imageMath a calculator for evaluating mathematical expressions with

1. imageMath a calculator for evaluating mathematical expressions with images, bands and spectral profiles Andreas Rabe andreas.rabe@geo.hu-berlin.de 22. Oktober 2012

2. Overview • imageMath evaluates mathematical expressions • arguments can be scalar numbers, images, bands or profiles • IDL based application for EnMAP-Box or ENVI

3. Understanding Operators • imageMath supports all IDL operators • extends the common operator logic to images 3

4. Understanding Operators What is a sensible operator logic? number + number = number 1 + 2 = 3

5. Understanding Operators What is a sensible operator logic? image + image = image • operator is applied component-wise

6. 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

7. Understanding Operators What is a sensible operator logic? Rules for argument pairs: image+image: no replication needed image+band: replicate band along image's spectral dimension image+profile: replication profile along image's spatial dimension image+number: replicate number along image's spatial and spectral dimension band+band: no replication needed band+profile: replicate band along profile's spectral dimension and replicate profile along band's spatial dimension band+number: replicate number along band's spatial dimension profile+profile: no replication needed profile+number: replicate number along profile's spectral dimension number+number: no replication needed

8. 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 = 1bversus 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.

9. 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:

10. Understanding Functions Image in Image out Trigonometric and Miscellaneous Math functions take an input image, calculate something for each componentand return a result image of same size.

11. 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.

12. 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.

13. Understanding Functions Image in Number out Band Statistics functions take an input image, calculate an image-wise statistic, and return a scalar number.

14. Usage Examples Masking an Image image*mask

15. Usage Examples Extracting Class-Specific Regions image*(class eq 1)

16. Usage Examples Scale Image Profiles between -10 and 10 float(image-spectralMinimum(image)) / spectralSpan(image) *20-10

17. Usage Examples Scale Image Bands between -10 and 10 float(image-spatialMinimum(image)) /spatialSpan(image) *20-10'

18. Usage Examples Spectral Similarity (root mean squared error) sqrt(spectralMean((image-profile)^2.))

19. Thank you very much for your attention. Any questions?