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Aucoin, P. J., Jr.

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s"Mai (380-10206) DESIGN SPECIFICATION FOR	 160- 2978,
in the EQOIPROBABLE BLOCKS OgNSITY
	 I
Sem:naESTIMATORY/CLASSIFIER/DOT SELECTOR (Lockheed 	 Vr
progra Electronics Co.) 19 p HC A02/MF A01 	 Uuclas
for any -	 CSCL 05B G3/+3 0020o
DESIGN SPECIFICATION
•	 FOR
SECONDARY ERROR SOURCES
EQUIPROBABLE BLOCKS
DENSITY ESTIMATOR/CLASSIFIER/DOT SELECTOR
Job Order 71-695
(TIRF 77-0058)
Prepared By
Lockheed Electronics Company, Inc.
Systems and Services Division
Iiouston, Texas
Contract NAS 9-15200
For
EARTH OBSERVATIONS DIVISION
SPACE AND LIFE SCIENCES DIRECTORATE
National Aeronautics and Space Administration
LYNDON B. JOHNSON SPACE CENTER
Houston, Texas
Dp cember 1977
LEC- 11676
JSC- 13824
DESIGN SPECIFICATION
FOR
EQUIPROBABLE BLOCKS
DENSITY ESTIMATOR/CLASSIFIER/DOT SELECTOR
Job Order 71-695
(TIRF 77-0058)
Prepared By
P.	 . Aucoin, Jr.
Lockheed Electronics Company
APPROVED BY
L^. Krumm, Supervisor
Applications Software Section
a x OA'11t plp
B. L. Carroll, Manager
LACIE Development and Evaluation Dept.
Prepared By
Lockheed Electronics Company, Inc.
For
Earth Observations Division
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
LYNDON B. JOHNSON SPACE CENTER
^.	 HOUSTON, TEXAS
December 1977
LEC- 11676
i
CONTENTS
Section Page
1.	 SCOPE. 1-1
2.	 APPLICABLE DOCUMENTS. 2-1
3.	 SYSTEM DESCRIPTION 3-1
3.1	 HARDWARE DESCRIPTION. 3-1
3.2	 SOFTWARE DESCRIPTION. 3-1
3.2.1	 LINKAGES	 . 3-7
3.2.2	 INTERFACES 3-7
3.2. 3
	
