Three general optical approaches to multiple degree of freedom object pattern recognition (where no stable object rest position exists) are advanced. These techniques include: feature extraction, correlation, and artificial intelligence. The details of the various processors are advanced together with initial results

Casasent, D.

English

NASA Technical Reports Server

Multiple Degree of Freedom Optical Pattern Recognition
D. Casasent
Carnegie Mellon University
Pittsburgh, PA 15213
ABSTRACT
Lf
- Three general optical approaches to multiple degree of freedom object pattern
/ recognition (where no stable object rest position exists) are advanced. These
techniques include: feature extraction, correlation, and artificial intelligence. The
details of the various processors are advanced together with initial results.
1. INTRODUCTION
This paper addresses object pattern recognition for multiple degree of freedom
(M-DOF) image cases. This is defined aS'the recognition and Identification of an object
with no stable rest position. We;emphaslze optical pattern recognition (OPR)
techniques and research for this pr01_lem,wlth recent results obtained at the Center for
Excellence in Optical Data Proc_gsing at Carnegie Mellon University, Three different
optical processing techniquesdre addressed and highlighted. These include: feature
extraction (Sectlon 2), correlation (Section 3) and optical artificial intelligence
(Section 4). "
2. OPTICAL FEATURE EXTRACTION FOR M-DOF PATTERN RECOGNITION
The geqeral feature extraction approach to pattern recognition [ 1 ] is diagramed in
Rgure 1. In this section, we emphasize different feature spaces that can be optically
realized. The feature extraction and classification techniques are established [2]. All
feature spaces we consider are in-plane distortlon-invariant. We achieve 3-D M-DOF
distortlon-invariance by training sets and use of linear discriminant functions (LDFs).
/
ZI_PUT f (x,y) _ FEATURE
OBJECT q GENERATOR
OPTICAL
F_ATUR E
EMTRACTOR
AND CLASSIFIER
DIGITAL
CLAS S,
-----_>OR IENTAT IO N,
CONFIDENCE
Rgure 1: Hybrid Optical/Digital Feature Extraction Processor Block Diagram
2.1 CHORD DISTRIBUTION FEATURE SPACE
This feature space consists of the distributions h(r) of the length (r) and the
distributions h(8) of the angles (O) of all chords associated with an input object. We
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allow gray-level objects, internal object points, and all chords associated with these
Input object points (if the internal object points are reliable) in our synthesis algorithm.
We achieve generation of this feature space [3-4] with the system block diagram In
Rgure 2. This feature space provides In-plane distortion-invarlance. We achieve out-
of-plane distortlon-invariance by the use of training set data and LDFs. The case
studies for which this feature space has been tested included a set of ship data and a
set of aircraft imagery [3,4]. The LDFs used were Fisher vectors and dominant
Karhuhen-Loeve eigenvectors. Most attractive results (.--. 95% correct classification)
were obtained.
h(0)
Rgure 2: Optical Chord Transform Feature Space Generation Block Diagram
°2.2 SPACE-VARIANT FEATURE SPACE
An attractive feature space that is in-plane distortlon-invariant can be obtained
from the Fourier transform of coordinate transformed in-plane data ['51. The resultant
system has a different Impulse response at each spatial point in the system. The
coordinate transform is chosen to make the features Invariant to different geometrical
distortions. A polar transform results In rotation invariance. If the logarithm of the axes
is taken, the features are scale invartant and a Mellin transform results. If we log the
radial axis in polar space, scale and rotation invarlance are both achieved. To obtain
shift-invariance, the object must be centered (by moments, etc.) or the coordinate
transform operations can be performed on the magnitude Fourier transform of the input
data. Figure 3a shows an optical system to achieve this. The coordinate
transformation (CT) is performed by a computer generated hologram (CGH) at P2' The
output feature space at P3 can be operated on in parallel by optical LDFs implemented
on another CGH. In this case, the class of the Input object is determined by the location
of a peak In P4 on a particular detector, or by the binary-encoded output value from a
set of N detectors. Figure 3b shows the block diagram of this space-variant processor
E63.
