودة بالملزمة (لكل كلمة !!!!)
#فهم_ماكو_درخ
3- دقة الكتابة والصور عالية جداً جداً جداً
4- هُنالك بعض المعلومات تم توضيحها بشكل تفصيلي جداً (تُعتبر لدى الطالب أو الطالبة بإنها معلومات مُبهمة ومع ذلك تم توضيح هذهِ المعلومات المُبهمة بشكل تفصيلي جداً
5- الملزمة تشرح نفسها ب نفسها بس تكلك تعال اقراني
6- تحتوي الملزمة في اول سلايد على خارطة تتضمن جميع تفرُعات معلومات الجهاز الهيكلي المذكورة في هذهِ الملزمة
واخيراً هذهِ الملزمة حلالٌ عليكم وإتمنى منكم إن تدعولي بالخير والصحة والعافية فقط
كل التوفيق زملائي وزميلاتي ، زميلكم محمد الذهبي 💊💊
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Maths in daytoday life by Gilad Lerman Department of Mathematics University of Minnesota
1. Mathematics in Everyday Life
Gilad Lerman
Department of Mathematics
University of Minnesota
Highland park elementary (6th graders)
2. What do mathematicians do?What homework do I give
my students?
• Example of a recent homework: Denoising
3. What do mathematicians do?What projects do I assign
my students?
• Example of a recent project:
Recognizing Panoramas
• Panorama:
• How to obtain a panorama?
wide view of a physical space
4. How to obtain a panorama
1. By “rotating line camera”
2. Stitching together multiple images
Your camera can do it this way…
E.g. PhotoStitch (Canon PowerShot SD600)
18. More Relation of Imaging and Math
Differences of numbers sharpening images
On left image of moon
On right its edges (obtained by differences)
We can add the two to get a sharpened version of the first
20. Real Life Applications
• Many…
• From a Minnesota based company…
• Their main job: maintaining railroads
• Main concern: Identify cracks in railroads,
before too late…
21. How to detect damaged rails?
• Traditionally… drive along the rail (very long) and
inspect
• Very easy to miss defects (falling asleep…)
• New technology: getting pictures of rails
23. How to detect Cracks?
• Human observation…
• Train a computer…
• Recall that differences detect edges…
Work done by Kyle Heuton (high school student at Saint Paul)
24. Summary
• Math is useful (beyond the grocery store)
• Images are composed of numbers
• Good math ideas good image processing