2.1. Geometry Model
Layover is an extreme case of foreshortening, and both of them are geometric distortions that occur in rugged mountainous areas.
Figure 1 shows the imaging geometry of a SAR sensor.
In the flat area, shown in
Figure 1a, the slant range distances of ground targets A and B from the sensor are
and
, respectively, and their projections on an acquisition plane are A’ and B’, respectively. There is a monotonic relationship between AB and A’B’.
When the SAR signal reaches a mountainous area that is less steep, it will generate a foreshortening phenomenon, as shown in
Figure 1b. AB is the fore slope, and the slant range
is shorter than
due to the existence of
. The echo of AB is concentrated on A’B’, and the signal is compressed compared with that of a flat area. Therefore, an unusually high BC occurs here, and the information of the SAR image is incorrect.
Once the slop angle is large, the foreshortening phenomenon will worsen; that is, layover, as shown in
Figure 1c.
is shorter than that in
Figure 1b, and B’, the echo of B, reaches the acquisition plane before A’, thus a top–bottom inversion occurs. These are the typical characteristics of layover. However, as with foreshortening, there is still a high BC in the layover area.
As the proposed method is suitable for both, foreshortening and layover are collectively referred to as layover for convenience in this study, just as they are in other similar studies.
2.2. BC Analysis
In general, common land cover includes built-up areas, water, woodland and farmland. The diversity in surface roughness, soil humidity and object structure is recorded using SAR sensors with different values, which can be used for the recognition of ground objects. For one single image, the interpretation usually depends on the BC value, which is calculated from the amplitude data.
The BC value of each pixel in a SAR image is calculated using Formula (1).
where
is the BC value,
is the value of pixel,
is the calibration parameter and
and
represent the
th row and
th column, respectively.
Some researchers have studied the BC values of different types of land cover [
23,
24,
25], and the approximate ranges of these values are shown in
Table 2, which are the important basis for many classification and recognition methods based on threshold. Among all the ground objects, water has the lowest value owing to the spectacular reflection. Built-up areas have the highest value due to the double-bounce scattering of right-angle structures. Additionally, the values of woodland and farmland are in the middle range, which will change slightly with the growth of vegetation.
With the same method, the BC value of layover can be obtained from several SAR images. We randomly select ten samples of layover areas 7 × 7 pixels in size, calculate the BC using Formula (1), and the average of these values is considered as the BC value of layover. The BC values of the samples are all no less than −8 dB, which is similar to those of the built-up area, and most of them are higher than those of the built-up area. The high BC of layover is generated because the echo of multiple ground targets is compressed to a few pixels. Therefore, the layover detection based on the analysis of BC is practicable.
As we all know, the building density of cities and suburbs is different. In a bustling city, there are many buildings crowded in a small space, especially in the case of high-rise buildings. Additionally, few large tracts of other ground objects will be there, such as water, woodland and farmland. However, suburbia and the countryside are another situation. Farmland occupies most of the land. Although there are also residential houses, they are generally low in height and sparse in distribution and are often surrounded by farmland.
Figure 2 shows the common distribution of built-up areas in cities and suburbs.
In the city, there are more buildings with right-angled structures, which are prone to double-bounce scattering. That is the main reason for the high value of BC there. In this study, these high-density built-up areas (as shown in
Figure 2a) are called “Dense building areas”, while low-density areas (as shown in
Figure 2b) are called “Sparse building areas”.
However, it should be noted that the BC of the built-up areas shown in
Table 1 is a general range, and there will be discrepancies for the different polarization images [
26]. The six images in
Figure 3 show the characteristics of Dense building areas, Sparse building areas and layover areas in VV and VH modes. It is visible from
Figure 3a,b that Dense building areas appear brighter in a VV image. That is because the SAR sensor is more sensitive to double-bounce scattering in the co-polarized mode than in the cross-polarized mode. Therefore, the BC of Dense building areas is higher in a VV image than that in a VH image. However, this does not happen in Sparse building areas and layover areas, as shown in
Figure 3c–f. In both of the two types of polarization SAR image, the BC of Sparse building areas remains lower, while that of layover areas is higher.
In order to quantify the difference discussed above, the BC of three types of areas was calculated using Formula (1). Every value in
Table 3 is the average of the BC values obtained from 30 samples in the corresponding areas that are 7 × 7 pixels in size. It can be seen that these values are consistent with the visual characteristics shown in
Figure 3.
In short, layover areas are similar to the built-up areas in terms of BC but are closer to Sparse building areas than Dense building areas in terms of the difference image between the VV and VH images. The BC values of the layover areas and Sparse building areas almost remain unchanged in the two types of polarization image, but there is a greater difference between them in the Dense building areas. Based on this, Dense building areas can be extracted from built-up areas. Additionally, then, the spatial relationship around built-up areas is used to further detect layover areas.