Land cover classification is a common task in analysing satellite images [32]. Our MRF mod-els can be readily applied to such problems as using appropriate sensors, different land prop-erties can be distinguished based on the gray-level distribution of pixels. Herein we show two examples of SPOT satellite image segmentation using different models and stochastic optimizations techniques [14, 20–24, 38].
In Fig. 1.8 we present a SPOT image of size 512 × 512 with ground truth data (see Fig. 1.9). In Table 1.1, we give the mean (µ) and the variance (σ2) for each of the 6 classes correspondig to different land coverages.
1.4. Application in remote sensing 21
255.0 0.0
Grey-levels
1.0
Density
SN R= 5dB Histogram
Supervised (0.6% error) Unsupervised (0.68% error)
Unsupervised
Parameter Initial Final Supervised
µ0 83.5 84.3 85.48
σ02 256.0 483.9 446.60
µ1 100.0 115.5 115.60
σ12 169.0 444.6 533.97
µ2 152.5 146.7 146.11
σ22 676.0 502.1 540.32
µ3 181.5 177.9 178.01
σ32 100.0 500.0 504.34
β 0.7 1.0 0.7
γ 0.1 0.1 0.1
Figure 1.7: Supervised and unsupervised segmentation results and misclassification rate with the Gibbs Sampler. We also compare the parameters obtained by the unsupervised algorithm to the ones used for the supervised segmentation [25, 36–38].
class 1 2 3 4 5 6
µ 65.3 81.3 75.4 98.5 82.5 129.0 σ2 6.4 12.7 14.9 16.8 9.46 183.2
Table 1.1: Parameters of the “assalmer” image.
As we can see, the classes 2 and 5 have nearly the same parameters, it is difficult to distinguish between them. Fig. 1.10 (resp. Fig. 1.11) shows the results obtained with the ICM (resp. the Gibbs Sampler). For these results, we give a map drawn by an expert (ground truth data, see Fig. 1.9). The classes 1−6 correspond to the regionsB3c, B3b, B3d, a2, hc and92aon the map. For the hierarchical model a slight improvement can be noticed for the results of the Gibbs sampler, however, for the ICM, the improvement is more significant.
In Fig. 1.12, another SPOT image with 10 classes is presented with overlayed ground truth data (The regions are drawn by an expert (Unfortunately, they are shifted up by some pixels. Please take it into account when evaluating the results.) In Table 1.2, we give the mean (µ) and the variance (σ2) for each class. Fig. 1.13 shows a supervised segmentation using the parameters listed in Table 1.2. Unsupervised result in Fig. 1.14 is comparable to the supervised one, but it requires more computing time and is more sensitive to noise. However, the main advantage is that unsupervised methods are completely data-driven. The only input parameter is the number of regions.
Figure 1.8: Original SPOT image “assalmer” with 6 classes.
1.4. Application in remote sensing 23
Figure 1.9: Ground truth data.
Monogrid model Ground truth data
Multiscale model Hierarchical model
Figure 1.10: Results of the ICM algorithm. Comparison with ground truth data.
1.4. Application in remote sensing 25
Monogrid model Ground truth data
Multiscale model Hierarchical model
Figure 1.11: Results of the Gibbs Sampler. Comparison with ground truth data.
1 3 2 10 4 8 5
7
l
6 9
Figure 1.12: Training areas on the “holland” image.
1.4. Application in remote sensing 27
Figure 1.13: Supervised segmentation result with10classes (Gibbs Sampler).
Figure 1.14: Unsupervised segmentation result with10classes (Gibbs Sampler).
1.4. Application in remote sensing 29
class 1 2 3 4 5 6 7 8 9 10
µ 54.61 73.57 159.96 122.84 129.90 146.65 82.56 100.57 93.85 182.34 σ2 93.10 4.10 31.31 8.90 37.42 15.83 35.58 308.86 93.71 73.18
Table 1.2: Parameters of the “holland” image.
I N T HIS C HAPTER :
2.1 Introduction . . . . 32 2.2 Unsupervised segmentation of color textured images . . . . 32 2.3 Segmentation of color images via reversible jump MCMC sampling . . . . 36 2.4 Multilayer MRF modelization . . . . 41 2.4.1 Application to motion segmentation and change detection . . . . 43
2. Complex features and parameter estimation Complex features and parameter estimation
I
n this chapter, we present our results on using more complex features (e.g. color, texture, motion) in MRF models and we also address the associated parameter es-timation problems:A monogrid MRF model which is able to combine color and texture features in or-der to improve the quality of unsupervised segmentations.
A novel RJMCMC sampling method which is able to identify multi-dimensional
Gaus-sian mixtures. This technique has been ap-plied to fully automatic color image segmen-tation.
A new multilayer MRF model has been proposed which is able to segment an im-age based on multiple cues (such as color, texture, or motion).
Application areas include motion seg-mentation (a crucial step in e.g. MPEG cod-ing) as well as change detection in aerial images.
2.1 Introduction
There are many features that one can take as observation for the segmentation process: gray-level, color, motion, different texture features, etc. However, most of the segmentation algo-rithms presented in the literature are based on only one of these features.
One way to combine various features is to design a joint probability distribution which is able to represent the union of the complex observation. This approach works well when the combined features are of similar nature (e.g. define a multivariate Gaussian density). Such a model is proposed in our work [28] for color textured image segmentation.
However, the human visual system is not treating different features jointly. Instead, mul-tiple cues are perceived simultaneously but in a parallel fashion and then they are integrated by our visual system in order to explain the observations. Following these ideas, we have developed multi-layer Markovian models and successfully applied it to color-texture [30, 31]
and color-motion segmentation [27, 29]. For example, an important problem is extracting regions of object motions in the presence of camera drift. This is a key issue in several ap-plications of aerial imagery. In surveillance and exploitation tasks [135] it can be used as a preliminary step of object detection, tracking and event analysis. On the other hand, in 2-D mosaicking [168] and in 3-D stereo reconstruction [55] independent object motions gener-ate outlier regions for image alignment, thus, they should be detected and skipped from the resulting static scene models. An efficient solution to this problem consists in a three-layer Markov Random Field which integrates two different features to statistically characterize the background membership of the pixels [1, 2].
In the following, we give a brief overview of these approaches.