image processing - bilkent universityduygulu/courses/cs554/notes... · binary image processing is a...
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Image Processing
CS 554 – Computer VisionPinar Duygulu
Bilkent University
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TodayImage Formation
Point and Blob Processing
Binary Image Processing
Readings:– Gonzalez & Woods, Ch. 3
Slides are adapted from Alyosha Efros andShapiro & Stockman
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Imaging Process
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Image Formation
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Sampling and Quantization
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Sampling and Quantization
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What is an image?We can think of an image as a function, f, from R2 to R:
• f( x, y ) gives the intensity at position ( x, y ) – Realistically, we expect the image only to be defined over a
rectangle, with a finite range:– f: [a,b]x[c,d] [0,1]
A color image is just three functions pasted together. We can write this as a “vector-valued” function:
f(x,y) = [r(x,y) g(x,y) b(x,y)]
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Images as functions
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What is a digital image?We usually operate on digital (discrete) images:
– Sample the 2D space on a regular grid– Quantize each sample (round to nearest integer)
If our samples are ∆ apart, we can write this as:f[i ,j] = Quantize{ f(i ∆, j ∆) }
The image can now be represented as a matrix of integer values
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Point ProcessingAn image processing operation typically defines a new
image g in terms of an existing image f.The simplest kind of range transformations are these
independent of position x,y:g = t(f)
This is called point processing.
Important: every pixel for himself – spatial information completely lost!
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Basic Point Processing
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Negative
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Image Enhancement
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Contrast Streching
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Image Histograms
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Neighborhood Processing (filtering)Q: What happens if I reshuffle all pixels within the
image?
A: It’s histogram won’t change. No point processing will be affected…
Need spatial information to capture this.
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Goal: Extract “Blobs”
What are “blobs”?– Regions of an image that are somehow coherent
Why?– Object extraction, object removal, compositing, etc.– …but are “blobs” objects?– No, not in general
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Blob’s coherenceSimplest way to define blob coherence is as similarity in brightness or color:
The tools become blobs The house, grass, and sky make different blobs
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The meaning of a blobOther interpretations of blobs are possible,
depending on how you define the input image:– Image can be a response of a particular detector
• Color Detector• Face detector• Motion Detector• Edge Detector
gx2+gy2
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Why is this useful?
AIBO RoboSoccer(VelosoLab)
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Ideal Segmentation
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Result of Segmentation
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ThresholdingBasic segmentation operation:
mask(x,y) = 1 if im(x,y) > Tmask(x,y) = 0 if im(x,y) < T
T is threshold– User-defined– Or automatic
Same ashistogram partitioning:
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As Edge Detection
gx2+gy2 gx2+gy2 > T
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Sometimes works well…
What are potentialProblems?
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…but more often not
Adaptive thresholding
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Region growing
– Start with initial set of pixels K– Add to K any neighbors, if they are within similarity threshold– Repeat until nothing changes
Is this same as global threshold? What can go wrong?
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Color-Based Blob SegmentationAutomatic Histogram Partitioning
– Given image with N colors, choose K– Each of the K colors defines a region
• not necessarily contiguous– Performed by computing color histogram, looking for modes
– This is what happens when you downsample image color range, for instance in Photoshop
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Finding modes in a histogram
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Mean-Shift (Comaniciu & Meer)
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Mean-Shift (Comaniciu & Meer)
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Issues:Although often useful, all these approaches work
only some of the time, and are considered rather “hacky”.
Can’t even handle our tiger:
Problem is that blobs != objects!
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Binary Image Processing
Binary images are handy in many cases (sprite extraction, compositing, etc).
Binary image processing is a well-studied field, based on set theory, called Mathematical Morphology
consists of a set of image analysis operations that are used to produce or process binary images, usually images of 0’s and 1’s.
0 represents the background 1 represents the foreground
000100100010000001111000100000010010001000
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Application Areas
Document Analysis
Industrial Inspection
Medical Imaging
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Operations
Separate objects from background and from one another
Aggregate pixels for each object
Compute features for each object
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Example red blood cell image• Many blood cells are
separate objects• Many touch to each
other – bad!• Salt and pepper noise
from thresholding• How usable is this
data?
• 63 separate objects detected• Single cells have area about 50• Noise spots• Gobs of cells
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• More uniform objects• More uniform background• Objects actually separated
More controlled images
• 15 objects detected• Location known• Area known• 3 distinct clusters of 5
values of area; 85, 145, 293
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Thresholding
Binary images can be obtained from gray level images by thresholding
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Assumptions for thresholding
• Object region of interest has intensity distribution different from background
• Region pixel likely to be identified by intensity alone: – intensity > a – intensity < b – a < intensity < b
• Works OK with flat-shaded scenes or engineered scenes.
