moments area of the object center of mass describe the image content (or distribution) with respect...
Post on 21-Dec-2015
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Moments
dxdyyxyxiM q
D
pqp ).,(,
0,0M area of the object
0,11,0 ,MM center of mass
describe the image content (or distribution) with respect to its axes
Centralized Moments
0,0
1,0
0,0
0,1
,
,
)()).(,(
M
My
M
Mx
dxdyyyxxyxiM qp
D
cqp
Moments are not invariant geometric transformations
To achieve invariance under translation
Hu Moments(contd.)
In addition he described a 7th invariant that is skew invariant
Other invariants are Legendre Moments Complex Zernike Moments
Image ReconstructionUnless we have all Nmax moments, the image cannot be reconstructed.The top order moments are good approximations of the images
2-12
0-8
Hough TransformProcedure to find occurrences of a shape”in an image
Assumes the “shape” can be described in some parametric form
Points in image correspond to a family of parametric solutions
A voting scheme is used to determine the correct parameters
Accumulator Space
A line in the cartesian space is a point in the hough spaceCreate an accumulator whose axis are the parameters Set all values to zero We “discretize” the parameter space
Parameter are quantized to fit into the finite p-space
For each edge point, votes for appropriate parameters in the accumulator Increment this value in the accumulator
Circle Detection
Consider a 2D circle It can be parameterized as:
r 2 = (x-a) 2 + (y-b)2
Assume an image point was part of a circle, it could belong to a unique family of circles with varying parameters: a, b, r
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