# Sub-pixel Sharpening

## Sub-pixel Sharpening of High Resolution Data

Funding agency: Belgian Federal Science Policy (BELSPO)

Research associate: Koen Mertens

Promoter: Robert De Wulf

Duration: 03/2002 – 08/2005

### Project objectives

This project aims at developing sub-pixel mapping algorithms using different heuristics:

When using linear optimization, the sub-pixel mapping algorithm searches the most suitable locations for the different class fractions within a pixel. Spatial dependence is assumed, i.e. the tendency for spatially proximate observations of a given property to be more alike than more distant observations. Land cover is spatially dependent both within and between pixels on the sole condition that the intrinsic scale of variation is not smaller than the scale of sampling imposed by the image pixels. Each class within a coarse resolution pixel is assigned a number of sub-pixels according to the fraction values. All this information is put into a number of linear equations. To solve these, the Simplex algorithm is used, maximising spatial dependence. NLC indicates how many different classes are involved, while NPLCi is the value calculated from the fraction images, to indicate how many sub-pixels are to be assigned to class i in that pixel.

When using genetic algorithms, every pixel is considered an individual, containing NP genes, representing sub-pixels. An initial random parent population is established. The population size determines the amount of individuals. The genes of each individual are allowed only NLC different values and only NPLCi genes of an individual are accorded to class i. Each individual is then given a Kappa-score depending on the location of its genes. The fittest individuals are chosen to become part of the mating population. New individuals originate from mating and crossover (cycle crossover). Mutation of a gene is not allowed because of the NPLCi restriction but inversion is permitted. The child population can then serve as a new parent population. This cycle repeats ‘number of generations’ times. The best individual to be evaluated throughout the entire process is kept as the final configuration of the pixel, during that iteration. Important parameters in this algorithm are the number of generations, the population size and the number of iterations. Sometimes a stable state is attained before the number of iterations is reached.

Although there is no real predefined standard yet for assessing the **accuracy of a sub-pixel mapping**, Cohen’s Kappa and the overall accuracy (fraction correctly classified) can be used to have an indication of how well the algorithm performs. An adjusted Kappa, that only takes into account, the sub-pixels that have a parent with a membership value for any class different from 1, could be a better measure. Obviously, in that case all sub-pixels are equal. These pixels will only raise Kappa without giving any information about the algorithm’s performance.

### Two key publications

Mertens, K., De Baets, B., Verbeke, L., De Wulf R., “A Sub-pixel Mapping Algorithm Based on Sub-pixel/pixel Spatial Attraction Models.” *INTERNATIONAL JOURNAL OF REMOTE SENSING* 27.15 (2006): 3293–3310.

Mertens, K., Verbeke, L., Westra, T., De Wulf, R., “Sub-pixel Mapping and Sub-pixel Sharpening Using Neural Network Predicted Wavelet Coefficients.” *REMOTE SENSING OF ENVIRONMENT* 91.2 (2004): 225–236.