# Presentation: 390313

## Thematic Mapping

- from
- Mixed Spatial Data Types

*John Richards*
*Research School of Information Sciences and Engineering*
*The Australian National University*

## The essential problem

- multispectral

- hyperspectral

- radar

- categorical and topographic

- thematic map

- from other agencies

- “classification”

## Consider the possibility of a distributed GIS

*remote sensing agency 1*

*soils agency*

*geological survey*

*mapping agency*

*Internet*

*remote sensing agency 2*

*user 1*

*user 2*

*user 3*

## thematic map

- classification

- Classification is a mapping from data to labels (symbols)

## multispectral data

## multispectral data

- statistical, neural and other numerical techniques are known to work well with multispectral data

## m and   are “learned” through training

- each pixel is described by a (data) vector of measurements

***m*** and **  are “learned” through training

- The pixels in each class are assumed to be distributed in a multidimensional normal fashion (Gaussian distribution)

## multimodality can be resolved (modelled) by clustering

## hyperspectral data

## For hyperspectral data there are two approaches

- requires careful treatment of the class covariance matrix

- requires spectral libraries and expert knowledge to be available

## There is a  problem with estimating the elements of the class conditional covariance matrix   from the available training data with hyperspectral data sets, which for c channels (or bands) is symmetric of size c x c

- Hyperspectral data analysis: the classification approach

- need *c(c+1)* independent samples to avoid singularity

- each pixel vector contains *c* spectral samples

*Therefore we need at least (c+1) training pixels per class – say 10(c+1) *

## Regularisation (approximation)

- Hyperspectral data analysis: the classification approach

- Simplification (truncation)

- Handling the ill-conditioned covariance matrix:

## Regularisation

- Hyperspectral data analysis: the classification approach

*Regularisation*

- a simple, more reliable estimate, such as the global covariance or even a diagonal version of the class conditional covariance

## Simplification

- Hyperspectral data analysis: the classification approach

*Simplification*

- The sub-matrices are independent.  Therefore:
-   The discriminant function is the sum of the discriminants of the blocks
-   The number of training samples is determined by the largest sub-matrix.

- assume zero correlation and thus covariance

- use original covariances

## For hyperspectral data there are two approaches

- standard classification methods
- (both parametric and non-parametric)

- requires careful treatment of the class covariance matrix

- requires spectral libraries and expert knowledge to be available

## Hyperspectral data analysis: interpretation by an expert

## Spectroscopic interpretation

- better to match diagnostic (absorption) features

## radar data

## Considerations when interpreting radar data

- scattering is more than from surface elements

- scattering is coherent

- signal to noise ratio is poor because of speckle

## image tone is a function of moisture content, incidence angle, wavelength and polarisation

- volume scattering (medium to bright image tone)

- corner reflector behaviour
- (very bright image tone)

*image tone is a function of moisture content, incidence angle, wavelength and polarisation*

- specular
- surface reflection
- (black on image)

- diffuse surface scattering (medium to dull image tone)

- radar platform transmits energy and receives the component that is scattered from features on the earth’s surface, from which an image is formed

## Particular data types have preferred methods for analysis

- multispectral

- hyperspectral

- radar

- statistical and neural methods

- library searching methods
- or approximate statistical

- backscatter modelling
- or sometimes statistical

- The techniques are not easily transferable between data types if good results are expected

## So how can we map from multiple data types?

## Sometimes a “stacked” data vector is formed

- multispectral

- hyperspectral

- radar

- categorical

## Sometimes a “stacked” data vector is formed

- multispectral

- hyperspectral

- radar

- categorical

## Multisource statistical classification has been proposed

- source independence is assumed, leading to

- decision rule

- stacked vector

## There are problems with the “stacked” vector approach

- May have very different dynamic ranges

- May have very different noise properties

- The different data types:

- May not be available simultaneously (???)

- May have different statistical properties

## Use the prior probability term in the maximum likelihood rule

- applying Bayes theorem leads to

## Use label relaxation

- pixel of interest

- iterate over the spatial neighbourhood

- iterate over the data sets

## Evidential classification is a useful fusion method

- a measure of evidence (called mass) is formed for each labelling possibility for a given pixel from a given data source

- labelling propositions can also be uncertain, in that mass can also be assigned to expressions such as

- 

- this suggests that there is residual doubt in our mind as to which of those two classes the pixel is in

***Dempster and Shafer***

## Evidential classification is a useful fusion method

## Evidential classification - cont

- the measures of evidence are fused using the “orthogonal sum”

- mass to class

**

- residual uncertainty

**

- mass to class

- mass to class

**

- the operation can be applied repetitively to handle more data sources

## Evidential classification - cont

- result of orthogonal sum

- reduced uncertainty

- favoured class

## Recall we want to operationalise a distributed GIS

*remote sensing agency 1*

*soils agency*

*geological survey*

*mapping agency*

*Internet*

*remote sensing agency 2*

*user 1*

*user 2*

*user 3*

## What should a GIS thematic mapping task do?

- Efficiently handle data from different sensors

- Allow quality of the data sources to be considered

- Allow categorical data to be “fused” with numerical data

- Allow each data source to be analysed separately

- Allow for classes from the combined data to be different from the classes found with the data sources separately

## Classes can be data specific

- multispectral

- maps

- radar

- hyperspectral

- wheat, pine trees, clear water, sand, clay, snow, alfalfa, grassland, etc

- volume scatterer, smooth surface, rough surface, moist, dry, strong reflector

- geochemical and biochemical composition

- soil types, geological units, land ownership, town planning, topography

## x

- How do the techniques match up?

- stacked vector

- evidential

- statistical

- data from different sensors

- incorporate categorical data

- analyse data sources separately

- handle data source quality

- combined data classes different

- relaxation labelling

- use priors

**x**

**x**

**x**

**x**

**x**

**x**

**x**

**x**

**x**

**x**

**x**

**x**

**x**

**x**

## Consider a human photointerpreter

*Although relatively poor in a quantitative sense, a human photointerpreter can cope with each of the issues*

## Uses expert knowledge

- How does a human photointerpreter handle mixed data?

- Tends to reason in labels

- And can handle relative data source quality (subjectively)

## How does a human photointerpreter handle mixed data?

- red

- infrared

- vegetation pixel

- % reflected
- sunlight

- 

- red band

- infrared band

## if condition then inference

- or, expressed another way

**if** (infrared/red) is high **then** probably vegetation

- This is a *production rule*, used in an *expert system*

**if**** **condition** ****then**** **inference

- The general form of a production rule is:

## Rules can be used

*to go from data to labels (ie for basic thematic mapping):*

**if** (infrared/red) is high **then** probably vegetation

**if** radar tone (DN) is dark **then** smooth cover type

## Rules can be used

*to go from data to labels (ie for basic thematic mapping):*

**if** (infrared/red) is high **then** probably vegetation

**if** radar tone (DN) is dark **then** smooth cover type

## Should fuse at the label level and not the data level

- water, soil,
- vegetation

- smooth, rough,
- moist, dry

- composition

*fuse labels*

*data*

*labels*

- composite label

## Should fuse at the label level and not the data level

- water, soil,
- vegetation

- smooth, rough,
- moist, dry

- composition

*fuse labels*

*data*

*labels*

- composite label

## Thus, how should a GIS thematic mapping task work?

## To refine an expert system or machine learning approach to thematic mapping that can be used in a production sense

- So what’s the outstanding challenge?

*To refine an expert system or machine learning approach to thematic mapping that can be used in a production sense*

## client

- So what’s the outstanding challenge?  It is to operationalise.

- consultant