The second Fundamental Theorem of Calculus makes calculating definite integrals a problem of antidifferentiation!
(the slideshow has extra examples based on what happened in class)
It's the deck for one Hulu internal machine learning workshop, which introduces the background, theory and application of expectation propagation method.
We define the definite integral as a limit of Riemann sums, compute some approximations, then investigate the basic additive and comparative properties
Lesson 26: The Fundamental Theorem of Calculus (Section 10 version)Matthew Leingang
The First Fundamental Theorem of Calculus looks at the area function and its derivative. It so happens that the derivative of the area function is the original integrand.
The second Fundamental Theorem of Calculus makes calculating definite integrals a problem of antidifferentiation!
(the slideshow has extra examples based on what happened in class)
It's the deck for one Hulu internal machine learning workshop, which introduces the background, theory and application of expectation propagation method.
We define the definite integral as a limit of Riemann sums, compute some approximations, then investigate the basic additive and comparative properties
Lesson 26: The Fundamental Theorem of Calculus (Section 10 version)Matthew Leingang
The First Fundamental Theorem of Calculus looks at the area function and its derivative. It so happens that the derivative of the area function is the original integrand.
Computing integrals with Riemann sums is like computing derivatives with limits. The calculus of integrals turns out to come from antidifferentiation. This startling fact is the Second Fundamental Theorem of Calculus!
Computing integrals with Riemann sums is like computing derivatives with limits. The calculus of integrals turns out to come from antidifferentiation. This startling fact is the Second Fundamental Theorem of Calculus!
Lesson 26: The Fundamental Theorem of Calculus (Section 4 version)Matthew Leingang
The First Fundamental Theorem of Calculus looks at the area function and its derivative. It so happens that the derivative of the area function is the original integrand.
Using implicit differentiation we can treat relations which are not quite functions like they were functions. In particular, we can find the slopes of lines tangent to curves which are not graphs of functions.
Computing integrals with Riemann sums is like computing derivatives with limits. The calculus of integrals turns out to come from antidifferentiation. This startling fact is the Second Fundamental Theorem of Calculus!
Computing integrals with Riemann sums is like computing derivatives with limits. The calculus of integrals turns out to come from antidifferentiation. This startling fact is the Second Fundamental Theorem of Calculus!
Lesson 26: The Fundamental Theorem of Calculus (Section 4 version)Matthew Leingang
The First Fundamental Theorem of Calculus looks at the area function and its derivative. It so happens that the derivative of the area function is the original integrand.
Using implicit differentiation we can treat relations which are not quite functions like they were functions. In particular, we can find the slopes of lines tangent to curves which are not graphs of functions.
Normal Labour/ Stages of Labour/ Mechanism of LabourWasim Ak
Normal labor is also termed spontaneous labor, defined as the natural physiological process through which the fetus, placenta, and membranes are expelled from the uterus through the birth canal at term (37 to 42 weeks
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
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!
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
2. Arithmetic operations
Addition: g (x, y ) = f1 (x, y ) + f2 (x, y )
Subtraction: g (x, y ) = f1 (x, y ) − f2 (x, y )
Multiplication: g (x, y ) = f1 (x, y ) · f2 (x, y )
Division: g (x, y ) = f1 (x, y )/f2 (x, y )
DIP - Lecture 3 2/11
3. Arithmetic operations
Addition: g (x, y ) = f1 (x, y ) + f2 (x, y )
Subtraction: g (x, y ) = f1 (x, y ) − f2 (x, y )
Multiplication: g (x, y ) = f1 (x, y ) · f2 (x, y )
Division: g (x, y ) = f1 (x, y )/f2 (x, y )
DIP - Lecture 3 2/11
4. Arithmetic operations
Addition: g (x, y ) = f1 (x, y ) + f2 (x, y )
Subtraction: g (x, y ) = f1 (x, y ) − f2 (x, y )
Multiplication: g (x, y ) = f1 (x, y ) · f2 (x, y )
Division: g (x, y ) = f1 (x, y )/f2 (x, y )
DIP - Lecture 3 2/11
5. Arithmetic operations
Addition: g (x, y ) = f1 (x, y ) + f2 (x, y )
Subtraction: g (x, y ) = f1 (x, y ) − f2 (x, y )
Multiplication: g (x, y ) = f1 (x, y ) · f2 (x, y )
Division: g (x, y ) = f1 (x, y )/f2 (x, y )
DIP - Lecture 3 2/11
6. Addition
Given that additive noise corrupts the image
f (x, y ) = g (x, y ) + η(x, y ), where η is also assumed to be
uncorrelated at every pixel (x, y ) and has zero mean.
Capture N images
{fi (x, y ) = g (x, y ) + ηi (x, y ), i = 1, . . . , N}.
1 N
Averaging images: g (x, y ) =
˜ N i=1 fi (x, y ).
Unbiased estimator: E {˜ (x, y )} = g (x, y )
g
2 1 2
Variance σg (x,y ) =
˜ N ση(x,y ) .
DIP - Lecture 3 3/11
7. Addition
Given that additive noise corrupts the image
f (x, y ) = g (x, y ) + η(x, y ), where η is also assumed to be
uncorrelated at every pixel (x, y ) and has zero mean.
Capture N images
{fi (x, y ) = g (x, y ) + ηi (x, y ), i = 1, . . . , N}.
