Presentation on theme: "Christine Lew"— Presentation transcript
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Christine LewDheyani MaldeEverardo UribeYifan ZhangSupervisors:Ernie EsserYifei Lou
BARCODE RECONITION TEAMSlide2
UPC BarcodeWhat type of barcode? What is a barcode? Structure?Our barcode representation? Vector of 0s and 1s Slide3
Mathematical RepresentationBarcode Distortion Mathematical Representation:
What is convolution?
Every value in the blurred signal is given by the same combination of nearby values in the original
signal and the kernel determines these combinations.
Kernel
For our case,
the blur kernel k, or point spread function, is assumed to be a GaussianNoiseThe noise we deal with is white Gaussian noise
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0.2 Standard DeviationSlide5
0.5 Standard DeviationSlide6
0.9 Standard DeviationSlide7
DeconvolutionWhat is deconvolution?It is basically solving for the clean barcode signal, .Difference between nonblind deconvolution and blind deconvolution:
Nonblind
deconvolution
:
we know how the signal was
blurred,
ie: we assume k is knownBlind deconvolution: we may know some or no information about how the signal was blurred. Very difficult.
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Simple Methods of DeconvolutionThresholdingBasically converting signal to binary signal, seeing whether the amplitude at a specific point is closer to 0 or 1 and rounding to the value its closer to.Wiener filterClassical method of reconstructing a signal after being distorted, using known knowledge of kernel and noise. Slide9
Wiener FilterWe have: The
Wiener
Filter solves for:
Filter is easily described in frequency domain.
Wiener filter defines
, such that
x =
, where
is the estimated original
signal:
Note that if there is no noise, r =0, and
So
reduces to
.
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0.7 Standard Deviation, 0.05 Sigma NoiseSlide11
0.7 Standard Deviation, 0.2 Sigma NoiseSlide12
0.7 Standard Deviation, 0.5 Sigma NoiseSlide13
Nonblind Deblurring using Yu Mao’s Method
By: Christine Lew
Dheyani MaldeSlide14
Overview
2 general approaches:

Yifei
(blind: don’t know blur kernel)
Yu Mao (nonblind: know blur kernel
General goal:
Taking a blurry barcode with noise and making it as clear as possible through gradient projection.
Find method with best results and least errorSlide15
Data Model
Method’s goal to solve
Convex Model
K: blur kernel
U: clear barcode
B: blurry barcode with noise
b = k*u + noise
Find the minimum through gradient projection
Exactly like gradient descent, only we project onto [0,1] every iteration
Once
we find min u, we can predict clear signal
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Classical Method
Compare with
Wiener
Filter in terms of error rate
Error rate: difference between reconstructed signal and ground
truth
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Comparisons for Yu Mao’s Method
Yu Mao’s Gradient Projection
Wiener
FilterSlide18
Comparisons for Yu Mao’s Method (Cont.)
Wiener
Filter
Yu Mao’s Gradient ProjectionSlide19
Jumps
How does the number of jumps
affect the result
?
What happens if we apply the amount of jumps to the different methods of deblurring?
Compared Yu Mao’s method &
Wiener
Filter
Created a code to calculate number of jumps
3 levels of jumps:
Easy: 4 jumps
Medium: 22 jumps
Hard: 45 jumps (regular barcode)Slide20
Created a code to calculate number of jumps:Jump: when the binary goes from 0 to 1 or 1 to 03 levels of jumps:
Easy: 4 jumps
Medium: 22 jumps
Hard: 45 jumps
(regular barcode)Slide21
How does the number of jumps affect the result (clear barcode)?Compare Yu Mao’s method & Weiner FilterSlide22
Comparison for Small Jumps (4 jumps)
Yu Mao’s Gradient Projection
Wiener
FilterSlide23
Comparison for Medium Jumps (22 jumps)
Yu Mao’s Gradient Projection
Wiener
FilterSlide24
Comparison for Hard Jumps (45 jumps)
Wiener
Filter
Yu Mao’s Gradient ProjectionSlide25
Wiener
Filter with Varying Jumps
 More jumps, greater error

Drastically
gets worse with more jumpsSlide26
Yu Mao's Gradient Projection with Varying Jumps
 More jumps, greater error

Slightly
gets worse with more jumpsSlide27
Conclusion
Yu Mao's method better
overall:
produces
less
error
from
jump cases: consistent error rate of 20%30%
Wiener
filter did not have a consistent error
rate:
consistent
only for small/medium jumps
at
45 jumps, 40% 50% error rateSlide28
Blind DeconvolutionYifan ZhangEverardo UribeSlide29
Derivation of ModelWe have:
For our approach, we assume that
, the kernel, is a symmetric pointspread function.
Since its symmetric, flipping it will produce an equivalent:
We
flip entire equation and began reconfiguration:
Y and N are matrix representations
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Derivation of ModelSignal Segmentation & Final Equation:
Middle bars are always the same, represented as vector [0 1 0 1 0] in our case.
We have to solve for x in:
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Gradient Projection
Projection of Gradient Descent ( firstorder optimization)
Advantage:
Allows us to set a range
Disadvantage:
Takes very long time
Not extremely accurate results
Underestimate signal
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Least Squares
estimates unknown parameters
minimizes sum of squares of errors
considers observational errors
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Least Squares (cont.)
Advantages:
return results faster than other methods
easy to implement
reasonably accurate results
great results for low and high noise
Disadvantage:
doesn’t work well when there are errors inSlide35
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Total Least Squares
Least squares data modeling
Also considers errors of
SVD (C)
Singular Value Decomposition
Factorization
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Total Least Squares (Cont.)
Advantage:
works on data in which others does not
better than least squares when more errors in
Disadvantages:
doesn’t work for most data not in extremities
overfits data
not accurate
takes a long time
xSlide38