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Geographisches Institut der Humboldt-Universität zu Berlin
Abteilung Geomatik
imageMath
a calculator for evaluating
mathematical expressions with
images, bands and spectral profiles
Andreas Rabe
[email protected]
22. Oktober 2012
Geographisches Institut der Humboldt-Universität zu Berlin
Overview
• imageMath evaluates mathematical expressions
• arguments can be scalar numbers, images, bands or profiles
• IDL based application for EnMAP-Box or ENVI
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Geographisches Institut der Humboldt-Universität zu Berlin
Understanding Operators
• imageMath supports all IDL operators
• extends the common operator logic to images
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Geographisches Institut der Humboldt-Universität zu Berlin
Understanding Operators
What is a sensible operator logic?
number + number = number
1+2=3
Geographisches Institut der Humboldt-Universität zu Berlin
Understanding Operators
What is a sensible operator logic?
image + image = image
• operator is applied component-wise
Geographisches Institut der Humboldt-Universität zu Berlin
Understanding Operators
What is a sensible operator logic?
image + band + number = image
+
+
replicate along missing dimensions
+
+
• missing dimensions are replicated
• operator is applied component-wise
Geographisches Institut der Humboldt-Universität zu Berlin
Understanding Operators
What is a sensible operator logic?
Rules for argument pairs:
image+image:
image+band:
image+profile:
image+number:
no replication needed
replicate band along image's spectral dimension
replication profile along image's spatial dimension
replicate number along image's spatial and spectral dimension
band+band:
band+profile:
band+number:
no replication needed
replicate band along profile's spectral dimension
and replicate profile along band's spatial dimension
replicate number along band's spatial dimension
profile+profile:
profile+number:
no replication needed
replicate number along profile's spectral dimension
number+number:
no replication needed
Geographisches Institut der Humboldt-Universität zu Berlin
Understanding Data Types
• imageMath supports all IDL data types
• casting functions and data type postfixes
casting functions and postfixes
1. = 1.
versus
float(1) = 1.
1b = 1b
versus
byte(1) = 1b
integer and floating-point division
1/2 = 0
versus
1./2. = 0.5
overflows and underflows
-1b = 255b (underflow)
10^5 = -31072 (overflow)
0-1b = -1 (no underflow, implicite type casting)
If your calculated images are all black, or appear to be randomly
generated, it is most likely an issue of data types.
Geographisches Institut der Humboldt-Universität zu Berlin
Understanding Functions
• imageMath functions can be arbitrary complex
• from simple type casting functions like byte() or float()
• to whole processing chains
Set of predefined functions:
Geographisches Institut der Humboldt-Universität zu Berlin
Understanding Functions
Image in Image out
Trigonometric and Miscellaneous Math functions take an
input image, calculate something for each component and
return a result image of same size.
Geographisches Institut der Humboldt-Universität zu Berlin
Understanding Functions
Image in Band out
Profile Statistics functions take an input image, calculate a
profile-wise statistic for each profile, and return a result band
of same spatial size.
Geographisches Institut der Humboldt-Universität zu Berlin
Understanding Functions
Image in Profile out
Band Statistics functions take an input image, calculate a
band-wise statistic for each band, and return a result profile
of same spectral size.
Geographisches Institut der Humboldt-Universität zu Berlin
Understanding Functions
Image in Number out
Band Statistics functions take an input image, calculate an
image-wise statistic, and return a scalar number.
Geographisches Institut der Humboldt-Universität zu Berlin
Usage Examples
Masking an Image
image*mask
Geographisches Institut der Humboldt-Universität zu Berlin
Usage Examples
Extracting Class-Specific Regions
image*(class eq 1)
Geographisches Institut der Humboldt-Universität zu Berlin
Usage Examples
Scale Image Profiles between -10 and 10
float(image-spectralMinimum(image))
/ spectralSpan(image)
*20-10
Geographisches Institut der Humboldt-Universität zu Berlin
Usage Examples
Scale Image Bands between -10 and 10
float(image-spatialMinimum(image))
/spatialSpan(image)
*20-10'
Geographisches Institut der Humboldt-Universität zu Berlin
Usage Examples
Spectral Similarity (root mean squared error)
sqrt(spectralMean((image-profile)^2.))
Geographisches Institut der Humboldt-Universität zu Berlin
Thank you very much for your attention.
Any questions?
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