1. Pathik Thakkar University of Texas at Dallas
Mixed Pixel Analysis
Pathik Thakkar
University of Texas at Dallas

2. Index Overview Problem Statement Introduction Literature Review
Proposed Method
Accuracy Assessment
Results
Conclusions
References

3. Overview
The spatial resolution of most satellite sensor systems imaging the earth is higher than the sizes of objects on ground.
Usually one pixel in the satellite image covers more than one object on the ground
Pixels in the image covered by more than one classes on the ground are mixed pixels.

4. Examples of Mixed Pixels
ASTER Image – 15 Meter Resolution
TM Image – 30 Meter Resolution

5. Examples of Mixed Pixels
ASTER Image - 4 Pixels (15 Meters)
TM Image – 1 Pixel (30 Meters)

6. Mixed Pixel Formation Reflectance of various classes
on the ground covered by the pixel
Resultant Pixel in the Image
Resultant Pixel in the image
With DN 160
(0.30 * * * 200)
Input class 1 – 30% Area with DN 100
Input class 2 – 20% Area with DN 150
Input class 3 – 50% Area with DN 200

7. Pure Pixels
Pure pixels also known as endmembers represent pure classes in the image.
Entire area covered by the pixel is usually the same type of land cover.
Usually very difficult to find pure pixels for all the classes from the image.
Key input to the unmixing process for mixed pixels.

8. Expected Unmixing Results
Unmixing should generate images with proportions of the all the classes in each image.
Output Image with
M Bands showing
proportion of each
pixel in each class
Original N-Band
Input Image
M - Pure Pixel
Classes/
Endmembers
Unmixing +

9. Problem Statement
Perform sub-pixel analysis from coarse resolution satellite imagery and estimate the abundance of composite materials from the image for the purpose of accurate image classification/interpretation using Neuro-fuzzy approach.

10. Introduction
Mixed Pixel analysis is the process of going beyond what’s visible from the image directly.
Mainly aims at deriving information about the proportions of objects/materials contained within each pixel.
Very well studied area of research with a lot of approaches to the problem

11. Introduction
Desirable properties of data to perform mixed-pixel analysis
High spatial resolution
Pure Pixels
Very high spectral resolution
Usually hyperspectral data with several hundred bands are used for such analysis
The electro-magnetic response of the ground material is contained in densely sampled bands

12. Introduction
The proposed approach performs the mixed pixel classification on Landsat TM Data
TM Data Does not have good enough spatial resolution (30 Meters)
TM Data Does not have good spectral resolution
(7 Bands)
This makes mixed-pixel analysis on Landsat TM data difficult.

13. Overview of the Process
Identify pure classes/ endmembers
Using in situ data
Using Statistical Methods like Pixel Purity Index or Simplex Maximum Angle Convex Cone (SMACC)
Using visual interpretation of a known area
Perform the unmixing
Using Linear Spectral Unmixing
Using Mixture Tuned Matched Fitting
Using Hypothesis Testing Hough Transform
Using Neuro-Fuzzy technique

14. Proposed Approach
A neuro-fuzzy system was evaluated for mixed pixel analysis using Landsat TM data.
A Learning Vector Quantization (LVQ) Neural Network was implemented to classify the image based on pure pixels obtained from visual interpretation.
Fuzzy memberships of all pixels in various classes were generated from the Neural Network classification output.
An application was developed in Visual C to evaluate the proposed method.
Results were compared with other established methods like Spectral Angle Mapper

15. Literature Review
Moody A. et al used a MLP based neural network and reported that the outputs of individual classes are proportional to their proportions.
When trained with pure pixels, the network consistently produces maximum outputs for largest sub-pixel class.
The network typically identifies the largest sub-pixel component but the certainty with which it does so decreases as pixels become increasingly mixed.

16. Literature Review
Foody G. and Arora M. used mixed pixels for training, allocation and testing strategies for supervised classifications.
They proposed a distance measure to estimate the accuracy of fuzzy classification methods.
Euclidean distance was used to obtain the difference between the actual ground data and classification results.
When the testing set comprised of pure pixels, maximum likelihood based approaches achieved higher classification results
Classifications using pure training and testing pixels were generally the most accurate.

17. Literature Review
Carpenter G. et al investigated the performance of ARTMAP neural networks for mixture estimation of vegetation mapping.
Site level vegetation fraction with each training set pixels were used in the training.
Concluded that topographic corrections of Landsat TM imagery does not improve results.

18. Literature Review Several other approaches
Multi-class land cover prediction at sub-pixel level using Hopfield network
Use of HTHH (Hypothesis Testing Hough Transform) to perform sub-pixel analysis
Linear Spectral Random Mixture Analysis of Hyperspectral Imagery
Recovering more classes than available bands for sets of mixed pixels
Illumination Invariant Unmixing of Sets of Mixed Pixels

19. Methodology A NeuroFuzzy system was used to perform analysis
Originally proposed by Qiu et al. to improve the understanding of the neural network classifiers using fuzzy systems
Uses a LVQ based neural network to perform classification

20. Methodology Four major components of the architecture
Fuzzification Interface
Neurofuzzy Learning
Neurofuzzy classification

21. Fuzzification Interface
Inputs into the system are fuzzified using a Gaussian function
A sigmoid function is not capable of modeling a range such as a class interval.
A triangular function will not ensure that all inputs are fuzzified in some class.
These are the reasons why Gaussian function was used.

