Second Moment (ASM) (Equation 2) (Haralick 1979)。 These were implemented into the Advanced  Texture  Heuristic module。

to 32 grey levels (Miyamoto and Merryman 2006)。 The grey level reduction took place using histogram equalization technique and then a look-up table was computed to hold the new grey level information。

Homogeneity The optimal way to compute the GLCMs was designed to perform some kind of global pre-computation, so that to    speed

up the inter-object GLCM creation function。 For each of the image pixel, a direction search was performed, to evaluate the grey level pair co-occurrences。 For the 4 different directions, a vector   was   designed   to   hold   the   overall     co-occurrence

information。 This way, no direction search was to be  performed

where Pij is the GLMC value。

When an object was retrieved from the MSEG priority list (Tzotsos and Argialas 2006), the texture homogeneity features were computed from the GLCM。 The mutual best match search procedure compared neighbour objects to the selected one, and computed the homogeneity texture features for those as well。 Before, the color and shape heterogeneity criteria were computed and involved to the scale parameter comparison, texture heterogeneity was computed, as the difference of the values of the homogeneity texture features。 These values, one for each direction and GLCM, were then compared with a threshold called texture parameter which can be defined by the user。 If the two objects are found to be compatible by  the texture parameter, then the computation of the spectral and shape heterogeneity takes place, in order to fulfil the mutual best match criterion, and the merge to occur。

The described heuristic, takes advantage of the texture parameter, to reduce the heterogeneity  computations。 This means that, when activated, the Advanced Texture Heuristic module, has greater priority than the scale parameter,  but cannot perform any merging, without color and shape compatibility of image objects。 If one wishes to perform segmentation using only texture features, the scale parameter can be set to a very large value, so that not to constrain the merging by the color and shape criteria。

In the following section, the optimization procedure for the GLCM computation is described。

2。4Implementation

Having to compute thousands of co-occurrence matrices, during a region merging segmentation procedure can be computationally painful。 If for each primitive object, a grey level reduction and a co-occurrence computation are performed, then the segmentation algorithm would slow down。

In order to tackle this problem, for the object-oriented algorithm, the GLCM computation should be optimized to be used with objects, rather than pixels。 A modification to the traditional methods was performed, so that to make the procedure faster but not less accurate。

At first, there was the problem of image band selection。 If the computation of the GLCM was to be performed for each band separately, the whole segmentation process would not be performed optimally。 Given that the Starting Point Estimation, worked very well with one selected band, the idea to use the same selection was tested。 So, instead of using all bands, the Advanced Texture Heuristic module can use the intensity band of the HSI colorspace, or the Y band of the YCbCr colorspace (used as default), or a principal component band of the image, or finally a single image band。

After the band selection, a grey level reduction was  performed at the selected band。 The final number of grey levels can be selected by the user, with a quantization parameter。 The default value, as used by many other GLCM implementations was set

twice during the pass stages。 After the completion of these vectors for all pixels, the segmentation procedure was initiated。 Each time an object co-occurrence matrix was to be used, the object triggered a pointer structure to call all pixel co- occurrence vectors and performed very quick texture feature computation within the object boundaries。