Isolating flat parts
Thresholding Based Segmentation
Isolate parts, then characterise later
Assume
Robert B. Fisher
School of Informatics
University of Edinburgh
• Dark part
• Light background
• Reasonably uniform illumination − > distinguishable
parts
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Motivating Example
Given this image, how might we label
pixels as object and background?
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Thresholding Introduction
Key technique: thresholding
Assume pixel values are separable
Part and typical distribution
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Spread: not quite uniform illumination + part color
variations + sensor noise
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Thresholding Algorithm
Thresholding: central technique
Thresholding Example 1
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for row = 1 : height
for col = 1 : width
if value(row,col) < ThreshHigh % inside high bnd
% & value(row,col) > ThreshLow % optional low bnd
output(row,col) = 1;
else
output(row,col) = 0;
end
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THRESHOLD
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Histogram
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Thresholded Image
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Threshold Selection 1
Convolution
Exploit bimodal distribution
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General purpose image (and signal) processing function
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Computed by a weighted sum of image data and a fixed
mask
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But:
• Distributions broad and some overlap − >
misclassified pixels
Linear operator: conv(a*B,C) = a*conv(B,C)
• Shadows dark so might be classified with object
Used in different processes: noise removal, smoothing,
feature detection, differentiation, ...
• Distribution has more than 2 peaks
So: smooth histogram to improve shape for selection
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Convolution in 1D
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X
Output(x) =
Histogram Smoothing for
weight(i) ∗ input(x − i)
Threshold Selection
i=−N
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Histogram Smoothing (in findthresh.m)
Convolve with a Gaussian smoothing window
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Input:
Gaussian Mask and Output:
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filterlen = 50;
% filter
thefilter = gausswin(filterlen,sizeparam); %
thefilter = thefilter/sum(thefilter); % unit
tmp2=conv(thefilter,thehist); % makes longer
% select corresponding portion
offset = floor((filterlen+1)/2);
tmp1=tmp2(offset:len+offset-1);
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Derivative of Gaussian Mask and Output:
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length
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norm
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Threshold Selection 2
Convolved Histogram Example
Assume 2 big peaks, brighter background is higher:
1. Find biggest peak (background)
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2. Find next biggest peak in darker direction
3. Find lowest point in trough between peaks
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FILTER SHAPE
SMOOTHED HISTOGRAM
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Peak Pick Code
Omit special cases for ends of array and closing ‘end’s.
peak = find(tmp1 == max(tmp1));
% find largest peak
% find highest peak to left
xmaxl = -1;
for i = 2 : peak-1
if tmp1(i-1) < tmp1(i) & tmp1(i) >= tmp1(i+1) ...
& tmp1(i)>xmaxl
xmaxl = tmp1(i);
pkl = i;
xminl = max(tmp1)+1;
for i = pkl+1 : peak-1
if tmp1(i-1) > tmp1(i) & tmp1(i) <= tmp1(i+1) ...
& tmp1(i)<xminl
xminl = tmp1(i);
thresh = i;
% find deepest valley between peaks
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Lecture Overview
1. Thresholding to differentiate object
from a constant and simple background
(not just white backgrounds: see also
bluescreening or chroma keying)
2. 1D Convolution
3. Histogram smoothing & threshold
selection
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