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Chromatic Aberration Based Depth Estimation in a Fluid Field

Nobuhiko Mukai1, Yuki Matsuura1, Masamichi Oishi2, and Marie Oshima2
1. Graduate School of Engineering, Tokyo City University, Tokyo, Japan
2. Institute of Industrial Science, The University of Tokyo, Tokyo, Japan
Abstract—One of the most challenging issues is to analyze the behavior of fluid body, and it is very difficult to capture the flow of liquid. Then, PIV (Particle Image Velocimetry) or PTV (Particle Tracking Velocimetry) are usually used in order to observe the flow in a fluid field. In PIV, tracer particles, which have some color, are thrown into the fluid body, and the scattered light reflected on the particles by irradiating laser is imaged. In fact, the frequency of the scattered light is slightly changed by the Doppler Effect, and the velocity of a particle can be measured by utilizing the fact that the frequency change is proportional to the particle velocity. On the other hand, PTV is a method to measure the particle velocity by tracking each particle in images obtained by a camera. In general, both of PIV and PTV can analyze only the 2D behavior of the particles so that some additional information is required to track the particles in 3D space such as stereo vision, de-focus of the image, and color of the particle. These systems, however, requires multiple cameras, multiple images, or multiple lights. Then, a new system has been developed, which estimates the distance from the camera to a particle by utilizing the relation between the frequencies of light reflected on the particle and the lengths to the particle. However, it is not always true that hue of color is proportional to the wavelength of light. Therefore, in this paper, we propose a depth estimation method of particle by utilizing chromatic aberration of lens and investigate the relation between the hue of color for a particle and the length from the camera. First, we measure the focal length of a particle from the camera by adjusting the height of the chromatic lens. Then, we obtain the relation between the hue of color for the particle and the length from the camera by approximating the experimental data. By analyzing the approximated calibration curve, we can clarify the relation between the hue of color and the wavelength. Finally, we can estimate the depth of the particle by using the obtained calibration curve. In addition, we measure the error between the expected value and the estimated one, and investigate the factors of the estimation error. In the end of the paper, we clarify the difficulty for the estimation of particle positions in 3D fluid field.

Index Terms—depth estimation, chromatic aberration, fluid field, PIV, PTV

Cite: Nobuhiko Mukai, Yuki Matsuura, Masamichi Oishi, and Marie Oshima, "Chromatic Aberration Based Depth Estimation in a Fluid Field," Journal of Image and Graphics, Vol. 6, No. 1, pp. 59-63, June 2018. doi: 10.18178/joig.6.1.59-63
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