#!/bin/bash
#
# Developed by Fred Weinhaus 10/18/2013 .......... revised 4/25/2015
#
# ------------------------------------------------------------------------------
# 
# Licensing:
# 
# Copyright © Fred Weinhaus
# 
# My scripts are available free of charge for non-commercial use, ONLY.
# 
# For use of my scripts in commercial (for-profit) environments or 
# non-free applications, please contact me (Fred Weinhaus) for 
# licensing arrangements. My email address is fmw at alink dot net.
# 
# If you: 1) redistribute, 2) incorporate any of these scripts into other 
# free applications or 3) reprogram them in another scripting language, 
# then you must contact me for permission, especially if the result might 
# be used in a commercial or for-profit environment.
# 
# My scripts are also subject, in a subordinate manner, to the ImageMagick 
# license, which can be found at: http://www.imagemagick.org/script/license.php
# 
# ------------------------------------------------------------------------------
# 
####
#
# USAGE: moments [-z] infile
# USAGE: moments [-h or -help]
# 
# OPTIONS:
# 
# -z     Replaces NAN or DBZ with 0; default shows NAN and/or DBZ
# 
###
# 
# NAME: MOMENTS 
# 
# PURPOSE: To compute shift, scale and rotation invariant image moments as well 
# as elliptical shape descriptors.
# 
# DESCRIPTION: ENTROPY computes Hu and Maitra shift, scale and rotation 
# invariant image moments as well as elliptical shape descriptors. Currently 
# this script is limited to grayscale images. If the input is not grayscale, 
# it will be converted to grayscale. The list of moments and shape descriptors 
# is sent to the terminal.
#
# OPTIONS: 
# 
# -z ... replace (not a number) NAN (from square root of negative value) or 
# (divide by zero) DBZ with 0 in Maitra moments. The default is to show NAN 
# and/or DBZ.
# 
# REFERENCES:
# http://en.wikipedia.org/wiki/Image_moments
# http://www.via.cornell.edu/ece547/text/survey.pdf
# 
# CAVEAT: No guarantee that this script will work on all platforms, 
# nor that trapping of inconsistent parameters is complete and 
# foolproof. Use At Your Own Risk. 
# 
######
# 

# set default values
zero="no"		# replace NAN with 0; choices are; yes or no; default=no


# set directory for temporary files
dir="."    # suggestions are dir="." or dir="/tmp"

# set up functions to report Usage and Usage with Description
PROGNAME=`type $0 | awk '{print $3}'`  # search for executable on path
PROGDIR=`dirname $PROGNAME`            # extract directory of program
PROGNAME=`basename $PROGNAME`          # base name of program
usage1() 
	{
	echo >&2 ""
	echo >&2 "$PROGNAME:" "$@"
	sed >&2 -e '1,/^####/d;  /^###/g;  /^#/!q;  s/^#//;  s/^ //;  4,$p' "$PROGDIR/$PROGNAME"
	}
usage2() 
	{
	echo >&2 ""
	echo >&2 "$PROGNAME:" "$@"
	sed >&2 -e '1,/^####/d;  /^######/g;  /^#/!q;  s/^#*//;  s/^ //;  4,$p' "$PROGDIR/$PROGNAME"
	}


# function to report error messages
errMsg()
	{
	echo ""
	echo $1
	echo ""
	usage1
	exit 1
	}


# function to test for minus at start of value of second part of option 1 or 2
checkMinus()
	{
	test=`echo "$1" | grep -c '^-.*$'`   # returns 1 if match; 0 otherwise
    [ $test -eq 1 ] && errMsg "$errorMsg"
	}

# test for correct number of arguments and get values
if [ $# -eq 0 ]
	then
	# help information
   echo ""
   usage2
   exit 0
elif [ $# -gt 2 ]
	then
	errMsg "--- TOO MANY ARGUMENTS WERE PROVIDED ---"
else
	while [ $# -gt 0 ]
		do
			# get parameter values
			case "$1" in
		  -h|-help)    # help information
					   echo ""
					   usage2
					   exit 0
					   ;;
			    -z)    # get  zero
					   zero="yes"
					   ;;
				 -)    # STDIN and end of arguments
					   break
					   ;;
				-*)    # any other - argument
					   errMsg "--- UNKNOWN OPTION ---"
					   ;;
		     	 *)    # end of arguments
					   break
					   ;;
			esac
			shift   # next option
	done
	#
	# get infile
	infile="$1"
fi