INPUTS . 3-7
3.2.4	 OUTPUTS 3-11
3.2.5	 STORAGE REQUIREMENTS . 3-11
3.2.6	 DESCRIPTION	 . 3-11
ii
1. SCOPE
This document contains a design specification for software to
implement an equiprobable blocks program system. This system
will, on option, perform the following functions.
a. Conditional probability functions
b. Classification
C. Dot selection
d. Block population comparison
Training fields will be user-provided. Test and sample fields,
also user-provided, are used in classification and comparison
options.
The equiprobable blocks program will be added as a processor to
the EOD-LARSYS pattern recognition system. It will be implemented
on the Purdue -LARS computer (IBM 370/148). (Conversion of the
EOD-LARSYS system from the UNIVAC EXEC 2 system at JSC to Purdue-
LARS is currently under way.)
2. APPLICABLE DOCUMENTS
• Final Design Specification for EOD-LARSYS Procedure 1, Houston,
Texas, August 1977, JSC-12742, LEC-10417.
• Job Order 63-1347-1695
• TIRF
• M. P. Gessamon, "A Consistent Non-Parametric Multivariate
Density Estimator Based on Statistically Equivalent Blocks",
Ann. of Math Stat., Vol. 41, No. 4, pp. 1344-1346, 1970.
• M. P. Gessamon and P. H. Gessamon, "A Comparison of Soma
Multivariate Discrimination Procedures", J. of Am. Stat. Assoc.,
Vol. 67, No. 338, pp. 468-472, 1972.
Yl
3. SYSTEM DESCRIPTION
6
3.1 HARDWARE DESCRIPTION
N/A
3.2 SOFTWARE DESCRIPTION
The Equiprobable Blocks processor will proceed computationally
along the following path.
Read block parameters, action options, features, spatial grid
and parameter D (option). Read training fields for each category
(class) defined. Read test fields, sample fields. For each
category, build the set of equiprobable blocks. This procedure
is described in detail later in this section. On option, read a
ground truth file, assign categories to training field pizels.
Depending upon action options, perform one or more of the follow-
ing:
^` t
e
a. Compute conditii
j=1, NC where z
category C  and
estimates along
category names,
Dnal probability density estimate, f(zjCj),
belongs to one of the training fields of
Cj is the jth category. Output these
with training field geometry, features,
and so on.
b. Classify the sample fields. This procedure is described in
detail later in the section. If there are more than two
categories defined, successive NC-1 sets of blocks are com-
bined to obtain the "best" set of blocks for classification.
Write a classification map file (MAPTAP).
C. Select dots based on an input spatial grid and maximum count
parameter D. The equiprobable block set used will be a
combination of blocks of all categories specified. Output
the dots selected.
d. Combine equiprobable block sets from blocks from each category
to form a combination block set. Compute the proportion of
pixels per category per block and output these results.
In all cases where test fields are input, compute the number of
pixels per category per block and output. In this way, if
training fields for categories are also provided as test fields,
a comparison of categories can be achieved.
Certain details of the comZ:,^.-ation procedure follow.
COMPUTATIONAL PROCEDURE: BLOCKS
Read training field pixels per category, sun angle correct on
option.
Construct a set of equiprobable blocks for each category j,
j=1, NC:
First compute block parameters
Option - compute
K. = FIX	 Mj	P QA
i=1 ij
 )
P = number of selected features
where Mj = number of pixels in training fields for
category j
Kj = minimum number of pixels per block
R Qij= number of subdivisions in each co-ord direction i
for each category j
v
Option - compute
1
^P
FIX
Option - compute
1
F. = FIXM. I+PJ	 J	 ) 1
P
Qij = FIX 
where Qij = Q  (Qij independent of i)
in each direction i (i.e., blockSecondly, determine cuts
boundaries)
M.
Compute rl] = FIXQ
iJ )
Sli = M
3 
- rlJQlJ
The first 
S1J 
block divisions will have rl7 + 1 pixels, the
last Q1J - SlJ block divisions will have 
rl7 
pixels, where
the right-hand boundary pixels are included in the block
division to the left.
Example
3 block divisions,
(strips) first
co-ordinate
J --v- co-ordinate 1
0
	
