Hard vs Soft ClassificationHard- versus soft-classifiers

Why use soft-classifiers?– Sub-pixel classification– Uncertainty of classification/scheme– Incorporating ancillary data (hardeners)

Soft Classification Scheme

(Soft or Fuzzy) Signatures

• Training sites (homogeneous vs. fuzzy)

Water Forested Wetland

Upland Forest

Sum

Site#1 0.7 0.2 0.1 1

Site#2 0.2 0.2 0.6 1

Site#3 0.5 0.1 0.4 1

… …

•Hard Classification - a pixel can only have one and only one category. •In urban regions, a pixel in reality may have more than one category because of the heterogeneity of the land cover composing that pixel. We call this a mixed pixel. •Soft or fuzzy classifiers - a pixel does not belong fully to one class but it has different degrees of membership in several classes. The mixed pixel problem is more pronounced in lower resolution data. In fuzzy classification, or pixel unmixing, the proportion of the land cover classes from a mixed pixel is calculated.

•Hard Classification - a pixel can only have one and only one category. •In urban regions, a pixel in reality may have more than one category because of the heterogeneity of the land cover composing that pixel. We call this a mixed pixel. •Soft or fuzzy classifiers - a pixel does not belong fully to one class but it has different degrees of membership in several classes. The mixed pixel problem is more pronounced in lower resolution data. In fuzzy classification, or pixel unmixing, the proportion of the land cover classes from a mixed pixel is calculated.

Land cover is usually onlypoorly represented by discrete classes for two main reasons, (1) pixels are often mixed –representing areas on the ground which have multiple land cover types and (2) land coverclasses often intergrade due to the continuous nature of vegetative land cover (Foody,

For example, the Oak Openings Region ofNW Ohio and SE Michigan is an extreme example of the continuous nature of landcover. By its very definition, savanna is a class that falls within the continuum betweenforest and savanna. It is a plant community consisting of scattered open-grown trees witha primarily herbaceous understory. “No definition that clearly separates savanna fromprairie and forest has been developed (Nuzzo, 1994).” This makes the use of a fuzzy orsoft classification appropriate.

•Zadeh defined fuzzy logic as, “a set of mathematical principlesfor knowledge representation based on degrees of membership rather than on crisp memberships of classical binary logic (Zadeh, 1965).”

•Researchers within the remote sensing field have adapted and/or applied fuzzy set theory to the classification of satellite imagery.

•Fuzzy set theory has been applied to classification to produce three main fuzzy classification methods including, (1) specific fuzzy classifiers (ex. fuzzy c-means & fuzzy k-means), (2) ‘softening’ the results of a crisp classification (ex. Maximum Likelihood Classifier), and (3) the use of artificial neural networks (Woodcock et al.,14 2000; Zhang et al., 2001).

Idrisi Soft Classifiers

•Foody states about accuracy: The methods generally used, such as the percentage correct allocation or kappa coefficient of agreement, are not without problems. It is, for instance, typicallyassumed that the classes are unordered (van Deusen, 1996).In many instances, however, the classes may be ordered yetthe conventional accuracy assessment techniques are used(e.g., Joria and Jorgenson, 1996). In such circumstances, theuse of a conventional accuracy assessment measure, designedfor application to nominal level data, will not make full useof the information content of the data and may not providean appropriate index of classification quality.

•It may sometimes be preferable to use approaches that can accommodate the ordinal nature of the data set such as the weighted kappa coefficient (Cohen, 1968; Foody et al., 1996). The analyst may at times be constrained to use a conventional measure of accuracy, for example, if evaluating the results againstpreviously published work to maintain consistency, but thepossibility that the measure does not fully use the datashould be recognized and its implications considered.

•Overall accuracy is the most common measure of evaluating the quality of classifications, although it does not take location into account. The kappa coefficient factors in the effect of chance in the classification.

•For example, a kappa value of 78% indicates that the classification is 78% better than a classification that resulted from random assignment. Therefore, kappa is lower than the overall accuracy.

•The weighted equivalents of overall accuracy and kappa can be used with fuzzy classification for accuracy.

•The arrangement shown in the following Table is used to assess the weighted overall accuracy and weighted kappa coefficient.

•This is similar to an error matrix except that the cell values are not absolute observations and computed values but proportions.

-A typical rule in a Sugeno fuzzy model has the following form:If Input 1 = x and Input 2 = y, then Output is z = ax + by + cFor a zero-order Sugeno model, the output level z is a constant(a=b =0).

3.2.1 Membership functionMembership function is the mathematical function whichdefines the degree of an element's membership in a fuzzy set.The Fuzzy Logic Toolbox includes 11 built-in membershipfunction types. These functions are built from several basicfunctions:-piecewise linear functions,- the Gaussian distribution function,-the sigmoid curve and-quadratic and cubic polynomial curve.

Two membership functions are built on the Gaussiandistribution curve: a simple Gaussian curve and a two-sidedcomposite of two different Gaussian curves

RESULTS:-at first sight, time necessary for fuzzy classification islonger comparing to maximum likelihood procedure,which takes several seconds to classify an image. But,if in ML procedure possible image transfer torecognizable format for certain software, formulation ofthe training areas, analysis concerning signatureseparability take place, than situation is quite different:fuzzy logic takes advantage of already created simplerules and image classification (started from thescratch in both procedures) equal or even less timeconsuming. Of course, different conditions duringimage capture must be taken into account.

-considering the level of classification accuracy, fuzzylogic can be satisfactory used for imageclassification.