As a demonstration of the use of this architecture for M-DOF object identification,
we consider a set of 9 different aircraft. These objects have no stable rest position and
thus represent an attractive application for an M-DOF processor. Since the feature
space at P3 is in-plane (scale, rotation and translation) invariant, we use a training set
to provide out-of-plane lnvariance (in pitch and roll of the aircraft). A relational graph
was devised to identify the class of the aircraft. At the first level of the graph, a
decision is made on the sub-class of the object (e.g. commercial, fighter, etc.). A
synthetic discriminant function (SDF) LDF was used at this node for this decision. At
subsequent nodes, the name class (F104, DC10, etc.) of the aircraft is determined.
This represents a multi-class graph (with greater than one decision, i.e. one of three
choices, made per node). A second binary graph (with one of only two decisions made
per node) was then devised using Fisher LDFs. In both graphs, different features (the
66
PI L1 P2
INPUT FT CT
f(x,y) LENS CGH
IRF_T re (_(.y)
06JE(;T
L2 P3 P4
CLASS
F OF OBJECT
SPACE CGH CLASSES
(a)
JCENTERBY: (mOl,'lO) OR 1
+t: T.NSFOm|
F'(,,C,,,,}
$P_E
f(x.y) _>_ POLARF(u,v) TRANSFORM
PIA_I TUOE .I.COORDINATE
FOURIER i TRANSFOR_
TRAI(SFORN F£({ .e)
_F_TURE EXTRACTORS THRESHOLD
LDFs _ CLASSIFIER
(b)
Figure 3: Optical Space-Variant Feature Space. (a) Optical System; (b) Block Diagram
optimal ones) are used at different nodes. The training set consists of 5 images per
object class (aircraft name class) at 0° and _+20° rotations in pitch and roll (recall that
the feature space is lnvarlant to yaw, as well as scale differences). The graphs were
then tested versus 0°, +10 °, +20 ° and -+30° in pitch and roll. (These are distortions for
which the feature space is not automatically invariant. In other tests on in-plane
distortions, all results were positive and thus are not Included in these M-DOF tests.)
The full test set thus consisted of 13 images for 9 different aircraft (117 images). The
results obtained were approximately 99% and 95% correct recognition for the two
graphs. This demonstrates the M-DOF performance of this feature space processor.
2.3 MOMENT FEATURE SPACE
A moment-based system (block diagramed in Figure 4) has also achieved M-DOF
recognition [7,8]. In this system, the moments are optically generated. The first level
classifier uses the ratio/_20/#02 to estimate the aspect of the object and a hierarchical
tree to estimate the object class. The results from these first-level estimators are used
to access 21 moments for each object class. These are then used in an iterative
second-level estimator to confirm the object class, its distortion parameters and the
confidence of the estimates. This M-DOF processor has been successfully tested on
data bases of pipe parts [7] and ship data [8].
67
_+
Cllss
I¢O_NT FI_ER Esttnwte
CLASSIFIER REFERENCE
Aspect mpq
._ ASPECT J [st|mateESTIHATOR OATABASE
i
ITERATIVE NONLINEAR
CLASS (_) LSN CLASS/ASPECT/DISTORTION
ORIENTATION (hi PARAMETER
C,ONFIDENC[-
RGIJRE 4: M-DOFMomenf-gasedPaffernRecognition System BIockDiagram
3. M-DOF OPTICAL CORRELATORS
Optical correlators represent one of the most powerful optical systems. They
provide shift-invarlant recognition of multiple objects in parallel in the presence of high.
clutter. With space-multiplexed filters, one can correlate an input scene versus
several filter functions in parallel and either produce multiple output correlation planes
or superimposed multiple correlation plane outputs. Frequency-multiplexed filters
also enable multiple output correlation planes. One can employ frequency-
multiplexed filters 8t each spatial-multiplexed filter location. With holographic optical
elements (HOEs) lenses on each filter, various summations of multiple output
correlation planes are possible. These architectures are limited in practice by the
number of 2-D correlation planes one can read out In parallel and by the lack of
distortion-invarlance in correlation matched spatial filters (MSFs). We now discuss
distortion-invariant MSFs, a hierarchical correlator and a symbolic correlator for M-
DOF processing.
3.1 DISTORTIOI_I-INVARIANT FILTERS
We have devised various techniques to synthesize distortion-invariant correlation
filters from training set data [9,10]. These are referred to as SDFs. We can specify
the peak value of the correlation output in most of these filters. The three types of
filters are: projection filters (these specify only the correlation peak value), output
