EE640FINALPROJECT
HEADSORTAILS
By Laurence Hassebrook
Initiated: April 2015, updated April 27
Contents
1. SUMMARY ............................................................................................................................................. 1 2. EXPECTATIONS ...................................................................................................................................... 2 3. INPUT DATA BASE ................................................................................................................................. 2 4. PREPROCESSING .................................................................................................................................... 4 4.1 Surface Image ...................................................................................................................................... 4 4.2 Z Smoothing Filters ............................................................................................................................. 5 5. PSD ESTIMATION AND CONTROL DATA DEFINTION ............................................................................. 7 APPENDIX ...................................................................................................................................................... 7 A. MAT5 formats ................................................................................................................................... 7 1. SUMMARY
The final project is a practical application of noise synthesis, analysis and stochastic systems
implementation. The primary goal is to simulate a small set of test data and then demonstrate the
ability to classify the test data as well as perform parameter estimation. A data base of 16 pennies
are grouped as 16 heads and 16 tails. The penny rotation is random and known as in-plane
rotation distortion. The penny data is in the form of 3-D scans having xw, yw and zw world
coordinates for each points. The data files are stored in a bitmap format, (i.e., “mat5 F format”)
whose intensity pixels are distributed on a uniform XY displacement. In this way, the bitmap
image intensity and zw values are distributed accurately in the XY plane and thus be processed
using 2-D image processing techniques including edge enhancement and in-plane rotation. We
chose coins as a data base because it is readily identifiable, available and precisely manufactured.
The techniques we use are application to numerous applications in industrial inspection,
automatic pattern recognition and artificial intelligence. We chose the penny because of its low
value and the understanding that we must respect the importance and integrity of currency.
1 The random variable within the data is the rotation angle and the random process is the surface
noise. There is also some feature variation between coins. When we test the data we will be
evaluating our ability to discriminate between heads and tails as well as estimating the rotation
angle of the test data. We will first select a single head and a single tail scan to be used to
develop our classifiers and angle estimators. From these two coin scans, we will select a
preprocessing algorithm that tends to orthogonalize the data. From that we will estimate the
PSDs of the coins. Using white Gaussian noise images and a filter based on the PSD results, we
synthesize a “training set” of control images representing the rotation distortion and the PSD of
the heads and tails data. Using the training set synthesis, we determine the maximum angle
between adjacent rotations which in turn determines the minimum size of the training set. Given
the training set correlation matrix, we form a filter bank based on the correlation matrix. From
that we form a maximum likelihood ration based filter bank for discriminating between heads
and tails based on the Rayleigh quotient. After classification we use the associated filters to
estimate the rotation angle.
2. EXPECTATIONS
The students are expected to turn in a single report per group. Each section starts with a
definition of what the student needs to show or implement. This may include mathematical
derivation and/or MATLAB implementation. The student will be provided with existing
MATLAB code to minimize development of software not directly related to the study of
stochastic systems.
3. INPUTDATABASE
The student should select one mat5 data set for heads and one for tails to represent that
particular class. The data was scanned using the multi-frequency Phase Measuring Profilometry
(PMP) [1] method. The format of the data is in MAT5 format [2] described in Appendix A. Use
PreviewDataSet.m to preview the data set. There are several controls in PreviewDataSet.m:








Targetselect: Index of selected target which varies between 0 and (N-1)
TurnOnImage: 0 for original images, 1 for median normalized gain and 2 for surface
normal.
TurnOnEdge: 0 for Z depth, 1 for Sobel with clipping threshold, and 2 for Moving Least
Squares filter.
SobelClip: The Sobel edge enhancement clips result based on SobelClip times Sobel
peak. So any values greater than SobelClip are set to the value of SobelClip.
TurnOnZSmoothing: 0 for no smoothing of Z coordinates, 1 for smoothing Z using filter.
FilterType: Smoothing filter type. 0 for none, 1 for Moving Average Rectangle and 2 for
Gaussian.
MAfilter: Width of MA filter and should be an odd number to be symmetric.
GausfilterSTD: Gaussian filter parameter which controls shape width.
2 two controls, and which control if the images are original, metallic, depth, sobel edgehance Z
and Moving Least Square Filtering.
Figure 1: Data set of penny heads with TurnOnImage=0.
3 Figure 2: Data set of penny tails, C matrix, with TurnOnImage=0.
4. PREPROCESSING
The data is pre-processed before viewing and usage. The student should indicate and show
their enhanced images selected as the training images for the target (i.e., heads) and clutter
(i.e., tails) classes. Indicate what filtering parameters are used and which enhancement
methods are used.
4.1SurfaceImage
For viewing, the C matrix can be used in original form (TurnOnImage=0) or median normalized
(TurnOnImage=1). Both options for both heads and tails of mat5 C matrix 0, are shown in Fig. 3.
For the median normalization, we select all pixels for I > ithresh and find the median value. All
pixels are scaled such that the median value is 128. The image is clipped to be between 0 and
255.
4 Figure 3: Image C of mat5 index 0. (top, left) Original heads image. (bottom, left) Median normalized head. (top, right) Original tail. (bottom, right) Median normalized tail.
4.2ZSmoothingFilters
The input Z data can be smoothed with two types of linear filters. By controlling the filter
parameter, the smoothing of the Z surface can improve the results of the edge enhancement
processes. In the mathematical equations we ignore the circular wrap that the finite image space
requires. In implementation, the origin is in the corner and is then wrapped around.
For FilterType=1, a Moving Average (MA) filter is convolved with the Z data matrix. The MA
filter is a Ma x Ma rectangular filter where Ma = MAfilter. The MA filter is defined as
 m 
 n 
 rect 

rect 
Ma 
M a 


hm, n  
M a2
and is convolved with the input Z matrix such that
Z s m, n   Z m, n   hm, n  .
For FilterType=2, a Gaussian filter is convolved with the Z data matrix.
5 hm, n  


2
2
1


exp1 m  n
2
2

E


where E is
E
M y 1 N x 1
  hm, n
m 0 n 0
Preview data offers two types of edge enhancement, Sobel edge enhancement and a differencing
Moving Least Squares filter. Both enhancement methods tend to orthogonalize the data which
should improve discrimination performance. Both are also sensitive to noise which are affected
by the smoothing process. The trade off in smoothing is too much will blur the features needed
for discrimination versus allowing surface noise that reduces performance. Results for both
methods and both classes are shown in Fig. 4.
Figure 4: (left column) Target image. (right column) Clutter image. (Top row) Sobel edge enhancement. (Bottom row) MLS filtering.
6 5. PSDESTIMATIONANDCONTROLDATADEFINTION
Based on the selected target and clutter preprocessed images, we synthesize control data to be
colored stationary noise having the same PSD as the target and clutter classes, respectively.
RANDOM INPLANE ROTATION AND THE CORRELATION MATRIX
COMPOSITE CORRELATION FILTER BANK
DETECTION AND DISCRIMINATION
ROTATION ANGLE ESTIMATION
REFERENCES
1. Jie-lin Li, L.G. Hassebrook and Chun Guan, “Optimized Two-Frequency Phase-Measuring-Profilometry
Light-Sensor Temporal-Noise Sensitivity,” JOSA A, 20(1), 106-115, (2003).
2. MAT5 format description: http://www.engr.uky.edu/~lgh/soft/softmat5format.htm
3. W. J. Chimitt and L.G. Hassebrook, “Scene reconstruction from partially overlapping images with use of
composite filters,” JOSA A, 16(9), 2124-2135, September (1999).
4. L. G. Hassebrook, B.V.K. Vijaya Kumar and L. Hostetler, "Linear Phase Coefficient Composite Filter
Banks for Distortion-Invariant Optical Pattern Recognition," Optical Engineering, 29, 1033-1043, (Sept.
1990).
5. L. G. Hassebrook, M. E. Lhamon, M. Wang and J. Chatterjee, "Postprocessing of Correlation for
Orientation Estimation," Optical Engineering, 36(10), 2710-2718, October, (1997).
APPENDIX
A. MAT5formats
The mat5 format consists of 5 matrices embedded into a single 32 bit Bitmap file. The mat5
image is My rows by Nx columns. The matrices are a color matrix C, an indicator matrix I, X
world coordinate matrix X, Y world coordinate matrix Y and Z world coordinate matrix Z.
Matrix
C
I
X
Y
Z
Dimensions
My x Nx x 3
My x Nx
My x Nx
My x Nx
My x Nx
Element format
3 bytes representing RGB
1 byte representing quality
4 byte float representing X world coordinates
4 byte float representing Y world coordinates
4 byte float representing Z world coordinates
Given a threshold “ithresh” the valid elements are where I(m,n) >=ithresh where I(m,n) varies
between 0 and 255.
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