• Does not work well with natural scenes.
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Use of histograms for threshold selection
• Cherry image with 3 regions
• Background is black• Healthy cherry is
bright• Bruise is medium
dark• Histogram shows two
cherry regions (black background has been removed)
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Histogram-directed thresholding
How can we use a histogram to separate animage into 2 (or several) different regions?
Is there a single clear threshold? 2? 3?
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Choosing Threshold
Detect peaks and valleys
Two distinct modes Overlapped modes
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Choosing threshold
• Find the deepest valley between two modes of bimodal histogram
• Fit two or more Gaussian curves to the histogram• Dynamic thresholding
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Cleaning up thresholding results
• Delete object pixels on boundary to better separate parts.
• Fill small holes• Delete tiny objects• (last 2 are “salt-and-
pepper” noise)
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Mathematical Morphology
Binary mathematical morphology consists of twobasic operations
dilation and erosion
and several composite relations
closing and opening conditional dilation . . .
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Dilation
Dilation expands the connected sets of 1s of a binary image.
It can be used for
1. growing features
2. filling holes and gaps
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Erosion
Erosion shrinks the connected sets of 1s of a binary image.
It can be used for
1. shrinking features
2. Removing bridges, branches and small protrusions
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Structuring Elements
A structuring element is a shape mask used inthe basic morphological operations.
They can be any shape and size that isdigitally representable, and each has an origin.
boxhexagon disk something
box(length,width) disk(diameter)
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Dilation with structuring elements
The arguments to dilation and erosion are
1. a binary image B2. a structuring element S
dilate(B,S) takes binary image B, places the originof structuring element S over each 1-pixel, and ORsthe structuring element S into the output image atthe corresponding position.
0 0 0 00 1 1 00 0 0 0
11 1
0 1 1 00 1 1 10 0 0 0
originBS
dilate
B ⊕ S
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Dilation
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Dilation
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Erosion with structuring elements
erode(B,S) takes a binary image B, places the origin of structuring element S over every pixel position, andORs a binary 1 into that position of the output image only ifevery position of S (with a 1) covers a 1 in B.
0 0 1 1 00 0 1 1 00 0 1 1 01 1 1 1 1
111
0 0 0 0 00 0 1 1 00 0 1 1 00 0 0 0 0
B S
origin
erode
B S
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Erosion
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Erosion
Original image Eroded image
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Erosion
Eroded once Eroded twice
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Opening and Closing
• Closing is the compound operation of dilation followed by erosion (with the same structuring element)
• Opening is the compound operation of erosion followed by dilation (with the same structuring element)
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Opening and Closing
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Example 1
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Example 2: try
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 00 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 00 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 00 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 00 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 00 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 00 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 01 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 1 1 1 01 1 1 1 11 1 1 1 11 1 1 1 10 1 1 1 0
B
S
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OPENING: The original image eroded twice and dilated twice (opened). Most noise is removed
Opening and Closing
CLOSING: The original image dilated and then eroded. Most holes are filled.
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Opening and Closing
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Boundary Extraction
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Boundary Extraction
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Region Filling
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Connected Component Labeling
Once you have a binary image, you can identify and then analyze each connected set of pixels.
The connected components operation takes in a binary image and produces a labeled image in which each pixel has the integer label of either the background (0) or a component.
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Extraction of Connected Components
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Labeling shown as pseudo-color
connectedcomponentsof 1’s fromthresholdedimage
connectedcomponentsof clusterlabels
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Connectivity
4-neighborhood 8-neighborhood
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Recursive labeling
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First Step : Run Length EncodingSegment each image row into groups of similar
pixels called runs– Runs store a start and end point for each contiguous
row of color
Original image RLE image
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Second Step : Merging Regions
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Final ResultsRuns are merged into multi-row regionsImage is now described as contiguous regions
instead of just pixels
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Blob PropertiesNow that we have nice, clean blobs, what can we do
with them?Compute Statistics:
– Area– Perimeter– Aspect ratio– Center of mass– best-fitting ellipse– Average color– Etc.
All this can be used to classify blobs and decide if they hold the objects we are interested in.
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Area an Centroid
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Perimeter pixels and length
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Circularity or elongation
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Circularity as variance of radius
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Bounding box
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Second moments
These are invariant to object location in the image.
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Axis of least inertiaAn axis which we could spin the pixels with least energy inputThe axis about which the pixels have least second moment
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Region Adjacency Graph
A region adjacency graph (RAG) is a graph in whicheach node represents a region of the image and an edgeconnects two nodes if the regions are adjacent.