# test that infile provided
[ "$infile" = "" ] && errMsg "--- NO INPUT FILE SPECIFIED ---"


# setup temporary images
tmpA1="$dir/moments_1_$$.mpc"
tmpB1="$dir/moments_1_$$.cache"
trap "rm -f $tmpA1 $tmpB1;" 0
trap "rm -f $tmpA1 $tmpB1; exit 1" 1 2 3 15
trap "rm -f $tmpA1 $tmpB1; exit 1" ERR

# read the input image into the temporary cached image and test if valid
convert -quiet "$infile" -colorspace gray -depth 8 +repage "$tmpA1" ||
	echo "--- 1 FILE $infile DOES NOT EXIST OR IS NOT AN ORDINARY FILE, NOT READABLE OR HAS ZERO size  ---"


# references
# http://en.wikipedia.org/wiki/Image_moments
# http://www.via.cornell.edu/ece547/text/survey.pdf
# Moment Functions In Image Analysis Theory And Application, R Mukundan and K R Ramakrishnan, Chapter 2. (see link below)
# http://books.google.com/books?id=SEAOgA-oCIkC&pg=PA15&lpg=PA15&dq=image+moment+kurtosis&source=bl&ots=ngcPHeIpy-&sig=6fT1roqvx4usTwnib4UxaPsWDX8&hl=en&sa=X&ei=8VVcUqSsOujUiwKC2IGoBA&ved=0CDkQ6AEwBA#v=onepage&q=image%20moment%20kurtosis&f=false

# compute raw moments
momentArr=(`convert $tmpA1 txt:- | tail -n +2 | tr -cs "0-9\n" " "  |\
awk -v PREC="double" '# AWK to compute raw image moments for grayscale image
{ M00 += $3; M10 += $1*$3; M01 += $2*$3; M11 += $1*$2*$3; 
M20 += $1*$1*$3; M02 += $2*$2*$3; M21 += $1*$1*$2*$3; M12 += $1*$2*$2*$3; M22 += $1*$1*$2*$2*$3; 
M30 += $1*$1*$1*$3; M03 += $2*$2*$2*$3; }
END { print M00, M10, M01, M11, M20, M02, M21, M12, M22, M30, M03; } '`)

M00=${momentArr[0]}
M10=${momentArr[1]}
M01=${momentArr[2]}
M11=${momentArr[3]}
M20=${momentArr[4]}
M02=${momentArr[5]}
M21=${momentArr[6]}
M12=${momentArr[7]}
M22=${momentArr[8]}
M30=${momentArr[9]}
M03=${momentArr[10]}

# compute total mass (intensity) (area if binary)
T=$M00

# compute mean
mean=`convert $tmpA1 -precision 15 -format "%[fx:$T/(w*h)]" info:`


# compute center of mass (centroid)
centx=`convert -ping $tmpA1 -precision 15 -format "%[fx:w/2]" info:`
centy=`convert -ping $tmpA1 -precision 15 -format "%[fx:h/2]" info:`
cx=`convert xc: -precision 15 -format "%[fx:$M00==0?$centx:$M10/$M00]" info:`
cy=`convert xc: -precision 15 -format "%[fx:$M00==0?$centy:$M01/$M00]" info:`


# compute central moments
momentArr=(`convert $tmpA1 txt:- | tail -n +2 | tr -cs "0-9\n" " "  |\
awk -v PREC="double" -v cx="$cx" -v cy="$cy" '# AWK to compute central moments for grayscale image
{ x=($1-cx); y=($2-cy); m11 += x*y*$3; 
m20 += x*x*$3; m02 += y*y*$3; m21 += x*x*y*$3; m12 += x*y*y*$3; m22 += x*x*y*y*$3; 
m30 += x*x*x*$3; m03 += y*y*y*$3; }
END { print m11, m20, m02, m21, m12, m22, m30, m03; } '`)


m00=$M00
m10=0
m01=0
m11=${momentArr[0]}
m20=${momentArr[1]}
m02=${momentArr[2]}
m21=${momentArr[3]}
m12=${momentArr[4]}
m22=${momentArr[5]}
m30=${momentArr[6]}
m03=${momentArr[7]}


