1. Image Abstract Data Types, and Operations on Images
CSE 373, Copyright S. Tanimoto, Image Abstract Data Types -

2. CSE 373, Copyright S. Tanimoto, 2002 Image Abstract Data Types -
Motivation
Image data makes up more than 75% of Internet data traffic.
Images are widely used in modern computing systems and applications.
A wide variety of algorithms work with image data.
CSE 373, Copyright S. Tanimoto, Image Abstract Data Types -

3. Mathematical Description
An image is a function mapping pixel positions to values.
Its domain is a set of the form D = {0, 1, ..., m-1}  {0, 1, ..., n-1}
Its range is a set of possible "pixel values." Different kinds of images have different ranges.
A binary image has range {0, 1}.
A monochrome image typically has range {0, 1, ..., 255}.
An RGB typically has range {0, 1, ..., 255}3.
CSE 373, Copyright S. Tanimoto, Image Abstract Data Types -

4. An Image Abstract Data Type
Data: Binary Images
I: {0, 1, ..., m-1}  {0, 1, ..., n-1}  {0, 1}
Methods:
PUTPIXEL: IMAGES  D  {0, 1}  IMAGES
GETPIXEL: IMAGES  D  {0, 1}
CSE 373, Copyright S. Tanimoto, Image Abstract Data Types -

5. Another Image Abstract Data Type
Data: Monochrome Images
I: {0, 1, ..., m-1}  {0, 1, ..., n-1}  {0, 1,...,255}
Methods:
PUTPIXEL: IMAGES  D  {0, 1, ..., 255}  IMAGES
GETPIXEL: IMAGES  D  {0, 1, ..., 255}
CSE 373, Copyright S. Tanimoto, Image Abstract Data Types -

6. Images: Array Implementation7 3 3 3 3 3 3 3 1 1 9 9 5 6 9 9
CSE 373, Copyright S. Tanimoto, Image Abstract Data Types -

7. Images: Quadtree Implementation7 3 3 3 3 3 3 3 1 1 9 9 3 9 5 6 9 9
Recursively quarter each image region whenever the pixel values are heterogeneous. Create a node for each region. 7 3 3 3 1 1 5 6
CSE 373, Copyright S. Tanimoto, Image Abstract Data Types -

8. Images: Run-Length Coding7 3 3 3
1x7;7x3;2x1;2x9;1x5;1x6;2x9 3 3 3 3 1 1 9 9 5 6 9 9
Using row-major (raster-scan) ordering, write out the number of pixels in each run followed by an "x" and the value of the pixels in the run. Separate runs with ";".
CSE 373, Copyright S. Tanimoto, Image Abstract Data Types -

9. CSE 373, Copyright S. Tanimoto, 2002 Image Abstract Data Types -
Median Filtering
"Salt-and-pepper" noise is present in many video images. It not only looks bad, but it can lead recognition algorithms astray.
One method for eliminating salt-and-pepper noise is to replace each pixel value by the median of the 9 values in its 3 by 3 neighborhood. 2 2 4 2 9 5 1 2 4 2
CSE 373, Copyright S. Tanimoto, Image Abstract Data Types -

10. Connected Components Analysis7 3 3 3 1 1 1 3 3 3 3 1 1 1 1 1 1 9 9 2 2 3 3 5 6 9 9 4 5 3 3
Two common method for computing this are: (1) stack-based depth-first search, and (2) merging components using the UNION-FIND technique.
CSE 373, Copyright S. Tanimoto, Image Abstract Data Types -

11. CSE 373, Copyright S. Tanimoto, 2002 Image Abstract Data Types -
Thresholding 7 3 3 3 1
 4 3 3 3 3 1 1 9 9 1 1 5 6 9 9 1 1 1 1
Any pixel with value greater than or equal to the threshold gets mapped to 1. Otherwise it's mapped to 0.
CSE 373, Copyright S. Tanimoto, Image Abstract Data Types -

12. Image Compression using Huffman Coding
Frequency
table:
1: 2
3: 7
5: 1
6: 1
7: 1
9: 4
Sorted
table:
5: 1
6: 1
7: 1
1: 2
9: 4
3: 7
Huffman Tree: 7 3 3 3 16 3 3 3 3 9 7 1 1 9 9 3 5 6 9 9 5 4
Code
3: 1
9: 01
1: 001
5: 00000
6: 00001
7: 0001 9 3 2 1
To build the Huffman tree, keep taking the two smallest-weight subtrees and merge them. To code a pixel, trace the path from the root to that leaf, writing a 0 whenever going left and 1 whenever going right. 2 1 7 1 1 6 5
CSE 373, Copyright S. Tanimoto, Image Abstract Data Types -

13. Convolution Filtering
Kernel K[1,1] 2 2 4 -1 1 2 9 5 -2 2 1 2 4 -1 1
I'[i,j] =  I[i+r,j+s] K[1+r,1+s]
Image I[i,j]
r, s = -1, 1
CSE 373, Copyright S. Tanimoto, Image Abstract Data Types -