project_PPT_final

LANDMARK BASED IMAGE
REGISTRATION USING THIN PLATE
SPLINE WITH FEATURE MATCHING
Under the Guidance of
Mr. Soumik Ghosh
Assistant Professor, UIT,Golapbag,Burdwan
Prepared By:
Ranjan Ganguli
ME2014-10014
Master of engineering
Department of Computer Science and Engineering
University Institute of Technology
Golapbag,Burdwan

Objective
• The purpose of this project is to produce
deformation of an input image using set of
landmark points and making a correspondence
between them.
Application: medical image processing, robotics

Review for Thin Plate Spline
• Rigid-body alignment
• Non-rigid deformation
– Intrinsic methods:
deforming the boundary
points
– An optimization problem
• Minimize shape distortion
• Maximize fit, smoothing After
Before
Source
Target

Thin Plate Spline deformation
Technique
Analogues to bending a thin sheet of metal extending to infinity[1]

Thin-Plate Spline
• Given corresponding source and target points
• Computes a deformation function for every
point in the 2D plane.

• Input
– Source points(black): p1,…,pn
– Target points(gray): q1,…,qn
• Output
– A deformation function f[p] for any point p..[2]
Thin-Plate Spline
pi
qi
f[p]

• Distortion or Bending Energy equation:
- Integral of second order partial derivatives
along x and y axis[3].
Thin-Plate Spline

Need to solve various matrix equations

• Thus ,the solution to this bending energy equation:
f(x,y) gives the surface heights of mapping all points
in the plane[1].
Thin-Plate Spline

Final deformed or warped image with a set of
landmark points
Thin Plate Spline
Original image Deformed image
Blue dots represent the landmark points

How to match “Feature Points“
between deformed image and original
image?

Matching Feature Points
Technique:
• Developed by David Lowe
• University of British Columbia
• Initial paper ICCV 1999
• Newer journal paper IJCV 2004
SIFT(SCALE INVARIANT FEATURE TRANSFORM)

Overall Procedure at a High Level
1. Scale-space extrema detection
2. Keypoint localization
3. Orientation assignment
4. Keypoint description
Search over multiple scales and image locations.
Fit a model to determine location and scale.
Select key points based on a measure of stability.
Compute best orientation(s) for each key point region.
Use local image gradients at selected scale and rotation
to describe each key point region.

Scale-space extrema detection
• Find the points, whose surrounding patches (with some
scale) are distinctive.
• An approximation to the scale-normalized Laplacian of
Gaussian (LoG)

Maxima and minima in a
3*3*3 neighborhood

Keypoint localization
• There are still a lot of points, some of them are
not good enough.
• The locations of key points may be not accurate.
• Eliminating edge points.

Eliminating edge points
• Such a point has large principal curvature across the
edge but a small one in the perpendicular direction
• The principal curvatures can be calculated from a
Hessian function
• The eigenvalues of H are proportional to the principal
curvatures, so two eigenvalues shouldn’t diff too much

Orientation assignment
• Assign an orientation to each keypoint, the keypoint
descriptor can be represented relative to this orientation
and therefore achieve invariance to image rotation
• Compute magnitude and orientation on the Gaussian
smoothed images

Orientation assignment
• A histogram is formed by quantizing the
orientations into 36 bins;
• Peaks in the histogram correspond to the
orientations of the patch;
• For the same scale and location, there could be
multiple keypoints with different orientations;

Feature descriptor
• Based on 16*16 patches
• 4*4 subregions
• 8 bins in each subregion
• 4*4*8=128 dimensions in total

Conclusion
This paper includes non-rigid based image
registration using Thin Plate Spline with Feature
Matching. Landmark has been selected either
manually through mouse or can be assigned
initially. SIFT helps deformed image illumination,
scale independent and matched with various
other images. Thus this process can widely
applicable to medical imaging , object
identification ,robotics etc where object are at
different positions all the time

Future Scope
• Method
1. Gauss-Newton Method
Advantage:
Easy to converge for small number of points.
2. - Quasi-Newton Method
Advantage:
Does not require calculation of image gradient
How do we get the original image from a
deformed image?
( Optimization)

Idea of Optimization
Pk+1 = Pk + ak.gk.
The value of ‘a’ and ‘g’ has to be calculated
-Gauss-Newton method
-Newton Quasi method

References
[1]F. L. Bookstein, “Principal warps: Thin-plate splines and the decomposition
of deformations,” IEEE Trans. Pattern Anal. Machine. Intell.
[2] Wahba, G. (1979). How to smooth curves and surfaces with splines and
cross-validation. Proc. 24th Conference on the Design of Experiments.
[3] Broomhead, David H.; Lowe, David (1988). "Multivariable Functional
Interpolation and Adaptive Networks" (PDF). Complex Systems.

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