9 - Mumford-Shah - Duration 05:50

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Del curso dictado por Duke University

Image and Video Processing: From Mars to Hollywood with a Stop at the Hospital

371 calificaciones

Duke University

Image and Video Processing: From Mars to Hollywood with a Stop at the Hospital

371 calificaciones

In this course, you will learn the science behind how digital images and video are made, altered, stored, and used. We will look at the vast world of digital imaging, from how computers and digital cameras form images to how digital special effects are used in Hollywood movies to how the Mars Rover was able to send photographs across millions of miles of space. The course starts by looking at how the human visual system works and then teaches you about the engineering, mathematics, and computer science that makes digital images work. You will learn the basic algorithms used for adjusting images, explore JPEG and MPEG standards for encoding and compressing video images, and go on to learn about image segmentation, noise removal and filtering. Finally, we will end with image processing techniques used in medicine. This course consists of 7 basic modules and 2 bonus (non-graded) modules. There are optional MATLAB exercises; learners will have access to MATLAB Online for the course duration. Each module is independent, so you can follow your interests.

De la lección

Image segmentation

Not all parts of the image are the same, and students will learn the basic techniques to partition an image, from simple threshold to more advanced graph cuts and active contours. This is the first unit where student will learn about image analysis and image interpretation, and will learn why this is important, e.g., in medical imaging and object recognition.

1 - Introduction to Segmentation - Duration 04:174:17

2 - On Edges and Regions - Duration 05:175:17

3 - Hough Transform with Matlab Demo - Duration 20:5920:59

4 - Line Segment Detector with Demo - Duration 03:203:20

5 - Otsu's Segmentation with Demo - Duration 14:2514:25

6 - Congratulations - Duration 00:170:17

7 - Interactive Image Segmentation - Duration 21:1321:13

8 - Graph Cuts and Ms Office - Duration 09:349:34

9 - Mumford-Shah - Duration 05:505:50

10 - Active Contours - Introduction with ipol.im and Photoshop Demos - Duration 05:585:58

11 - Behind the Scenes of Adobe's Roto Brush - Duration 31:29 - Optional breaks at 20:30 and 27:2631:29

12 - End of the Week - Duration 00:210:21

Conoce a los instructores

Guillermo Sapiro
Professor
Electrical and Computer Engineering

Hello, and welcome back. I want to discuss now the Mumford-Shah

Image Segmentation technique, and I'm going to do that with one example.

Let's just look at this image. We talk that image segmentation means

labeling the image. We want to label every segment that has

some coherence in it with a different name, with a different number.

One way of doing that is, of course, basically, painting that segment with a

uniform, or a very smooth grey value. And that's the type of stuff that the

Mumford-Shah algorithm and technique tries to do.

Let's just discuss that. Here, we have an original image.

Don't pay attention to these two for the moment.

It's going to be very clear in just a few seconds.

And this is the result of one implementation of Mumford-Shah image

segmentation. So, very rich gray values become just a

few smooth segments. Looks like almost like quantization when

we talk about image compression. So, the first part is that we want to

approximate the original image by just a few segments that are either constant or

very smooth. Of course, we want an approximation.

So, one of the terms that this Mumford-Shah needs to include is a

penalty from deviating too much from the original image.

Of course, piece wise smooth, or piece wise constant, I could make this whole

image wide. So, that's one very smooth segment.

But it's very far, if I do that, it would be very far from the original image.

So, one of the things is we have to somehow penalize for the difference

between these two images. For example, the mean square error.

We already talk about it very early on in this class.

So, one penalty is the mean square error. We want to get the piece wise smooth

version of this image, but not very far from it.

Now, you might wonder, okay, if you're going to penalize for the mean

square error, why not to keep the image itself?

That's very clever, but we don't achieve any segmentation.

So, how do I know I don't achieve any segmentation?

Because I'm going to add a term that penalizes for having too many boundaries

in the segmented image. So, these are the regular edges of this

image. Very strong edges.

These are boundaries of the segments that we have here.

I don't want to have too many. I don't want to have all these.

I'm going to penalize for the number of edges for how many, how much do I pay for

having boundaries. So that would be another term.

I'm going to basically, on one hand, I want to penalize for very large

differences, and on the other hand, I'm going to penalize for edges.

So, if you have too much edges, you are going to pay a price.

Bec, so, if I keep the image as it is, I have no error here but I have lot of

edges. Basically, every pixel becomes a segment,

so I'm paying a very large penalty for edges.

If I have a flat image, I don't pay any penalty for edges, but I pay a very high

penalty for error. And then, I have to do a compromise

between these two and that's what Mumford-Shah basic concept is, to write

formulations that compromise between a representation of the image that is too

far from the original image. We want to simplify representation not

too far from the original image, and we also don't want to pay a high price and

get too many segments. Now, there are many ways of doing this.

There's some beautiful mathematical theory behind different formulations that

do this compromise. Some theory relates even to compression.

You have to compress this image and this edges, and then you try to optimize for

that, yours and my, need to compare for the

error. And some very beautiful techniques with, in the framework of what's called

variation and formulations, and, energy formulations really, a lot of very

beautiful mathematical theory, which actually relates to the mathematical

theory that we're going to be discussing next week when we talk about geometric

differential equations and geometric varation of problems.

But, here's the concept.

And very often in image processing, you have a concept and the multiple ways

of implementing that concept. And I want to make sure that you

basically learn during this class, the concept behind Mumford-Shah.

I should also mention to you that this concept of approximation and penalty for

too many edges applies also beyond image segmentation.

And people have extended the framework of Mumford-Shah type of formulations to

image registration and many, many other image and video processing problems.

Thank you very much. See you in the next video.

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