255
Qlj = 3, Mj = 7, rlj - 2 1 
5 
l = 1
In order to know which pixels go into the block divisions, an
I,
ordering on the first co-ordinate must be made. This will be
the time-consuming part of the computation. The pixels
involved will belong to the training fields of category J.
1
This ordering process also determines the co-ordinate valve
of the cut. The cuts must be made so that no two are at the
same location. (The original requirements document resolves
this.)
i=2: X = r 2j Q2j + S 2
where X = r lj + 1 for the first S lj pixels
r lj for the others
Compute r 2 j = FIX 4X
2j
S 2 = X - r2jQ2j
The first S 2 secondary divisions in each strip will contain
r 2 + 1 pixels, (upper or "right" boundaries included), the
rest will contain r 2 Pixels.
Example	 T co-ordinate 2
255
0	
J -► co-ordinate 1
0
	 255
i=3, . . . P
This process should be continued for i=3, 	 .P. At each
stage, the pixels must be ordered in the ith co-ordinate
(channel) for block division inclusion determination.
P
There will be n Q., blocks at the conclusion.
i=1 1J
The volume of each block must be computed and stored. These
are computed from block boundaries which have been st}red.
Once the blocks have been formed for each category, the
options are exercised.
22tion to compute conditional probability density estimates:
f(Z I c j ) ti	 1(M j +1 VOLj
where: Z belongs to the sample fields,
Mj = number of pixels in category j training
fields,
VOL j = volume of the block of category j
containing the pixel Z.
Output these estimates.
Option to classify the test fields:
The "best" set of blocks must first be determined. In the
case where only Z categories are specified, the best set is
determined as follows.
Using the training fields of category 2 as test fields,
classify these fields using the blocks of category 1. Compute
the proportion of pixels misclassified. Next, take the
training fields of category 1 as test fields and classify
t
using the blocks of category 2. Compute the proportion mis-
classified. Select the block set yielding the smaller
proportion of misclassification for use in classification of
sample fields.
In the case of more than 2 categories (NOCAT>2), successive
combinations of NOCAT-1 block sets are used to classify the
remaining category training fields and the proportion of
misclassification is computed. The block combination of
blocks from NOCAT-1 block sets yielding the smaliast pro-
portion of misclassification is used in classification.
The process of classification is as follows. Given a set
of blocks and sample fields, for each pixel Z in the sample
fields, determine which block contains it. Next, for each
category, determine the proportion of pixels from the train-
ing fields in that block. The category having the Largest
proportion will claim the pixel Z. In case of ties, pixels
will be allocated among the categories involved in the ties.
7hese classification results will be outputted under the
EOD-LARSYS NL,PTAP format for subsequent display.
Option to select dots:
Here the combined set of blocks over all categories is uti-
lized. Normally, only one category will have been defined
under this option. (The equiprobable blocks will be built
from all the training fields.) The sample field provided
will be overlaid with the spatial grid provided. The D
(or fewer) grid intersections contained in each block will
be selected. If there are more than D intersections in a
particular block, the D dots closest (using L 2 distance) to
the center of the block will be chosen. If no grid is provided,
the D pixels closest to the center of each block will be selected.
i
The spatial co-ordinates of the set of selected dots will be
outpuc..^id.
Option to combine category training sets:
All training fields will be combined to form an equiprobable
block set. The proportion of pixels in each block from each
training category will be determined and outputted. Also,
the proportion for test field categories will be determined
and outputted.
3.2.1 LINKAGES
The Equiprobable Blocks processor will use the FORTRAN IV-G
compiler, IBM system routines, EOD-LARSYS utility routines, and
EOD-LARSYS common blocks GLOBAL, ISOLNK and INFORM. A new
common block EQUPRB will be created for other transfers of data
among subprograms.
3.2.2 INTERFACES
The Equiprobable Blocks processor will require as an input file
an MSS data tape (ERIPS-type unload tape). It will be invoked
from the MONTOR routine of EOD-LARSYS upon encountering a
control input card of the form $EQUPRB. Back-to-back runs with
the DISPLAY processor of EOD-LARSYS will be possible.
3.2.3 INPUTS
a. Processor card
Keyword
$EQUPRB
b. New Control Cards
Keyword	 Parameter	 Function
CHANNEL DATA-C1'C2' " 'CNOFET2 Channel numbers to be used.
(Default:	 1,2,...,16) These must be a subset of
channels available on the
MSS data tape.
NCPASS N Number of channels per
(Default: N-4) pass.	 Used to group
channels into passes
(acquisitions).
SUNANG TAPE Sunangles for sun angle
or correction.	 If TAPE
S 1 ,...SNA parameter specified, sun-
angles are extracted from
the MES Universally for-
matted data tape.
DATAFI INPUT/UNIT-N,FILE-M Unit and file numbers for
(Default:
	 N-3,	 M=1) an MSS data tape.
FORMAT U or F Universal or LARSYS III
MAPTAP OUTPUT/UNIT-N,FILE=M Unit number and beginning
(Default:	 N-2,	 M-1) file number for the optional
(Card ignored if classification map file
classification option group.
not specified)
DSTTAP OUTPUT/UNIT=N,FILE-M Unit number and beginning
(Default:
	