22. Fuzzification Interface
Does not guarantee membership
Closed Function
Difficult to model class intervals
Open Function
Closed function with Infinite memberships

23. Neuro-Fuzzy Learning
Two parameters (c, σ) of the Gaussian function are fine-tuned by the fuzzy neural network algorithm.
Traditional LVQ learning algorithm is used for the training of parameter c
If x belongs to c Otherwise

24. NeuroFuzzy Learning
A new rule was proposed that simulates the standard deviation parameter of the Gaussian Function
η is the learning rate.
If x belongs to c Otherwise

25. Neuro-Fuzzy Classification and Defuzzification
Defuzzification is the reverse of the fuzzification process.
Normally hard classification maps are obtained by comparing all the membership grades of a pixel.
Here, the membership of each pixel in each class was normalized and fuzzy class memberships were generated.

26. Architecture of the Network

27. Accuracy Assessment
Orthophoto images were used to derive accurate information about the proportions of the mixed pixels of the original image.
Polygons were digitized in ArcGIS over the pixel area in to four categories.
Accurate information about 24 pixels was derived from the image.

28. Accuracy Assessment Orthophoto Original Pixel Overlaid on the Image
Identified Proportions

29. Accuracy Assessment
The proportions were calculated from the outputs of Neuro-fuzzy and linear unmixing results and compared with the actual data.
A squared distance error was used to find the total error in the selected set of mixed pixels for each class.

30. Results
Performed the analysis using the proposed method on a Landsat TM Image
Using the same set of pure pixels/Training data performed the analysis using Linear Spectral Unmixing

31. Input Dataset Landsat TM Image 30x30 Meter spatial resolution
6 Bands Spectral Resolution
False Color image of bands 4-3-2
Four classes Identified
Urban
Water
Vegetation
Dry Land

32. Regions of Interest

33. Network Training

34. Urban Class
NeuroFuzzy
Linear Unmixing

35. Vegetation Class
NeuroFuzzy
Linear Unmixing

36. Water Class
NeuroFuzzy
Linear Unmixing

37. Dry Land Class
NeuroFuzzy
Linear Unmixing

38. Error Plot

39. Analysis
Conclusions about the analysis results were derived from visual interpretation of all the results.
Neural Network classifies the primary components of the pixel correctly.
However, the accuracy of proportion estimation is a question.
From visual interpretation, it looks like the accuracies are less when there are more components in the mixed pixel.

40. Analysis Quantitative evaluations confirm that!
Primary reason for the error introduced in the analysis
Difference between
Endmembers
Class Means
A more rigorous error estimation approach with custom software tools will provide more accurate evaluations.

41. Next steps
Modify the network architecture to train it using endmembers and not class means
A probable candidate is a LVQ network instead of the modified fuzzy LVQ
Estimate the amounts of error introduced with more rigorous error estimation techniques
Use mixed pixels in training

42. These left me thinking!!
“The resolution of the image is determined by the smallest distance that can be identified between two objects”
What will be the gray value of such a pixel? Can we
make out the white spot in the resultant pixel in the
image?

43. References
(Moody, Gopal et al. 1996; Foody 1997; Foschi and Smith 1997; Warner and Shank 1997; Brown, Lewis et al. 2000; Stefanov, Ramsey et al. 2001; Hao, Bin et al. 2004; Liu, Seto et al. 2004; Wang and Zhang 2004)
Brown, M., H. G. Lewis, et al. (2000). "Linear spectral mixture models and support vector machines for remote sensing." Ieee Transactions on Geoscience and Remote Sensing 38(5):
Foody, G. M. (1997). "Fully fuzzy supervised classification of land cover from remotely sensed imagery with an artificial neural network." Neural Computing & Applications 5(4):
Foschi, P. G. and D. K. Smith (1997). "Detecting subpixel woody vegetation in digital imagery using two artificial intelligence approaches." Photogrammetric Engineering and Remote Sensing 63(5):
Hao, Z., W. Bin, et al. (2004). A new scheme for detection and classification of subpixel spectral signatures in multispectral data. Advances in Neural Networks - Isnn 2004, Pt :
Liu, W. G., K. C. Seto, et al. (2004). "ART-MMAP: A neural network approach to subpixel classification." Ieee Transactions on Geoscience and Remote Sensing 42(9):
Moody, A., S. Gopal, et al. (1996). "Artificial neural network response to mixed pixels in coarse-resolution satellite data." Remote Sensing of Environment 58(3):
Stefanov, W. L., M. S. Ramsey, et al. (2001). "Monitoring urban land cover change: An expert system approach to land cover classification of semiarid to arid urban centers." Remote Sensing of Environment 77(2):
Wang, Y. Q. and X. S. Zhang (2004). "A SPLIT model for extraction of subpixel impervious surface information." Photogrammetric Engineering and Remote Sensing 70(7):
Warner, T. A. and M. Shank (1997). "An evaluation of the potential for fuzzy classification of multispectral data using artificial neural networks." Photogrammetric Engineering and Remote Sensing 63(11):

44. Questions ?