correlation filters (these specify the shape of the correlation function), and peak to
sidelobe ratio (PSR)filters (these maximize PSR, but cannot control the correlation
peak value). These filters have been synthesized to recognize an object independent
of its aspect view. Initial tests have been most successful for ATR, ship and aircraft
targets.
3.2 HIERARCHICAL CORRELATORS
These distortion-invariant filters allow one filter to recognize an object
Independent of distortions. They thus significantly reduce the number of filters
necessary and hence ccrrelation planes to be analyzed. The use of K multiple filters
with binary encoding of the outputs enables K filters to recognize 2 K object classes.
Control of the filter peak outputs to L levels allows F filters to handle LF object classes.
Thus, these filters allow large object class problems with a small number of filters and
with the other advantages of a correlator. In extensive tests, we find that as the size of
the problem to be solved increases, the filter's perfortTlance degrades. A proposed
68
solution to this Is a hierarchical correlator [1 1]. In the first level of this system, PSR
filters are used to locate regions of Interest (ROIs) or candidate objects in the scene.
Correlation filters are then used in the second level to test each location and the shape
of the correlation peak there. In the final level of the hierarchical system, projection
filters are used to confirm the object class and to identify it and to determine its
orientation.
3.3 SYMBOUC CORRELATORS
One can view correlation outputs from multiple filters as a symbolic description of
the input object. The use of multiple multiplexed filters with symbolic post-processing
offers significant potential for M-DOF multiple object pattern recognition in parallel.
4. OPTICAL ARTIFICIAL INTELLIGENCE
Various optical AI processors have recently emerged and have been advanced.
Initial remarks on each are now advanced. More extensive tests on all are necessary to
more fully assess each. The relational graph processor in Figure 3 is one approach.
The automatic organization of data into sub-classes as employed in this processor is a
useful technique for any knowledge base or Inference system. A model-based
description of objects Is another approach that is most attractive because of its
efficient storage and its ability to easily generate different object aspect views. A
reference function generator using.this concept is quite general purpose and useful for
filter synthesis and generation of the filters for correlators and for the memory matrices
in assoclative processors. Successful initial tests on aircraft data has been most
attractive using these approaches. We expect future work to concentrate on optical AI
techniques, hopefully with attention to system realization and to more extensive
testing.
5. SUMMARY AND CONCLUSION
Figure 5 shows one version of three levels of the hierarchical vis:.on processing
system, the scene and object elements involved in each and the type of processing
employed at each level, As seen and as was briefly described above, there is a
significant role for optics in each level of vision.
ACKNOWLEDGMENTS
The support of future work in this area by a NASA JPL contract is gratefully
acknowledged.
REFERENCES
1.D. Casasent, "Hybrid Optical/Digital Image Pattern Recognition: A
Review", Proc. SPIE, Vol.52_____88,pp. 64-82, January 1985.
2. R.O. Duda and P.E. Hart, Pattern Classification and Scene Analys!s, Wiley
& Sons, New York, 1973.
3. D. Casasent and W.T. Chang, "Generalized Chord Transformation for
59
I,o,,,
T
Ih'PUT
bL_CES
• EXPERT
SYSTEMS
OBJECT
CLASSlTICATION
TEMPLATE
MATCIIING
SEC._IE_'rED
OBJECT RrCIONS
I'L_%L
BASED
Ai
TECHNIQUES
FEATURE
EXTRACTORS
CORRELATORS
EI)CES
VEI{'I'ICI_
"I'I'_X'I'URI.;S
NOISE I_'.|'.'_MOVAL
IMAGE
ENI-b_NCEM_NT
SYMBOLIC
ASSOCIATWE
INFERENCE/
HIERARCI IICAL
FEATURE
EXTRACTORS
F.I)CE EKI£._,NCE.MENT
IIOUCII TRANSFORM
INTERPOLATE
FILTERS
DEBLUT(
RE; R.ESENTATION OPERATIONS ROLE FOR
OPTICS
Figure 5: Hierarchical Levels of Vision, Scene, and Object Recognition
and the Role for Optics in Each
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4. D. Casasent and W.T. Chang, "Parameter Estimation and In-Plane
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Considerations", Proc. SPIE, Vol. 625, pp. 220-225, January _ 986.
7O


Multiple degree of freedom optical pattern recognition

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