The Simple Profile passes were based on the merging criterion of the mutual best match between neighboring objects。 This criterion, sometimes is sub-optimal, due to computation cost (many virtual merges occur and few of them are producing real merges)。 This heterogeneity heuristic was found optimal at minimizing the scene heterogeneity after region merging procedures (Baatz and Schäpe 2000)。 An accuracy-to-speed ratio module has been implemented, including the global heterogeneity heuristics。 The accuracy refers to the global heterogeneity cost that is added to the image with each merge that occurs during segmentation (Tzotsos and Argialas 2006)。

2。3Advanced Texture Heuristics

The basic objective of the Advanced Texture Heuristic module was to build upon MSEG’s simple profile modules, in order to improve segmentation results。 Since texture is a key photo- interpretation element, it was decided to use rather more complex texture features, than first order texture features (e。g。 standard deviation, variance)。

Since second order texture features are widely used in pixel classification (Haralick et al 1973, Materka and Strzelecki 1998), there was a need to test them for segmentation purposes and specifically as an add-on to the MSEG algorithm (Tzotsos and Argialas 2006)。

Given that MSEG is a region merging algorithm, it should be taken under consideration that not all state of the art methods for modeling texture are compatible with a hybrid segmentation algorithm。 The recent literature has shown that Markov Random Fields, Wavelets and Gabor filters, have great potential for texture analysis (Materka and Strzelecki 1998)。 Their disadvantage is that they are very complex and time consuming to be used with a procedure, involving thousands of virtual merges。 At the same time, wavelets and Gabor filters are incapable to be used locally, within the boundaries of a single  –

and sometimes very small - primitive object。 Markov Random Fields are easier to adopt for region-based texture segmentation, but they were found incompatible with the current merging search method, since they are based on Bayesian reasoning。

A traditional method for modeling texture, which has been proved very good for practical purposes in supervised classification (Haralick et al 1973, Schroder and Dimai  1998), is based on the Grey Level Co-occurrence Matrix (GLCM)。 GLCM is a two dimensional histogram of grey levels for a pair of pixels separated by a fixed spatial distance。 The Grey Level Co-occurrence Matrix approximates the joint probability distribution of this pair of pixels。 This is an insufficient approximation for small windows and a large number of grey levels。 Therefore the image data have to be pre-scaled to reduce the number of grey levels in the image。 Directional invariance can be obtained by summing over pairs of pixels with different orientations (Schroder and Dimai 1998)。

From the GLCM several texture measures can be obtained, such as homogeneity, entropy, angular second moment, variance, contrast etc (Haralick et al 1973)。 To compute the GLCM, several optimization methods have been introduced (Argenti et al 1990, Miyamoto and Merryman 2006)。 Most applications of GLCM for remote sensing images, at pixel-level, included computation of the co-occurrence matrix less often for the whole image, and more often for a predefined image sliding window of fixed size。

In order to employ the second order texture features  into MSEG, it was obvious that a GLCM should be computed for each primitive image object, during the merging procedure (Figure 2)。

Figure 2: A 3-dimensional representation of the Co-occurrence matrices that have to be computed for a given orientation。 Ng are the possible grey levels and N is the total number of primitive image objects (source: Miyamoto and Merryman 2006)。

The Advanced Texture Heuristic module, performed the GLCM computation for each initial image object before any merge could occur at any given segmentation pass。 Then, for each primitive object texture features were computed。 The basic idea of this module was the implementation of a similarity measure, in order to decide whether two image objects are compatible in texture to be merged。 A good similarity measure would be a homogeneity criterion based on the second order texture features。 Haralick has indicated as good texture similarity measures,  the  Homogeneity  (Equation  1)  and  the     Angular