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IMAGE MOSAICING Summer School on Document Image Processing. Thotreingam Kasar MEDICAL INTELLIGENCE AND LANGUAGE ENGINEERING LAB, DEPARTMENT OF ELECTRICAL ENGINEERING, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA – 560 012. Image Mosaicing.

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image mosaicing summer school on document image processing

IMAGE MOSAICING Summer School on Document Image Processing

Thotreingam Kasar

MEDICAL INTELLIGENCE AND LANGUAGE ENGINEERING LAB,

DEPARTMENT OF ELECTRICAL ENGINEERING,

INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA – 560 012

image mosaicing
Image Mosaicing
  • Given multiple images of a scene, with some degree of overlap, how do we seamlessly blend them into a single composite image?

The basic ingredients

  • Registration
  • Warping
  • Blending
methods for image mosaicing
Methods for Image Mosaicing

Direct Method

  • Preferred for images without many prominent details
  • Windows of pre-defined size or even the entire images are used for the correspondence estimation
  • Can handle only translation and small rotation
  • Sensitive to intensity changes, due to noise, varying illumination, and/or by using different sensors

Feature based Method

  • Generally faster than direct methods
  • More robust against scene movement
  • Robust estimation algorithms available
  • Suitable for fully automatic mosaicing
  • The respective features might be hard to detect and/or unstable in time
projective geometry
Projective Geometry
  • Set of rays in 3-D space with each point representing a projective point
  • Planes through the origin are interpreted as lines
slide5

Homogeneous Co-ordinates

  • A line in a plane (ax + by + c = 0) can be represented as (a, b, c)T

ax + by + c = 0

(ka)x + (kb)y + kc = 0

Thus, (a, b, c)T and (ka, kb, kc)Tare homogeneous vectors.

  • A point X=(x,y)T lies on the line (a, b, c)T if

ax + by + c = 0

or, (x, y,1)T·(a, b, c)T = 0

Thus, the point (x,y)T inR2 is represented as a 3-vector by adding a final

co-ordinate of 1.

Any arbitrary homogeneous point P=(x1, x2, x3)T represents the point (x1/x3, x2/x3) in R2

} are the same lines for any k ≠ 0

2 d transformations
2-D Transformations
  • Translation
  • Rotation
  • Scaling

We can combine all the multiplicative and translation terms for 2-D geometric transformations into a single 3x3 matrix using Homogeneous Coordinates

geometric transformations
Geometric Transformations

RIGID

AFFINE

PERSPECTIVE

imaging geometry

Image 1

Image2

X’

X

O

y’

y

x’

x

IMAGING GEOMETRY

The general projective transformation of one projective plane to another is represented as

  • For a pair of matching points (x, y) and (x’, y’) in the world and image plane respectively, the projective transformation in inhomogeneous form is
  • 4 point correspondences lead to 8 such linear equations which can be solved up to an insignificant multiplicative factor.
feature detection
Feature Detection

Harris corner is widely used to localize interest points

Large intensity change in both directions

Small intensity change

Large intensity change in one direction

Local maxima of the Response function R gives the corners

ransac
RANSAC
  • Randomly select 4 point matches
  • Estimate homography Hi
  • Count the consensus set Si
  • If |Si|> T, return Hi
  • Repeat N times and return the model with max|Si|

p = P(at least 1 of the random samples is free from outliers)

w = P(any selected data point is an inlier)

e = (1-w) is the probability that it is an outlier

At least N selections are required where (1-w4)N = 1-p

ransac1
RANSAC

For a sample size of 4, the values of N required to ensure with a probability p =0.99 that at least 1 of the sample is free from outliers

feature correspondence
Feature Correspondence

Target Image 1

Reference Image

Target Image 2

Registered Image 1

Registered Image 2

blending
BLENDING
  • Simple Averaging
  • Feathering - A weighting function is associated with each image decaying from a maximum at the centre to zero at the image boundary

Where M and N represents the dimensions of the image and

(x0, y0) is the image center

mosaic construction
Mosaic Construction

Target image 1 Reference Image Target image 2

Mosaic output

why mosaicing
Why Mosaicing?
  • Satellite image Analysis
  • Medical image analysis
  • 3-D Scene reconstruction and Robotic Navigation
  • Creating Super-resolution images
  • Video representation and indexing

To enhance the limited field of view of camera

Some Applications

discussions
Discussions
  • Stable Feature Localization
  • Invariant Feature Extraction
  • Sub-pixel registration
  • Blending