This document discusses change detection using a hypothesis test-based approach. It describes how hypotheses are formulated as either a null hypothesis (H0) of no change or an alternative hypothesis (Hk) of a change at a given position k between images. A generalized likelihood ratio test is used to compute the difference in log-likelihood between the hypotheses. A threshold is then applied to determine if the difference is significant enough to indicate a true change. The approach aims to detect step changes over time in images for applications like monitoring natural disasters. Non-local filtering can also be used to increase the effective number of looks and improve detection performance.

1. CHANGE DETECTION
HYPOTHESIS TEST BASED
APPROACH
By
Reshmi B S
Koshy G

2. WHAT IS A HYPOTHESIS?
• Assumption which has to be proved or disproved
• A statement about the value of a population parameter
developed for the purpose of testing.
• Ex: The mean monthly income from all sources for
systems analysts is $3,625.
• Twenty percent of all juvenile offenders ultimately are
caught and sentenced to prison.

3. Hypothesis testing
• A procedure, based on sample evidence and probability
theory,
• Used to determine whether the hypothesis is a
reasonable statement and should not be rejected, or is
unreasonable and should be rejected
• Hypothesis testing is a statistical method that is used in
making statistical decisions using experimental data.
• Hypothesis Testing is basically an assumption that we
make about the population parameter.

4. Null hypothesis and Alternate
hypothesis
• Null Hypothesis – statement about the value of a
population parameter.
• Null hypothesis is a statistical hypothesis that assumes
that the observation is due to a chance factor.
• Represent a theory which has been put forward, either
because it is believed to be true
• Compare two method A and B- proceeding with two
methods are equally useful

5. • Alternate Hypothesis – statement that is accepted if
evidence proves null hypothesis to be false.
• the alternative hypothesis shows that observations are
the result of a real effect.
• Method A is better than Method B

7. • Select the appropriate test statistic and level of
significance.
• Refers to the degree of significance in which we accept or
reject the null-hypothesis. Usually 5%.
• State the decision rules.
• The decision rules state the conditions under which the
null hypothesis will be accepted or rejected.

8. • Compare the computed test statistic with critical value.
• If the computed value is within the rejection region(s), we
reject the null hypothesis; otherwise, we do not reject the
null hypothesis.
• Interpret the decision.
• State a conclusion in the context of the original problem.

9. ERROR

10. CHANGE DETECTION
• For monitoring and mapping purposes
• For the analysis of regions affected by natural disasters
or man-made changes.
• It is based on the detection of a step change pattern with
a generalized maximum likelihood ratio test

12. Hypotheses
• To test two hypotheses in each position k of the time
series of n images : •
• H0: there is no change (all the intensities in time have the
same underlying reflectivity); •
• Hk: there is a change of reflectivities at position k
(between tk and tk+1);
• The likelihood Lk of Hk is given by :

13. • The true reflectivity are unknown
• A generalized maximum likelihood ratio test is computed
• Replaces these values by their maximum likelihood
estimators which are the empirical means
• Test depends only on ratio of reflectivities

14. • The difference of log-likelihood between Hk and H0 is:
• with L the number of looks.
• Ratio of intensities, R
• Hk has always a better likelihood than H0: whatever the “true”
situation, it is easier to fit the intensity values with two
reflectivities than with one.
• To determine for which value ΔHk there is the more important
change, and if this change is significant

15. Threshold
• A threshold has to be set to decide whether the ΔHk value
represents a change or not
• The distributions of ΔHk depend on 4 parameters:
• the number of looks L,
• the ratio R of intensities,
• the position k of the discontinuity
• the number n of images

16. DETECTION
• As the number of looks increases performances improves
• To increase the equivalent number of looks of the time
series filter is used
• Filter allows the computation of an equivalent number of
looks Leq for each pixel
• where w(s, t) are the weights computed by the non local
approach in the search window.

19. REFERENCES
• Michelle M. Horta, Nelson D. A. Mascarenhas , Change Detection In Multitemporal Hr
Sar Images: A Hypothesis Test-based Approach, IEEE International Geoscience And
Remote Sensing Symposium, 2012
• I. Kanellopoulos, G. G. Wilkinson T, Moons, Machine Vision and Advanced Image
Processing in Remote Sensing, Springer, 1st edition 1999