Programming Assignment 3

CS 302 - Data Structures

Dr. George Bebis

Goal: Represent image regions using lists and perform galaxy classification

• Builds on previous two programming assignments.

(1) Represent image regions in a list for easier processing.

(2) Compute region features.

Project Objectives

• Improve your skills with manipulating unsorted/sorted lists

• Improve your skills with using templates

• Learn about feature extraction and classification.

Region Features

• Image regions can be characterized using various features: – Geometric

– Photometric

Geometric Features

• The geometry of a region can be characterized using:– Size

– Position

– Orientation

– Shape (e.g., circular,

elliptical)

• Many of these features could be computed using a family of functions called moments.

Moments

• The moments of order (p,q) of a region R are:

Rji

qpqp jiM

,,

(i,j) є R

Note: moments have their roots in probability theory and are used to characterize probability density functions (pdfs).

- Mean (i.e., first order moment) - Variance (i.e., second order central moments).

Region Area (i.e., size)

• The area of a region is defined by the number of pixels in the region (i.e., size).

• Can be computed using zero order moments (i.e., p=q=0) :

0,0M (i,j) є R

Rji

qpqp jiM

,,

Region Center (i.e., centroid)

• The centroid of a region (i.e., center coordinates) can be computed using first order moments (p=1 or q=1):

0,0

0,1

M

Mx

0,0

1,0

M

My

Rji

qpqp jiM

,,

Central Moments

• To make region descriptors invariant with respect to location, moments can be calculated with respect to the centroid of the region (i.e., central moments):

Rji

qpqp yjxi

,, )()(

Rji

qpqp jiM

,,

Principal Axes

• The principal axes of a region can be used to characterize the

shape and orientation of a region.

Amin and Amax

Principal Axes (cont’d)

• The principal axes, Amin and Amax, of a region can be computed using the principal moments λmin, λmax:

• The principal moments involve first and second order central moments:

21,10,22,0

22,0

20,22,00,2max 42

2

1)(

2

1

21,10,22,0

22,0

20,22,00,2min 42

2

1)(

2

1

0,0maxmax MA 0,0minmin MA

Region Orientation

• The direction of the largest principal axis can be used to specify the orientation of a region:

)(tan1,1

0,2max1

Region Eccentricity (i.e., Elongatedness)

• A useful measure of a region’s circularity is its eccentricity (i.e., elongatedness).

• Can be easily computed using the ratio between the principal axes:

max max

min min

Aeccentricity

A

Example

Photometric Properties

• Measures characterizing region intensity, for example:– Mean and median of the gray-levels.

– Minimum and maximum intensity values.

Object Classification - Example

• Objects could be classified in different categories using various region properties, for example:

– Large/Small/Medium

– Elongated/Circular

Represent regions in a sorted list: listOfRegions

Geometric properties

Intensity properties

List of pixels

x,y

x,y

x,y

Geometric properties

Intensity properties

List of pixels

x,y

x,y

x,y

Geometric properties

Intensity properties

List of pixels

x,y

x,y

x,y

…

listOfRegion:sorted with respectto “size”

listOfPixels:unsorted

• Nodes store info about each region (i.e., “RegionType”)• Sub-lists store the coordinates of pixels in each region - i.e., “PixelType” -- unsorted

Extra credit: template lists

template<class ItemType>

struct NodeType {

ItemType info;

NodeType<ItemType>* next;

};

listOfRegions: ItemTypeshould be “RegionType”

listOfPixels: ItemType should be “PixelType”

Geometric properties

Intensity properties

List of pixels

x,y

x,y

x,y

you needto definethem!

This is object

composition!

Extend computeComponents

int computeComponents(inputImage, outputImage, listOfRegions)

• computeComponents should return the following info:– the labeled image (same as before)

– the number of regions (same as before)

– a list of regions (new)

• Modify BFS or DFS– Use one of them in this assignment

int computeComponents(inputImage, outputImage, listOfRegions)

outputImage --> whiteconnComp=0;

for (i=0; i<N; i++) for(j=0; j<M; j++) if(inputImage[i][j] == 255 && outputImage[i][j]==255) { ++connComp; label = connComp; findComponentDFS(inputImage, outputImage, i, j, label, regionregion); // or findComponentBFS(inputImage, outputImage, i, j, label, regionregion); INSERT region into “listOfRegions”INSERT region into “listOfRegions” }return connComp;

(client function)

type“RegionType”

findComponentDFS(inputImage, outputImage, i, j, label, region)

Stack.MakeEmpty();

Stack.Push((i,j)); // initialize stackwhile(!Stack.IsEmpty()) { Stack.Pop((pi,pj)); INSERT (pi,pj) into “listOfPixels” of “region”INSERT (pi,pj) into “listOfPixels” of “region” outputImage[pi][pj] = label * 10; for each neighbor (ni,nj) of (pi,pj) // push neighbors if(inputImage[ni][nj] == 255 && outputImage[ni][nj] == 255) { outputImage[ni][nj] = -1; // mark this pixel Stack.Push((ni,nj)); }}COMPUTE geometric and photometric propertiesCOMPUTE geometric and photometric propertiesand populate “region” and populate “region”

type RegionType

Geometric properties

Intensity properties

List of pixels

x,y

x,y

x,y

void deleteSmallComponents(listOfRegions, threshold)

• Step through the list nodes and delete all the regions whose size is less than a user-specified threshold (e.g., 20-30 pixels).

(client function)

Hint: You would not have to visit all the nodes since the list

will be sorted from the smallest to the largest region!

“deleteSmallComponents”will be useful for debuggingyour program (i.e., keep largeregions only)

Classify regions• Add a new option in the driver called “classify regions”

– Given an input image (i.e., from Image Gallery 2Image Gallery 2), your program should extract and represent the regions as described.

– Prints a summary of the regions found and their properties (e.g., position, size, orientation, eccentricity, mean intensity etc.)

– Prints min/max values of size, eccentricity, and mean intensity.

Classify regions (cont’d)

• Then, your program should print the following sub-menu:

(1) display regions with size between values A and B

(2) display regions with orientation between values A and B

(3) display regions with eccentricity between A and B

(4) display regions with mean intensity between A and B

(5) back to the main menu

Display your results• Traverse listOfRegionslistOfRegions

• Find the nodes satisfying the constraint chosen by the user– For each such node, traverse its listOfPixelslistOfPixels

– For each pixel, copy its original value in a new image

• Display the resulted image! original image

output image

Geometric properties

Intensity properties

List of pixels

x,y

x,y

x,y

Geometric properties

Intensity properties

List of pixels

x,y

x,y

x,y

Geometric properties

Intensity properties

List of pixels

x,y

x,y

x,y

…

Example: