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Occluded Surfaces Shape from First-Order Scattering Light Using Observed Peaks of Reflected Light

It is important to measure entire 3D shapes of objects in various fields. Many 3D shape measurement techniques which use camera images have been proposed. However, they cannot measure occluded surfaces, i.e. object surfaces on an opposite side from cameras or areas hidden by other objects or the object itself.

We aim to measure the shape of occluded surfaces. In traditional methods, entire shapes are obtained by combining partial shapes which are reconstructed while changing the position of cameras. However, it takes human cost and time cost because we cannot find whether there are occluded surfaces before observation. Our method can avoid these problems. Compared with Velten's method, our method doesn't require expensive equipments.

We estimate reflecting points on occluded surfaces by observing first-order scattering light in a laser beam under Tyndall Effect. Tyndall Effect is a phenomenon that light scatters in participating media, thus light can be observed not only in the direction of travel but also in other directions under Tyndall Effect. Miki et al. estimate occluded reflecting points based on a property that intensity of reflected light decreases depending on distance from the reflecting point, and use intensity of all pixels. Intensity of pixels are generally affected by noise, especially noise is dominant in low intensity pixels where reflected light is not observed. Their method has a problem that accuracy of estimation is low quality because they estimate a location of reflecting light based on such information.

Instead of using intensity of all pixels, we estimate a location of a reflecting point based on locations of peaks, where a peak is a pixel which has higher intensity than pixels around it. The peaks can be generally detected around the true position even if intensity of the peaks includes noise. The peaks are observed in first-order scattering light of reflected light and aligned on a line. The reflecting point exists on the same line. Furthermore, the reflecting point exists on a line of incident light. Thus, we can find the reflecting point as the cross point of the line of reflected light and incident light.

Reflecting points are estimated as following procedures. First, we extract peaks that have locally maximum intensity along with x-axis and y-axis on an observed image in order to identify peaks of first-order scattering light of reflected light in the image. Secondly, we extract candidate points of a reflecting point on a line of incident light and in the object region. Then we calculate likelihood of candidate points by voting on the intensity of obtained peaks with Hough Transform. We improve accuracy of estimation by the voting. Finally, as the reflecting point we find the candidate point that has the highest likelihood among the candidate points. After that, we reconstruct shapes based on triangulation considering refraction from estimated reflecting points.

We conducted two experiments. In the first experiment, we evaluate the accuracy of our method. The average error of the reflecting points estimated by our method is about 1/10 comparing with the one by Miki's method. However, in some cases, estimated points are greatly away from the true points. These results are caused by noise and that the likelihoods are not normalized. In the second experiment, we applied our method to a mirror, an ashtray and a rice bowl for investigating what kind of objects can be measured by our method. The experimental result showed that the mirror is almost measured and a part of refleting points estimation to the ashtray is success. However, most of estimation of the ashtray and the rice bowl is failed. The reflecting light was not directly observed by cameras, in that cases observed intensity is regarded as an outlier. In the experiment, such outlier is frequently observed and it reduces the accuracy of reflecting point estimation. Futhermore, This is also caused by the fact that peaks could not be sufficiently detected and multi reflection. Detecting peaks robustly, normalizing likelihoods and removing outliers are left as future works.