Affiliations: [a] Universidad Mayor, Núcleo de Matemática, Física y Estadística, Santiago, Chile | [b] Sandoz Farmacéutica, Madrid, Spain | [c] Universitat Pompeu Fabra, Barcelona, Spain
Correspondence:
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Corresponding author: Vanel Lazcano, Universidad Mayor, Santiago 08544, Chile. E-mail: vanel.lazcano@umayor.cl.
Abstract: This paper discussed an anisotropic interpolation model that filling in-depth data in a largely empty region of a depth map. We consider an image with an anisotropic metric gij that incorporates spatial and photometric data. We propose a numerical implementation of our model based on the “eikonal” operator, which compute the solution of a degenerated partial differential equation (the biased Infinity Laplacian or biased Absolutely Minimizing Lipschitz Extension). This equation’s solution creates exponential cones based on the available data, extending the available depth data and completing the depth map image. Because of this, this operator is better suited to interpolate smooth surfaces. To perform this task, we assume we have at our disposal a reference color image and a depth map. We carried out an experimental comparison of the AMLE and bAMLE using various metrics with square root, absolute value, and quadratic terms. In these experiments, considered color spaces were sRGB, XYZ, CIE-L*a*b*, and CMY. In this document, we also presented a proposal to extend the AMLE and bAMLE to the time domain. Finally, in the parameter estimation of the model, we compared EHO and PSO. The combination of sRGB and square root metric produces the best results, demonstrating that our bAMLE model outperforms the AMLE model and other contemporary models in the KITTI depth completion suite dataset. This type of model, such as AMLE and bAMLE, is simple to implement and represents a low-cost implementation option for similar applications.
