1. Lecture 1: Images and image filtering
CS6670: Computer Vision
Noah Snavely
Lecture 1: Images and image filtering
Hybrid Images, Oliva et al.,

2. Lecture 1: Images and image filtering
CS6670: Computer Vision
Noah Snavely
Lecture 1: Images and image filtering
Hybrid Images, Oliva et al.,

3. Reading
Szeliski, Chapter

4. What is an image? We’ll focus on these in this class
Digital Camera
We’ll focus on these in this class
(More on this process later)
The Eye
Source: A. Efros

5. = What is an image? A grid of intensity values
(common to use one byte per value: 0 = black, 255 = white)
255 20 75 95 96
127
145
175
200 47 74 =

6. What is an image?
We can think of a (grayscale) image as a function, f, from R2 to R:
f (x,y) gives the intensity at position (x,y)
A digital image is a discrete (sampled, quantized) version of this function x y
f (x, y)
snoop
3D view

7. Image transformations
As with any function, we can apply operators to an image
We’ll talk about a special kind of operator, convolution (linear filtering)
g (x,y) = f (x,y) + 20
g (x,y) = f (-x,y)

8. Question: Noise reduction
Given a camera and a still scene, how can you reduce noise?
Answer: take lots of images, average them
Take lots of images and average them!
What’s the next best thing?
Source: S. Seitz

9. Image filtering
Modify the pixels in an image based on some function of a local neighborhood of each pixel 5 1 4 7 3 10
Some function 7
Local image data
Modified image data
Source: L. Zhang

10. Linear filtering
One simple version: linear filtering (cross-correlation, convolution)
Replace each pixel by a linear combination of its neighbors
The prescription for the linear combination is called the “kernel” (or “mask”, “filter”) 6 1 4 8 5 3 10
0.5 1 8
Local image data
kernel
Modified image data
Source: L. Zhang

11. Cross-correlation
Let be the image, be the kernel (of size 2k+1 x 2k+1), and be the output image
This is called a cross-correlation operation:

12. Convolution
Same as cross-correlation, except that the kernel is “flipped” (horizontally and vertically)
Convolution / cross-correlation are commutative and associative
This is called a convolution operation:

13. Convolution
Adapted from F. Durand

14. Mean filtering 90 10 20 30 40 60 90 50 80 * = 1

15. Linear filters: examples* 1 =
Original
Identical image
Source: D. Lowe

16. Linear filters: examples* 1 =
Original
Shifted left
By 1 pixel
Source: D. Lowe

17. Linear filters: examples1 * =
Original
Blur (with a mean filter)
Source: D. Lowe

18. Linear filters: examples
Sharpening filter (accentuates edges) 1 2 - * =
Original
Source: D. Lowe

19. Sharpening
Source: D. Lowe

20. Smoothing with box filter revisited
I always walk through the argument on the left rather carefully; it gives some insight into the
significance of impulse responses or point spread functions.
Source: D. Forsyth

21. Gaussian Kernel
Source: C. Rasmussen

22. Mean vs. Gaussian filtering

23. Gaussian filter
Removes “high-frequency” components from the image (low-pass filter)
Convolution with self is another Gaussian
Convolving two times with Gaussian kernel of width = convolving once with kernel of width * =
Linear vs. quadratic in mask size
Source: K. Grauman

24. Sharpening revisited = = What does blurring take away? – + α
original
smoothed (5x5)
detail = –
Let’s add it back:
original
detail
+ α
sharpened =
Source: S. Lazebnik

25. unit impulse (identity)
Sharpen filter
blurred image
image
unit impulse (identity)
Gaussian
scaled impulse
Laplacian of Gaussian
f + a(f - f * g) = (1+a)f-af*g = f*((1+a)e-g)

26. Sharpen filter
unfiltered
filtered

27. Convolution in the real world
Camera shake = *
Source: Fergus, et al. “Removing Camera Shake from a Single Photograph”, SIGGRAPH 2006
Bokeh: Blur in out-of-focus regions of an image.
Source:

28. Questions? For next time: Next time:
Read Szeliski, Chapters 1,
Next time:
See you on Tuesday, Sept. 8!
Feature and edge detection