| Summary: | Transparent object detection and reconstruction are significant, due to their practical applications. The appearance and characteristics of light in these objects make reconstruction methods tailored for Lambertian surfaces fail disgracefully. In this paper, we introduce a fixed multi-viewpoint approach to ascertain the shape of transparent objects, thereby avoiding the rotation or movement of the object during imaging. In addition, a simple and cost-effective experimental setup is presented, which employs two single-pixel detectors and a digital micromirror device, for imaging transparent objects by projecting binary patterns. In the system setup, a dark framework is implemented around the object, to create shades at the boundaries of the object. By triangulating the light path from the object, the surface shape is recovered, neither considering the reflections nor the number of refractions. It can, therefore, handle transparent objects with a relatively complex shape with the unknown refractive index. The implementation of compressive sensing in this technique further simplifies the acquisition process, by reducing the number of measurements. The experimental results show that 2D images obtained from the single-pixel detectors are better in quality with a resolution of <inline-formula><math display="inline"><semantics><mrow><mn>32</mn><mo>×</mo><mn>32</mn></mrow></semantics></math></inline-formula>. Additionally, the obtained disparity and error map indicate the feasibility and accuracy of the proposed method. This work provides a new insight into 3D transparent object detection and reconstruction, based on single-pixel imaging at an affordable cost, with the implementation of a few numbers of detectors.
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