# compute radii of gyration
Rx=`convert xc: -precision 15 -format "%[fx:$m00==0?0:sqrt($M02/$M00)]" info:`
Ry=`convert xc: -precision 15 -format "%[fx:$m00==0?0:sqrt($M20/$M00)]" info:`
Rc=`convert xc: -precision 15 -format "%[fx:$m00==0?0:sqrt(($m20+$m02)/$m00)]" info:`


# compute the elliptical angle, major (a) and minor (b) axes eccentricity (e) and intensity (k)
# set angle to 0 for constant grayscale, since m20=m02
angle=`convert xc: -precision 15 -format "%[fx:$m20==$m02?0:0.5*atan(2*$m11/($m20-$m02))]" info:`
degrees=`convert xc: -precision 15 -format "%[fx:$angle*180/pi]" info:`
a=`convert xc: -precision 15 -format "%[fx:$m00==0?0:sqrt((2/$m00)*(($m20+$m02)+sqrt(4*$m11*$m11+($m20-$m02)*($m20-$m02))))]" info:`
b=`convert xc: -precision 15 -format "%[fx:$m00==0?0:sqrt((2/$m00)*(($m20+$m02)-sqrt(4*$m11*$m11+($m20-$m02)*($m20-$m02))))]" info:`
e=`convert xc: -precision 15 -format "%[fx:$a==0?0:sqrt(1-($b/$a))]" info:`
k=`convert xc: -precision 15 -format "%[fx:$a==0?0:$m00/(pi*$a*$b)]" info:`

# compute normalized moments
n00=1
n01=0
n10=0
n11=`convert xc: -precision 15 -format "%[fx:$m00==0?0:$m11/pow($m00,(1+(1+1)/2))]" info:`
n20=`convert xc: -precision 15 -format "%[fx:$m00==0?0:$m20/pow($m00,(1+(2+0)/2))]" info:`
n02=`convert xc: -precision 15 -format "%[fx:$m00==0?0:$m02/pow($m00,(1+(0+2)/2))]" info:`
n21=`convert xc: -precision 15 -format "%[fx:$m00==0?0:$m21/pow($m00,(1+(2+1)/2))]" info:`
n12=`convert xc: -precision 15 -format "%[fx:$m00==0?0:$m12/pow($m00,(1+(1+2)/2))]" info:`
n22=`convert xc: -precision 15 -format "%[fx:$m00==0?0:$m22/pow($m00,(1+(2+2)/2))]" info:`
n30=`convert xc: -precision 15 -format "%[fx:$m00==0?0:$m30/pow($m00,(1+(3+0)/2))]" info:`
n03=`convert xc: -precision 15 -format "%[fx:$m00==0?0:$m03/pow($m00,(1+(0+3)/2))]" info:`


# compute hu invariant moments
I1=`convert xc: -precision 15 -format "%[fx:$n20+$n02]" info:`
I2=`convert xc: -precision 15 -format "%[fx:($n20-$n02)^2 + 4*$n11*$n11]" info:`
I3=`convert xc: -precision 15 -format "%[fx:($n30-3*$n12)^2 + (3*$n21-$n03)^2]" info:`
I4=`convert xc: -precision 15 -format "%[fx:($n30+$n12)^2 + ($n21+$n03)^2]" info:`
I5=`convert xc: -precision 15 -format "%[fx:($n30-3*$n12)*($n30+$n12)*( ($n30+$n12)^2 - 3*($n21+$n03)^2 ) + (3*$n21-$n03)*($n21+$n03)*( 3*($n30+$n12)^2 - ($n21+$n03)^2 )]" info:`
I6=`convert xc: -precision 15 -format "%[fx:($n20-$n02)*( ($n30+$n12)^2 - ($n21+$n03)^2 ) + 4*$n11*($n30+$n12)*($n21+$n03)]" info:`
I7=`convert xc: -precision 15 -format "%[fx:(3*$n21 -$n03)*($n30+$n12)*( ($n30+$n12)^2 - 3*($n21+$n03)^2 ) - ($n30-3*$n12)*($n21+$n03)*( 3*($n30+$n12)^2 - ($n21+$n03)^2 )]" info:`
I8=`convert xc: -precision 15 -format "%[fx:$n11*( ($n30+$n12)^2 - ($n03+$n21)^2 ) - ($n20-$n02)*($n30+$n12)*($n03+$n21)]" info:`



