Using texture to tackle the problem of scale in land-cover classification
3.3 Fusion of gradient images and segmentation
Given the resulting complementary texture and intensity gradient images, these must be fused to form a single gradient image before application of the watershed transform. A schematic of proposed fusion process is dis- played in Fig. 8.
Fig. 8 Schematic of the complementary texture and intensity gradient image fu- sion process
Intensity is a point property therefore using a non-linear diffusion proc- ess which preserves boundary localization we can locate intensity bounda- ries accurately to the pixel scale. Texture on the other hand is a spatial property and therefore any features used to describe it must be calculated within a neighbourhood. This makes it difficult to accurately localize tex- ture boundaries. In fact the approach we employed will only localize tex- ture boundaries accurately to half the spatial scale of the corresponding feature extraction used. In Fig. 7 (b) we can see that some building texture boundaries are not located entirely correctly (Corcoran and Winstanley 2007).
Simply performing a summation of texture and intensity gradient im- ages as is standard in previous approaches without taking this uncertainty into account introduces two drawbacks (O'Callaghan and Bull 2005; Chaji and Ghassemian 2006). If corresponding boundaries are located in differ- ent positions, a sum of their gradient values will give a double peaked ef- fect, with neither peak being a true measure of the actual boundary gradi- ent. This double peak effect will also result in the segmentation algorithm returning a false boundary object. These effects are demonstrated in Fig. 9.
Complementary Intensity Gradient Image
Normalization
Summation
Texture/ Intensity Gradient Image Normalization / Summation
Complementary Texture Gradient Images
Morphological Dilation
(a) (b)
(c) (d) Fig. 9 A primitive-object boundary has both an intensity and texture gradient re-
sponse shown in (a) and (b) respectively. Although both gradients correspond to the same boundary they are located in different positions. Simply performing a summation will result in a double peaked effect in the resulting gradient image as shown in (c). Neither peak is a true measure of actual boundary gradient. Also segmentation will return a false boundary object. We propose to dilate the texture gradient before summation with the result of this summation shown in (d). The peak of (d) is an accurate value of boundary gradient magnitude. The watershed segmentation algorithm will locate the boundary at this peak which is the location of the intensity boundary therefore minimizing spatial uncertainty
To overcome these downfalls we add a requirement of texture gradients which are later fused with intensity gradients in this manner. This require- ment states: the boundary response should be uniform over a scale greater than the scale of localization. To achieve this we dilate the texture gradient images using a disk shaped structuring element (Soille 2002). The structur- ing element used has a radius equal to the boundary localization scale of the original gradients. Our original texture gradient extraction algorithm extracts gradients accurate to half the scale of the feature extraction per- formed therefore we dilate with a similar scale structuring element. This increases the area over which the gradient operator responds to a texture boundary fulfilling the above requirement. Fig. 9 displays visually the re- sult of applying this strategy.
Before a summation of individual gradient images is performed, each must be normalized to weigh its contribution. Shao and Forstner (1994) proposes to normalize by variance or maximum filter response. O'Cal- laghan and Bull (2005) normalizes by maximum filter response followed
by normalization by the sum of filter response. There is no strong evidence to suggest one normalization technique is superior so we choose to normal- ize each gradient magnitude image by its maximum response. This scales each image to the range [0 1]. We then sum the individual texture gradient images and normalize this again by the maximum value giving a single texture gradient image. We then divide the intensity gradient image by four times its median value and the texture gradient image by its median value. This step aligns the noise floor of each function (O'Callaghan and Bull 2005). Finally the single intensity and texture gradient images are summed to form a final gradient image. All further segmentation analysis is performed on solely this image. Example complementary intensity, complementary texture and fused complementary intensity/texture gradient images are displayed in Fig. 10 (a), (b) and (c) respectively.
(a)
(b) (c) Fig. 10 Intensity and texture gradient images for Fig. 3 (a) are displayed in (a) and
(b) respectively. These are fused in (c) to form a single gradient image
To perform segmentation we use the marker-controlled watershed trans- form (Soille 2002). In practice, direct computation of the watershed algo- rithm results in over-segmentation due to the presence of spurious minima.
To overcome this, the gradient image is first filtered using a marker func- tion, in this case the H-minima transform, to remove all irrelevant minima (Soille 2002). Intensity being a point property is not affected by the uncer- tainty principle and therefore offers superior boundary localization com-
pared to texture. If a boundary has both an intensity and texture boundary, the crest of the gradient magnitude image will be located at the intensity boundary. The watershed algorithm will therefore locate boundaries using an intensity boundary as opposed to a texture boundary where possible and minimize spatial uncertainty. This effect is illustrated in Fig. 9.