Overview

With support from the NIMS project, we continue to make progress on the multiscale sensing problem. The particular application is study of sunlight patterns on forest floors, using a combination of PAR sensors (for sparse direct local measurements) and cameras (for high sampling density indirect measurements). The working hypothesis is that the combination of these two sensing modes can yield higher spatio-temporal fidelity with fewer resources than employing either sensing mode alone.

Approach & Accomplishments

The work is proceeding in two threads. One thread is direct reconstruction of the field through interpolation of samples. The low fidelity data, which is the image taken by the camera in the sunlight distribution application, is processed first to obtain the global information. The image processing algorithm has been improved in this past year to yield better results than reported last year. The algorithm segments the image based on the features in the image. No previous knowledge is assumed about features in the image. Instead, the features are recognized from the statistical distribution of the pixels' values. Pixels with similar features form a cluster in the pixel value distribution. Peaks in the distribution (i.e., the cluster center) are located through the mean shift algorithm. Pixels having strong features are allocated to feature clusters. Pixels having weak features are grouped together and are treated as a special cluster. Once all the pixels are allocated to certain feature clusters, all the connected pixels in the same cluster are recognized as an object. In this way, the image is segmented into objects. Objects smaller than a certain size are treated as noise and merged into larger objects. Sunflecks and shadows (the area where no portion of the sun can be observed when facing up) usually exhibit strong features in the image while transition areas exhibit weak features. Hence, after the image segmentation step, the field is partitioned into smaller homogeneous subfields in the three categories: sunflecks, shadows and penumbra (the area where partial sun can be observed if facing up).

After the field is segmented, each homogeneous subfield is sampled and reconstructed separately due to the differences in their smoothness. Even though the camera cannot measure the incident light intensity accurately, it can provide a good indication of the smoothness of each subfield. The camera response curve is linear in the middle intensity range and sublinear in the low and high intensity range. The high and low intensity areas generally correspond to the sunflecks and shadows, respectively. If one sample from such an area confirms that, only a small number of samples are taken since both sunflecks and shadows have small variance. Otherwise, the image intensity value is calibrated against the camera’s response curve and then the same steps as for areas in the middle intensity range are followed. For areas in the middle intensity range, the variance of the intensity is obtained. This variance gives an overestimate of the roughness of the incident light intensity distribution. Based on this variance, samples are allocated and the field is reconstructed through linear interpolation. The algorithm is tested both using lab setup and real field image. Fig 1 shows the result for the real field.

Figure 1. Reconstruction result (right) for the true field (left)

Another thread of the work focuses on the model based reconstruction. In our study, we are only interested in the photosynthetically active radiation (PAR) portion. The PAR reaching the ground is composed of both direct solar PAR and diffused sky PAR. The PAR inside the canopy can be further divided into four parts: a) direct solar PAR that has penetrated through the canopy without scattering by foliage S; b) diffuse sky PAR that has penetrated through the canopy without scattering by foliage D; c) diffuse PAR due to scattering of direct solar radiation by foliage H s; d) diffuse PAR due to scattering of diffuse sky radiation by foliage H d. H d is negligible in general. Hence, in our study, we only characterize the other three parts.

From the origin of the radiation, D and H s can be modeled as Gaussian random variables. The sunlight distribution in an open area is shown in Fig 2. This is measured through a camera by getting the difference of the two consecutive images to remove the effect of reflectance difference. A fitted Gaussian distribution is also presented as a comparison. This distribution should be the sum of the true sunlight distribution and the camera noise. As can be seen in the graph, the Gaussian distribution with  =1.974 fits very well. Since we get a Gaussian distribution with  =1.085 for a similar image under indoor lamp illumination, the results confirm that the diffuse sky light has a Gaussian distribution

Figure 2. Light distribution in an open area

From collected data, the distribution of the under canopy light due to the direct beam can be seen to follow Beta distribution. But for a different canopy, the parameters of the Beta distribution can be quite different. The situation is further complicated by the different wind conditions encountered each day. Due to the penumbra effect, it is difficult to derive the direct solar radiation distribution analytically. It is also hard to collect enough data so that extracting the distribution and correlation function for direct beam from experimental data is also impractical. Therefore, we turned to simulation to solve the problem.

The simulation result is validated by comparing with the theoretical analysis and collected data. Fig. 3 shows that the sunspeck distribution of the simulated result matches theoretical analysis well.

Figure 3. Sunfleck distribution

Future Directions

Models such as the sunlight distribution model and correlation model need to be extracted from the simulation result and collected data for different areas. These models can then be applied to the reconstruction process to provide improved reconstruction results. Since the variance of the reflected light intensity is usually equal to or larger than the incident light intensity, the number of samples estimated based on the variance of the reflected light intensity measured by the camera generally give a larger value than needed. This problem is especially severe in the area where the ground texture is very complex. Hence, an adaptive sampling algorithm can be applied to each homogeneous subfield portion in the image.

People

Faculty: Greg Pottie and William Kaiser

Students: Kathy Kong and Richard Pon