5 - Introduction to local neighborhood operations - Duration 06:46

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Do curso por Duke University

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

422 classificações

Duke University

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

422 classificações

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.

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Spatial processing

Some of the most basic tools in image processing, like median filtering and histogram equalization, are still among the most powerful. We will describe these and provide a modern interpretation of these basic tools. Students will then become familiar with simple and still popular approaches. We will also include non-local means, a more modern technique that still uses classical tools.

1 - Introduction to image enhancement - Duration 19:11 - Optional break at 08:3319:11

2 - Demo - Enhancement & Histogram modification - Duration 03:533:53

3 - Histogram equalization - Duration 19:56 - Optional breaks at 04:40 and 11:3019:57

4 - Histogram matching - Duration 08:318:31

5 - Introduction to local neighborhood operations - Duration 06:466:46

6 - Mathematical properties of averaging - Duration 11:0011:00

7 - Non-Local means - Duration 07:277:27

8 - IPOL Demo - Non-Local means - Duration 03:383:38

9 - Median filter - Duration 07:207:20

10 - Demo - Median filter - Duration 01:311:32

11 - Derivatives, Laplacian & Unsharp masking - Duration 14:24 - Optional breaks at 05:21 and 11:3314:24

12 - Demo - Unsharp masking - Duration 03:103:11

13 - Gradients of scalar and vector images - Duration 05:575:57

14 - Concluding remarks - Duration 01:121:12

Conheça os instrutores

Guillermo Sapiro
Professor
Electrical and Computer Engineering

When we were talking about histogram modification, either equalization or

matching, we were replacing the grey value of a pixel only based on its actual

grey value. And we weren't looking at the surrounding

area of the image. What we're going to do next is we're

going to do spatial operations. So, we're going to basically replace the

pixel value at the given pixel depending on what's happening around the pixel.

So, there's going to be influence of the neighborhood.

So if we have a complete image, we're going to look at the pixel and we see

here magnifications of that, or let us observe here.

We're going to decide what to replace the pixel value here with depending on what's

happening around it. So, it's not going to be any more just

okay, I decide how am I going to change depending on my own pixel value. We're

going to say how these pixel's going to change depending on neighborhood pixels.

And the simplest of those operations is basically averaging.

So, we are going to replace the pixel here by the average of let's say, a three

by three neighborhood around it. Of course, we have to normalize.

If we are averaging nine pixels, we have to divide by nine.

We can also do weighted averages, so we can average in a sense that, yourself,

the pixel its self, waits four.

And those that are in four neighborhood, remember we talked about four and eight

neighborhood structures, those are, are in four will count double and those that

are in diagonal, we just count single. And then, we basically align sixteen

things, 1 + 2 is 3, + 1 is 4, + 2 is 6, and so on.

So, we will have to normalize by sixteen. So this is just an average, this is a

weighted average. Let's see their facts of this in a real

image. What we have here is an image, and this

is a good image because it has structures of different sizes.

And what we are going to see for each one of these other images is that local

average, and we take neighborhoods of different sizes.

We go from three to thirteen. So this is 3, 5, 9, 15, and 35.

So we go from three to 35. The, the larger the neighborhood, the

more pixels we are averaging. And we see the effect of that.

Here when we average by three we don't see much of a change, there is some

change here within the defined structure, but let's just jump to the 35.

So this is a window of 35, a neighborhood of 35 and we see that a lot of things get

blurred and I'm going to explain in a second why, give you the intuition behind

that. So a lot of the structure gets blurred.

If we are using a neighborhood of only 15, less things get blurred.

We see that here, for example, this is much easier to distinguish the bars here

than it is here. And, that depends on the distance between

the objects. So, why are we getting blur?

Because here, for example, this point. Imagine that we have a 35 by 35 window

around it. So, we end up averaging the block of the

pixel with the grey around it, and then it gets a bit brighter.

So this was very dark, black. This is bright, and if we're averaging

pixels around it, the average basically goes up for this pixel.

And when we're averaging here, because some of the pixels in the neighbor, in

the neighborhood are dark, the average here would basically go down.

And then, we're clarifying this blurring effect.

Let me just illustrate with that one dimensional function.

If I'm basically averaging this with this, and this, clearly the pixel value

of this goes down because of the effect of this.

So, this will be replaced by something around here.

This one, if I'm averaging with this one and maybe

with a pixel here, then it goes slightly up.

And then, this perfectly sharp profile becomes a bit of a smooth profile because

I'm averaging things on the side. We're going to see later towards the

second part of this course, how to basically average without rating these

blurring effect. But this is just to illustrate a very

simple operation which is local averaging,

and how neighbors, and basically the size of the neighbors affect what's happening

on the pixel. Now, you might wonder, is this operation

important? Yes, it is.

Although, it's going to blur. The basic idea is that we are not going

to average with a window size of 35. We need to design window sizes that are

appropriate for the particular problem. For example, if we have this image and we

want to get rid of some of the very small objects in the image.

We, maybe they're noise or maybe they're basically stars or particles that we

don't care about them too much. Then, we can do a local filter of this

image. In this case, it was used a 15 by 15

image. We're blurring the image but we're

somehow getting rid of these small particles.

So, a small particle here will be basically average with a lot of black

pixels around it. And then, it's value will go so much

down, so much close to zero then when I threshold I get basically only the

regions of interest, the larger and the very bright regions.

So, we first blur and then we threshold. And we got rid of all these which we

consider noise and we only get the really important objects in scene.

So this very simple operation is very powerful for tasks like this.

More interesting, this very simple averaging operation has really

interesting mathematical properties that I'm going to explain next.

And those are important because they're going to help us to develop other type of

averaging operations that, for example, do not blur edges.

And we're going to do that explanation of the mathematical properties and

relationships that this simple averaging has with other structures in the next

video. Thank you.

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