Region description

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Region description

• Information that lets you recognise a region.

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Introduction

• Region detection isolates regions that differ
  from neighbours
• Description identifies property values
• Labelling identifies regions

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Contents

• Features derived from binary images
• Structure
• Region (CCA)
• Shape
• Texture
• Surface shape

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Features derived from binary images

• Connected component analysis
• Perimeter
• Area

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Connected Component Analysis

• To identify groups of connected pixels
• To label separate regions

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Algorithm

• First pass
• If zero neighbours have a label
• Pixel receives the next free label
• If one or more neighbours have same label
• Pixel receives same label
• If two or more neighbours have different labels
• Pixel receives one label, equivalence is
  recorded
• Second pass
• Relabel all equivalent labels

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Borders

• Straight lines
• Chain codes
• Polylines
• Curved lines
• Splines
• Circles
• Phi-S
• Snakes

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Chain Codes
Trace the object outline - follow pixels on
boundary Code directions of movement Description
is position independent, orientation
dependent Can use differential chain codes
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Perimeter From Chain Code
Even codes have length 1 Odd codes have length
?2 Perimeter length even ?2 odd
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Area From Chain Code
0
1
2
3
4
5
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h
0
h1/2
h
0
-h-1/2
-h
-h1/2
h-1/2
h is measured from an arbitrary datum, e.g. y
co-ordinate of start of codes.
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Crack Codes

• These follow pixel boundaries
• Not pixel centres
• Same representation of displacement
• Longer coding
• More accurate

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• Demo

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Polyline Representation

• Represent the line by a set of joined line
  segments
• Polyline and original endpoints coincide
• Segments interpolate edge points
• Computed by curve splitting or segment merging
• Decomposing initial curve
• Combining curve segments

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Polyline Splitting(cf Hopalong last week)

• For each curve segment
• D maximum distance of segment to line between
  endpoints
• If D gt threshold
• Insert a vertex

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Segment Merging

• May be necessary between endpoints of adjacent
  segments
• Use edge following techniques

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Curved Line Sections

• Polyline representation is suitable for linear
  sections
• Curved sections are inefficiently represented
• Alternatives
• Splines
• Circles

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B-Splines

• A curve represented by control points
• Endpoints fixed by two control points
• Shape controlled by two control points

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• If control points can be found
• Curve is compactly represented

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Fourier Descriptors

• Represent co-ordinates of boundary points as
  complex numbers
• They can be Fourier transformed
• Coefficients of transform are the Fourier
  descriptors
• Retain more or fewer according to desired accuracy

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Example
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Phi-S Curves

• (?i, si)
• characteristic of the objects shape
• independent of location
• dependent on orientation

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Snakes, Active/Dynamic Contours

• Borders follow outline of object
• Outline obscured?
• Snake provides a solution

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Algorithm

• Snake computes smooth, continuous border
• Minimises
• Length of border
• Curvature of border
• Against an image property
• Gradient?

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Minimisation

• Initialise snake
• Integrate energy along it
• Iteratively move snake to global energy minimum

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Texture

• Two definitions
• A pseudoregular arrangement of a primitive
  element
• A pseudorandom distribution of brightness values

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Examples
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Classification

• A useful property for identifying surfaces
• Aerial photographs
• Medical imagery

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Structural Texture Representations

• Require
• Texture primitive - texel
• Placement rule
• Ideal for regular - man-made - textures

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Fourier Descriptors

• Placement rule ? periodicity
• Can use
• Autocorrelation
• Fourier transform
• To recognise it

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Fourier Descriptor

• Compute modulus of transform
• Energy in different regions is characteristic of
  texture

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Markov Random Field Representations

• Each pixel value a combination of neighbours plus
  noise
• Find coefficients of model
• Characterise texture
• Least squares minimisation

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Statistical Descriptions

• Better suited to pseudorandom, natural textures
• First Order statistics
• Second order statistics

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First Order Statistics

• Statistical descriptions of grey level
  distribution
• Mean grey value
• Deviation of grey values
• Coefficient of variation
• etc.
• Can give useful results
• Generally too sensitive to factors other than
  identity of surface

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Second Order Statistics

• Measures involving multiple pixels
• Joint difference histogram
• Histogram of differences between adjacent pixels
• Co-Occurrence matrices
• Measure frequency of specific pairs of grey values

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Co-Occurrence Matrices

• Define a relative separation vector
• e.g. 3 pixels across, 2 up
• Use each pair of pixels separated by the vector
  as matrix indices
• Increment this matrix element
• Shape of matrix characterises the texture
• Can be characterised by factors derived from it.

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Edge Frequency

• Density of microedges is characteristic of
  texture
• Apply an edge detector
• Sobel is suitable
• Threshold result
• Compute density of edge elements

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Shape from

• To recover shapes of objects in a scene
• By identifying spatial properties of surface
  patches

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Shape from Motion

• From
• 4 views
• Of
• 3 non-colinear points
• Can compute
• motion and relative locations of points

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Shape from Photometric Stereo

• Capture images of a scene in two cameras
• Must know
• Cameras separation
• Cameras relative orientation (parallel in
  example)
• Co-ordinates of corresponding points in images

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Plan view of cameras optical paths.
Image plane
Optical centres
Scene
(x, y,z)
camera 1
x
(x, y, f)
d
centre line
xd
d
camera 2
z
f
(x, y, f)
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Provided that cameras are aligned separation
is known corresponding points are
identified The points depth can be
computed. Correspondence problem examined later.
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Shape from Shading

• For matt surfaces, proportion of incident light
  reflected depends on
• Surface reflectance
• Surface orientation with respect to light source

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• If k can be estimated
• Image value for q 0
• Can estimate cos q, hence q throughout image.
• Surface orientation is not determined uniquely
• Two angles are needed

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Shape from Texture

• Apparent texture of a surface is dependent on the
  surfaces
• Orientation
• Range

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Method

• Must be able to identify fundamental texture
  elements
• Assume they are invariant
• Compute mapping to transform each element to a
  standard appearance
• Mapping determines surface orientation.

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Summary

• Binary image features
• Skeleton
• Boundaries
• Texture
• Shape from

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• There is no reason why anyone would want a
  computer in their home
• Ken Olsen, chairman DEC, 1977