1 N
Averaging images: g (x, y ) =
˜ N i=1 fi (x, y ).
Unbiased estimator: E {˜ (x, y )} = g (x, y )
g
2 1 2
Variance σg (x,y ) =
˜ N ση(x,y ) .
DIP - Lecture 3 3/11
8. Addition
Given that additive noise corrupts the image
f (x, y ) = g (x, y ) + η(x, y ), where η is also assumed to be
uncorrelated at every pixel (x, y ) and has zero mean.
Capture N images
{fi (x, y ) = g (x, y ) + ηi (x, y ), i = 1, . . . , N}.
1 N
Averaging images: g (x, y ) =
˜ N i=1 fi (x, y ).
Unbiased estimator: E {˜ (x, y )} = g (x, y )
g
2 1 2
Variance σg (x,y ) =
˜ N ση(x,y ) .
DIP - Lecture 3 3/11
9. Addition
Given that additive noise corrupts the image
f (x, y ) = g (x, y ) + η(x, y ), where η is also assumed to be
uncorrelated at every pixel (x, y ) and has zero mean.
Capture N images
{fi (x, y ) = g (x, y ) + ηi (x, y ), i = 1, . . . , N}.
1 N
Averaging images: g (x, y ) =
˜ N i=1 fi (x, y ).
Unbiased estimator: E {˜ (x, y )} = g (x, y )
g
2 1 2
Variance σg (x,y ) =
˜ N ση(x,y ) .
DIP - Lecture 3 3/11
10. Addition
Given that additive noise corrupts the image
f (x, y ) = g (x, y ) + η(x, y ), where η is also assumed to be
uncorrelated at every pixel (x, y ) and has zero mean.
Capture N images
{fi (x, y ) = g (x, y ) + ηi (x, y ), i = 1, . . . , N}.
1 N
Averaging images: g (x, y ) =
˜ N i=1 fi (x, y ).
Unbiased estimator: E {˜ (x, y )} = g (x, y )
g
2 1 2
Variance σg (x,y ) =
˜ N ση(x,y ) .
DIP - Lecture 3 3/11
12. Subtraction
Can be used to highlight manufacturing defects in an industry.
Figure: Manufactured
Figure: Required PCB Figure: Error
PCB
Reference: C omputer Vision System for Printed Circuit Board
Inspection, Fabiana R. Leta, Flavio F. Feliciano, Flavius P. R.
Martins, ABCM Symposium Series in Mechatronics 2008.
DIP - Lecture 3 5/11
13. Image interpolation (Digital zoom)
Technically, it deals with estimating/creating data at locations
where it is unknown.
Simple schemes:
Pixel replication: If the magnification factor is an integer
multiple simply copy grey values to neighboring unknown
pixels.
DIP - Lecture 3 6/11
14. Image interpolation (Digital zoom)
Technically, it deals with estimating/creating data at locations
where it is unknown.
Simple schemes:
Pixel replication: If the magnification factor is an integer
multiple simply copy grey values to neighboring unknown
pixels.
DIP - Lecture 3 6/11
15. Image interpolation (Digital zoom)
Technically, it deals with estimating/creating data at locations
where it is unknown.
Simple schemes:
Pixel replication: If the magnification factor is an integer
multiple simply copy grey values to neighboring unknown
pixels.
DIP - Lecture 3 6/11
16. Image interpolation (Digital zoom)
Technically, it deals with estimating/creating data at locations
where it is unknown.
Simple schemes:
Pixel replication: If the magnification factor is an integer
multiple simply copy grey values to neighboring unknown
pixels.
DIP - Lecture 3 6/11
18. Nearest neighbor interpolation
Let the unknown pixel be (x , y ). If the nearest neighbor is
(x, y ), then f (x , y ) = f (x, y ).
DIP - Lecture 3 8/11
19. Nearest neighbor interpolation
Let the unknown pixel be (x , y ). If the nearest neighbor is
(x, y ), then f (x , y ) = f (x, y ).
DIP - Lecture 3 8/11
20. Nearest Neighbor Interpolation example
Figure: (top-left) Original: 200 × 200, (top-right) Resampled from 128 × 128, (bottom-left) Resampled from
64 × 64, (bottom-right) Resampled from 32 × 32
DIP - Lecture 3 9/11
21. Bilinear interpolation
Assume the image satisfies the following rule within the 4
nearest neighbors of the point (x , y ):
f (x, y ) = ax + by + cxy + d
Since f is known at 4 points, we can solve a 4 × 4 linear
system of equations to get a, b, c, d. Use the above equation
with these coefficients to compute f (x , y ).
DIP - Lecture 3 10/11
22. Bilinear interpolation
Assume the image satisfies the following rule within the 4
nearest neighbors of the point (x , y ):
f (x, y ) = ax + by + cxy + d
Since f is known at 4 points, we can solve a 4 × 4 linear
system of equations to get a, b, c, d. Use the above equation
with these coefficients to compute f (x , y ).
DIP - Lecture 3 10/11
23. Bilinear interpolation
Assume the image satisfies the following rule within the 4
nearest neighbors of the point (x , y ):
f (x, y ) = ax + by + cxy + d
Since f is known at 4 points, we can solve a 4 × 4 linear
system of equations to get a, b, c, d. Use the above equation
with these coefficients to compute f (x , y ).
DIP - Lecture 3 10/11