None) file number for the optional
(Card ignored if DST output of conditional
output option not probability density esti-
invoked) mates.
3-
N1 , CATNAMl,...
NNOCAT' CATNAMNOCAT
Category names corresponding
to ground truth numbers
GTNAN'
Keyword
GTTAP
Function
Unit and file numbers of
ground truth tape
INPUT/UNIT=N,FILE=M
N	 N=1 designator for strategy
(to be provided) for assign-
ing pixel category number
from subpixel category
numbers (used ii numbers
are not all the same)
GTVOTE
f
Keyword	 Parameter unction
CATNAM	 Category namel,...,
category na.meNOCAT
i
t
Category names.
These names should match
those specified in CLASSNAME
field description cards
appearing after control
card input.
BLOCK
DOTGRD
DOTMAX
OPTION
Q/{Qij} i=1,NOFET2,
j=1,NOCAT
or
K/Ni } j=1,N0CAT
If card omitted or
parameter field blank,
default block option
is used.
X/xl,.••'xDOTX
Y/yl"* ''yDOTY
(Default: Pick D pixel
closest to the center
each block).
D
(Default: D=1)
CNDPRB
CLASS
DOTS
Q blcck option.
K block option.
Spatial dot grid. If dot
option not invoked, this
card(s) is ignored.
Maximum number of clots
per block.
Compute conditional
probabilities.
Compute conditional
probabilities and classify
test pixel fields.
Select dots using spatial
grid overlay on test field.
GT	 Use ground truth information
to label training field
pixels.
'k1*11-/a
Keyword	 Parameter	 Function	 i
COMBIN	 Combine all category
training fields to make
a combined block set.
Compute proportion of
pixels per category per
block for training fields,
test fields.
PASS	 Perform all operations
separately by pass, create
output files by pass. Used
for providing input to
the multi-temporal Bayes
classifier. The number of
acquisitions is computed
from CHANNEL and NCPASS
control card information.
TEST	 Create blocks for each
category. Do not compute
conditional probability
density estimates. Compute
proportion of pixels in
test fields in each block
of each category. Also,
include pixel category
numbers in appropriate
positions in each two cut
subdivisions.
PRINT
	 PROJ/f(ci,ci))
	 Two-dimensional cuts of
(Default: Print all
	 blocks to be printed.
2-D cuts)
CNDPRB	 Print conditional
probability density
estimates.
Keyword Parameter	 Function
*END*
CLSMAP	 Print classification map.
NOTE: All results from
DOTS, COMBIN, and/or
TEST options are printed.
Terminates control card
input.
C. Field Cards
Field cards will be handled exactly as for EOD-LARSYS,
except that DESIGN header cards will include TRAIN, SAMPLE,
and TEST designators, as well as OTHER and UNIDENTIFIABLE.
3.2.4 OUTPUTS
Files MAPTAP and/or DSTTAP are output where appropriate.
3.2.5 STORAGE REQUIREMENTS
TBD
3.2.6 DESCRIPTION
The set of subprograms outlined below will provide the processor
building blocks.
Subprogram	 Function
EQUPRB	 Main driver.
SET15	 Reads control cards, set data and options.
RDDAT	 Reads training/test/sample fields, establish
field vertices and enclosing rectangles.
Reads MSS data tape, extracts radiance valves
for selected channels, perform sun angle
correction.
3
/fl
Subprogram	 Function
BLOCK	 Builds blocks for specified category.
COMBIN	 Combines blocks from specified categories.
CLSTST	 Classifies sample pixel fields.
SLTDOT	 Performs dot selection.
PIXPRO	 Computes proportion of pixels from each
training category and for test fields in
each block of specified block set.
PRPROJ Print 2-D cuts of specified block set.
PRDOTS Print spatial co-ordinates of selected dots.
PRMAP Prints classification map.
PRBLK Prints specified block set information.
PRCND Prints conditional probability density
estimates.
WRTCND Writes file of conditional probability
density estimates.
WRTMAP Writes classification map.
GTASG Read ground truth tape, assign category number
and hence name to training field pixels,	 thereby
breaking up the training fields by cacegury.
For any set of six subpixels of ground truth
corresponding to a training field pixel,
	
if
the six subpixels do not all have the same
category number, a strategy will be selected
to choose a number to label the training field
pixel.
•F I
a
/S
Common block /GLOBAL/ may be expanded to include the unit and
file number of DSTTAP. Common block /ISOLNK/ will pass the sun
angle information. A new common block /EQUPRB/ will pass block,
data, and option information among subprograms.
The overall architecture will follow that of EOD-LARSYS as
closely as possible.


Design specification for equiprobable blocks density estimatory/classifier/dot selector

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