1. 2011 IEEE International Geoscience and Remote Sensing Symposium 26/07/2011 Vancouver, Canada SATELLITE IMAGE ARTIFACTS DETECTION BASED ON COMPLEXITY DISTORTION THEORY Avid ROMAN GONZALEZ Mihai DATCU Avid Roman Gonzalez

2. OUTLINE The Artifacts, problematic. Rate-Distortion Function Kolmogorov Complexity Kolmogorov’s Structure Function Experiments and Results Conclusions Avid Roman Gonzalez

3. ARTIFACTS : The artifacts are artificial structures that represent a structured perturbation of the signal. Therefore, these artifacts induce errors in the indexation of the images. 3/47 Avid Roman Gonzalez

4. ARTIFACTS KINDS : Aliasing Strips . . . Saturation Blocking 4/47 Avid Roman Gonzalez

7. RATE-DISTORTION FUNCTION: The Rate-Distortion (RD) Functionis given by the minimum value of mutual information between source and receiver under some distortion restrictions. The RD function shows how much compression (lossy compression) can be used without loss of distortion preset value. 7/47 Avid Roman Gonzalez

8. Images with different compression factor (cf) Imagecf 1 Imagecf 2 Imagecf 2 . . . Imagecf n Decompression Image Features Vector (compressionerrors) JPEG LossyCompression +- Classification For the artifacts detection, we propose to use the RD function obtained by compression of the image with different compression factors and examine how an artifact can have a high degree of regularity or irregularity for compression. 8/47 Avid Roman Gonzalez

9. KolmogorovComplexity is the length of a shortest program to compute x on a universal Turing machine K(x) is a non calculable function 15 x (Write 0) Write 1010001010111011 9/47 Avid Roman Gonzalez

10. Kolmogorov’sStructureFunction An approximation of the RD curve using the Kolmogorov complexity theory could be the Kolmogorov Structure Function (KSF). The relation between the individual data and its explanation (model) is expressed by Kolmogorov’s structure function. The original Kolmogorov structure function for a data x is defined by: Where: S is a contemplated model for x. αis a non-negative integer value bounding the complexity of the contemplated S. 10/47 Avid Roman Gonzalez

11. Kolmogorov’sStructureFunctionforTextureDiscrimination To evaluate the behavior of the KSF for different textures, we use de Brodatz images databases. We show the textures used for this experiments. Avid Roman Gonzalez

12. We can observe that the KSF can discriminate more or less the different structure, the curve KSF has a similar shape for each texture group, but the level is different. Avid Roman Gonzalez

13. ArtifactsDetectionUsingKolmogorov’sStructureFunctionApproach To detect artifacts using Kolmogorov Structure Function (KSF), the first step is to watch the behavior of the KSF curve for images with artifacts and images without artifact. One aspect to consider is how to generate the candidates for the necessary space S. For this purpose, we have generated the candidates using 2 methods: Candidates generation by JPEG lossy compression and Candidates generation by genetic algorithm. Avid Roman Gonzalez

14. KSF using jpeg lossy compression KSF using genetic algorithm We can observe that the better discrimination is done when we generate the candidates for the space S using the JPEG lossy compression. Also using JPEG lossy compression the approximation to the Rate-distortion analysis is better. Avid Roman Gonzalez

15. We use the jpeg lossy compression for generate candidates and to draw the Kolmogorov Structure Function for each patch of a satellite image and try to detect the artifacts. For this experiments we use an image with aliasing introduces manually. Aliasing detection in city environmental using KSF and candidate generation with JPEG lossy compression Avid Roman Gonzalez

16. CONCLUSIONS The Kolmogorov structure function represents the relationship between an element or data with its model, structure, or explanation. In this work, we have used the Kolmogorov structure function as a approximation of rate-distortion function using Kolmogorov complexity theory and the complexity-distortion theory, so we can examine the complexity of the images to be analyzed, this complexity would be related to the presence or absence of artifacts. 16/47 Avid Roman Gonzalez

17. CONCLUSIONS The generation of candidates for to calculation the Kolmogorov structure function is an important step, in this work was done experiments using 2 methods, generation of candidates by jpeg lossy compression and candidate generation using genetic algorithms, we obtain better results using lossy jpeg compression. 17/47 Avid Roman Gonzalez

18. THANK YOU FOR YOUR ATTENTION avid.roman-gonzalez@ieee.org http://www.avid-romangonzalez.com Avid Roman Gonzalez