# compute maitra invariant moments
# NOTE: sqrt means that get NAN for B1 or B4, when I2 or I5 are negative.
# Note sure if best to force to zero or leave as NAN
if [ "$zero" = "yes" ]; then
	B1=`convert xc: -precision 15 -format "%[fx:$I2<0?0:sqrt($I2)/($I1+quantumscale)]" info:`
else
	[ "$I1" = "0" ] && B1="DBZ" || \
		B1=`convert xc: -precision 15 -format "%[fx:sqrt($I2)/($I1+quantumscale)]" info:`
fi

[ "$I1" = "0" -o "$I2" = "0" -a "$zero" = "no" ] && B2="DBZ" || \
	B2=`convert xc: -precision 15 -format "%[fx:$I3*$m00/($I1*$I2+quantumscale)]" info:`

[ "$I3" = "0"  -a "$zero" = "no" ] && B3="DBZ" || \
	B3=`convert xc: -precision 15 -format "%[fx:$I4/($I3+quantumscale)]" info:`

if [ "$zero" = "yes" ]; then
	B4=`convert xc: -precision 15 -format "%[fx:$I5<0?0:sqrt($I5)/($I4+quantumscale)]" info:`
else
	[ "$I4" = "0" ] && B4="DBZ" || \
		B4=`convert xc: -precision 15 -format "%[fx:sqrt($I5)/($I4+quantumscale)]" info:`
fi

[ "$I1" = "0" -o "$I4" = "0"  -a "$zero" = "no" ] && B5="DBZ" || \
	B5=`convert xc: -precision 15 -format "%[fx:$I6/($I1*$I4+quantumscale)]" info:`

[ "$I3" = "0" -a "$zero" = "no" ] && B6="DBZ" || \
	B6=`convert xc: -precision 15 -format "%[fx:$I4/($I3+quantumscale)]" info:`



#list results
echo ""
echo "Image: $infile"
echo ""
echo "Raw Moments"
echo "M00=$M00"
echo "M10=$M10"
echo "M01=$M01"
echo "M11=$M11"
echo "M20=$M20"
echo "M02=$M02"
echo "M21=$M21"
echo "M12=$M12"
echo "M22=$M22"
echo "M30=$M30"
echo "M03=$M03"
echo ""
echo "Central Moments"
echo "m00=$m00"
echo "m10=$m10"
echo "m01=$m01"
echo "m11=$m11"
echo "m20=$m20"
echo "m02=$m02"
echo "m21=$m21"
echo "m12=$m12"
echo "m22=$m22"
echo "m30=$m30"
echo "m03=$m03"
echo ""
echo "Normalized Central Moments"
echo "n00=$n00"
echo "n10=$n10"
echo "n01=$n01"
echo "n11=$n11"
echo "n20=$n20"
echo "n02=$n02"
echo "n21=$n21"
echo "n12=$n12"
echo "n22=$n22"
echo "n30=$n30"
echo "n03=$n03"
echo ""
echo "Hu Invariant Moments"
echo "I1=$I1"
echo "I2=$I2"
echo "I3=$I3"
echo "I4=$I4"
echo "I5=$I5"
echo "I6=$I6"
echo "I7=$I7"
echo "I8=$I8"
echo ""
echo "Maitra Invariant Moments"
echo "B1=$B1"
echo "B2=$B2"
echo "B3=$B3"
echo "B4=$B4"
echo "B5=$B5"
echo "B6=$B6"
echo ""
echo ""
echo "Miscellaneous Parameters"
echo "Total Mass = $T"
echo "Mean = $mean"
echo "X Center of Mass (XCOM) = $cx"
echo "Y Center of Mass (YCOM) = $cy"
echo "X Radius of Gyration = $Rx"
echo "Y Radius of Gyration = $Ry"
echo "COM Radius of Gyration = $Rc"
echo "Ellipse Angle (radians) = $angle"
echo "Ellipse Angle (degrees) = $degrees"
echo "Ellipse Semi-Major Axis = $a"
echo "Ellipse Semi-Minor Axis = $b"
echo "Ellipse Eccentricity = $e"
echo "Ellipse Intensity = $k"
echo ""

exit 0