Change Detection between Intensity Images

Introduction

In the previous study we demonstrated the capability of segmentation to improve the classification of a set of simulated 3-look SAR images. Segmentation provides an adaptive function by maximising the segment size and matching the shape of the largest possible homogeneous region, consistent with the data. We introduced the prior knowledge that every image in the sequence has fundamentally the same regions and boundaries with only variation in the RCS within each region. Under these conditions we may perform joint segmentation over every image in the sequence. The common boundaries reinforce one another and help to overcome speckle noise. Thus the properties of each segment represent the most accurate estimates that can be obtained.

In some applications a sequence of images is available but we believe that although the underlying scene structure (segments) have not changed, the RCS will/may have changed between individual images. An example is a set of fields with growing crops: we want to monitor the growth between images. Then, we are concerned with detecting those regions that have changed in intensity.

Joint segmentation is ideally matched to this process since it constructs a set of segments that are common to each image. It is therefore possible to study the temporal development of identical regions of these images.

Two methods of change detection are considered here, neither of which requires any prior knowledge. Thus these methods are both unsupervised methods.

The first considers the sequence of images and detects whether the intensity within each region is constant throughout the sequence or not. This is based on temporal texture and uses the normalised log texture for the sequence in each element.

The second performs a maximum likelihood search for the position of a step change in each element over the sequence. It compares the likelihood of a step at all points with there being no change. Thus this offers additional indformation compared with the first method in that it bothe detects the presence of a change and determines its position in the sequence.

To demonstrate these approaches we simulate a sequence of ten images with six different classes, shown in Figure 6.2, whose cross-section varies from sample to sample as shown in Figure 6.3.

Figure 6.2: Test pattern of 6 defined classes used in this study for simulating image intensity.

Figure 6.3: Plot of the mean intensity in each of the classes from Figure 6.2 during the sequence of images.

From Figure 6.3 we see that there is a change of -5 in the RCS of the red class at image number 4, one of 1 in the blue class at image number 5 and one of -2 in the green class at image number 6. The purpose of this study is to detect these changes.

Comparison of classification methods

As indicated above there are two different Maximum Likelihood tests that can be performed to test for changes. The first is to test the hypothesis that there has been a change in each region or not, at any point in the sequence. We shall call this change detection. The second method addresses the more sophisticated question of where any change is detected. Thus it provides information both on the existence and position of such a change. We shall name this positional change detection.

As before we shall compare results after the same four types of processing, namely:

Upper Limit:

change detection on the average intensity in each ground truth region over the sequence

Joint Segmentation:

change detection on the average intensity in each segment over the sequence

3x3 window:

change detection on the average intensity over a 3x3 window over the sequence

Lower Limit:

change detection on the intensity in each pixel over the sequence.

Change detection

The output of this method is expected to be a map of those regions in the sequence where changes have been detected compared with those regions where no changes were found. Only two hypotheses are possible for the entire sequence. From figures 6.2 and 6.3 we note that changes are expected in the red, blue and green classes only. Thus the predicted changes are illustrated in Figure 6.4.

Figure 6.4: Predicted regions of change (white) and no change (black) in the image sequence.

The ML test for homogeneity with a gamma-distributed PDF is given by the normalised log measure,

$$U = \overline{log(I)} - log(\overline{I})$$ (1)

where the bars indicate averaging over all the pixels in a give segment for the complete sequence of images. If there is no change in RCS then the data is merely gamma distributed about its mean value with an order parameter equal to the effective number of looks (3 for these images). Any type of fluctuation in RCS will result in an increase in $U$. Thus changes can be detected by applying a suitable threshold to the normalised log image, formed from the sequence. The exact choice of threshold is selected to yield a reasonably low rate of false detections of change, in the absence of variations in the RCS.

When this analysis is applied to the sequence of images we obtain the results shown in Figure 6.3.2. If we compare the results with the expected ones we note that with single pixels (a) only the strongest change is visible, corresponding to the red class in Figure 6.2. After applying a 3x3 window (b), changes corresponding to the green class are visible. The result after joint segmentation (c) is considerably better with all classes being detected. Indeed, the changes resemble the predicted ones in Figure 3.

Figure 6.3.2(a): Detected Changes using single pixels

Figure 6.3.2(b): Detected Changes using a 3 by 3 filter

Figure 6.3.2(c): Detected Changes using joint segmentation

Figure 6.3.2(d): Detected Changes using Prior Knowledge

When the Upper Limit is considered, in which the predefined class boundaries determine the regions, the result is further improved so that the result is almost indistinguishable from Figure 6.4.

The performance comparison can be quantified in terms of the probability that changes are correctly detected, shown in Table 6.3.2.

