Region Detection

Defining regions of an image

Introduction All pixels belong to a region

Object Part of object Background

Find region Constituent pixels Boundary

Region Detection A set of pixels P An homogeneity predicate H(P) Partition P into regions {R}, such

that

iRi1

n

P

H iR True

H iR jR False

Point based methods – thresholding If

Regions are different brightness or colour

Then Can be differentiated using this

Global thresholds Compute threshold from whole image

Incorrect in some regions

Local thresholds Divide image into regions Compute threshold per region Merge thresholds across region

boundaries

Region Growing All pixels belong to a region Select a pixel Grow the surrounding region

Slow Algorithm If a pixel is

Not assigned to a region Adjacent to region Has colour properties not different to

region’s Then

Add to region Update region properties

Split and Merge Initialise image as a region While region is not homogeneous

Split into quadrants and examine homogeneity

Recursive SplittingSplit(P){ If (!H(P)) {

P subregions 1 … 4;Split (subregion 1);Split (subregion 2);Split (subregion 3);Split (subregion 4);

}}

Recursive Merging If adjacent regions are

Weakly split Weak edge

Similar Similar greyscale/colour properties

Merge them

Edge Following Detection

Finds candidate edge pixels Following

Links candidates to form boundaries

4/8 ConnectivityProblem

Contour Tracking Scan image to find first edge point Track along edge points

Spurs? Endpoints?

Join edge segments

Edge Linking Aggregate collinear chain codes

Colinear?• Sequential least squares• tolerance band

Sequential Least Squares Accumulate best fitting line to segments and

error When error exceeds a threshold, finish

segment

Tolerance Band Accumulate best fitting line to segments If new point lies more than from line, finish

segment

1. Take the first k edges from the list 2. Fit a line segment between the first and last 3. If the normalised maximum error is too large, shorten the sublist to the point of maximum error and return to step 2. 4. If the fit succeeds, compare this and the previous segments, if they are colinear, join them. 5. Advance the window of edges to get another k edges in the sublist and return to step 2.

Hop Along Algorithm

Examples An example would show an edge

detected image There would be a record of the

edge points constituting each edge segment

Scale Based Methods Structures observed depend on

scale of observation

Analysis Processing of an image should be

at a level of detail appropriate to structures being sought Image pyramid Wavelet transform

Image PyramidReducing resolution

Pixels in each layer computed by averaging groups of pixels in layer below. OrUse scale dependent operators – e.g. Marr Hildreth.

Wavelet Transform Transform image data Select coefficients Reverse transform

Watersheds of Gradient Magnitude Compare geographical watersheds

Divide landscape into catchment basins

Edges correspond to watersheds

Algorithm Locate local minima Flood image from these points When two floods meet

Identify a watershed pixel Build a dam Continue flooding

Examplewatersheds

local minima

watershed point

watershed point dam

Representing Regions Constituent pixels Boundary pixels

Region map As an array of region labels

Pixel value = region label

Summary Region detection

Growing Edge following Watersheds

I think there is a world market for maybe five computersThomas J Watson, chairman IBM, 1943