Table 6.3.2: Probability of correct detection of changed regions for the different processing methods

Method	Pcor
Single Pixel	0.626
3 by 3 window	0.805
Joint Segmentation	0.971
Upper Limit	0.996

If we compare the probability of false classification (1-Pcor), we see that this progresses from 37% for single pixels to 19% for 3x3 window, 3% for joint segmentation and 0.4% for the Upper Limit. The considerable advantage offered by joint segmentation before change detection is obvious.

Positional change detection

Positional change detection offers the opportunity to detect both the presence of a change and its position. The likelihood that a change occurs at a position $K$ in a sequence can be shown to be given by

$$(K) = -K log(\overline{I_{1}}) - (M - k)log(\overline{I_{2}}) + M log( \overline{I_{0}})$$

where the bars denote the average values in each segment over the first $K$ images (region 1), the second $M-K$ images (region 2) and all $M$ images (region 0) respectively. Once again we can apply a threshold to ensure that the detected change is unlikely to be caused by speckle noise when no change is expected.

The predicted pattern of changes is expected to be given by the red, green and blue classes in Figure 6.2. The actual detections are shown in Figure 6.3.2. The single pixel results (a) show that only the red change, with an RCS step of 5, is reasonably detected. After a 3x3 window (b) the green change, with step of 2, is reasonably well defined and the blue change, with a set of 1, is partially detected. Following segmentation (c), all the changes are well detected. Finally, the Upper Limit shows almost no difference from the expected changed classes in Figure 6.2

Figure 6.3.2(a): Detected Changes using Single Pixels

Figure 6.3.2(b): Detected Changes using 3 by 3 filter

Figure 6.3.2(c): Detected Changes using Joint Segmentation

Figure 6.3.2(d): Detected Changes using Prior Knowledge
The colours indicate detected changes at the different positions within the image sequence. Brown (position 1), magenta (2), cyan (3), red (4), blue (5), green (6), yellow (7) and white (8).

Once again, the most useful comparison is in terms of the detection probabilities, as summarised in Table 6.3.2. The probability of correctly detecting the change at the correct position in the sequence is listed for the four different processing methods. The average result over all 8 possible positions is compared with the specific results for the three positions (4, 5, and 6) where change is predicted.

Table 6.3.2: Probability of detecting changes at the correct position within a sequence. The average probability is calculated over all 8 possible positions. The specific results for the known change positions are also listed.

Method	Average	Position 4	Position 5	Position 6
Single Pixel	0.8618	0.9004	0.5123	0.5640
3 by 3 window	0.9433	0.9782	0.7322	0.8970
Segmentation	0.9925	0.9944	0.9729	0.9897
Upper Limit	0.9996	0.9998	0.9991	0.9995

The single pixel results confirm the fact that only the strong change (4) is reasonably detected. The average false classification probability is 14%. The 3x3 window gives better response for all three positions of change, with the results graded in order of step strength (4, 6 and 5) and an average false classification probability of 5.7%. Again, there is a considerable improvement using joint segmentation with an average false classification of only 0.75%. The individual detection probabilities are again in order of step strength. Finally, the Upper Limit is almost exact with an average false classification probability of only 0.04%. Once again the individual detection probabilities are in order of step strength.

In making these comparisons we observe the advantage of using defined edge maps for the regions of interest, where these are available and can be trusted. However, it must be noted that agricultural regions, such as fields, are very unlikely to be completely homogeneous. The Upper Limit offers no capability for detecting these inhomogeneities. Furthermore, they will tend to degrade so-called Upper Limit results, whereas they will have much less impact on joint segmentation. Perhaps most important is the fact that depending on existing edge maps excludes any possibility of extrapolating beyond available map data. With segmentation extrapolation is automatic.

Finally, it is instructive to compare the detection probabilities in the two methods of change detection. From this comparison one would deduce that the detection of change together with its position is more sensitive than the simple change detection process. Since positional change detection offers additional information as well as being more sensitive, this is the technique that should be preferred.

Conclusions

• Joint segmentation offers a valuable precursor to change detection because it adapts the region size to the data and presents a common set of boundaries for the whole sequence of images.
• The Upper Limit provides the most sensitive method for detecting changes. However, it suffers from three disadvantages:
  • It cannot detect inhomogeneities within the defined regions.
  • The sensitivity is degraded by any inhomogeneities.
  • It only process within defined regions, with no extrapolation capability such as that possessed by segmentation.

• Joint segmentation is somewhat less sensitive than the Upper Limit but is considerably better than using a 3x3 window, which in turn is better than single pixels.
• Positional change detection is more sensitive than change detection alone and offers additional important information; namely, the position in the sequence of any change detected. Therefore we reccommend that change detection should always adopt the simultaneous detection of change and its position.