## 2 State of the Art
The model achieves state-of-the-art performance in the KITTI data set, outperforming contemporary models. [PERSON] et al. [15] proposed a model using Dynamic Spatial Propagation Networks. This type of network dynamically estimates the parameters of an affinity. The authors proposed a diffusion suppression procedure to stop diffusion close to the edges of the color image. The most relevant feature of this model is its rapid convergence compared to models with similar architectures. The paper in [16] presents a deep learning model for depth completion that creates content-dependent and spatially variant kernels. The authors proposed a new convolutional factorization to store the large amount of data associated with these kernels' parameters. This new factorization reduces the computational cost of the model. The proposed model outperforms others in the NYU_V2 and KITTI data sets. Nevertheless, one of the most well-known limitations of deep learning depth completion models is their huge number of parameters (requiring millions of parameters). Researchers are aware of this drawback, and some improvements have been explored in this direction, for instance, in the work of [PERSON] et al. [17]. Their proposal can reduce the number of parameters by up to 96% compared to similar approaches. Thanks to that, the authors can deploy their model on an FPGA, achieving real-time performance (interpolating 11.1 images per second). Although these are relevant advances, there is still a need to develop more computationally efficient (non-deep-learning) solutions capable of providing relatively high-quality depth maps with much less computational effort. In this paper, we follow this direction, presenting a simple interpolator based on the infinite Laplacian. This model has already been successfully applied in other image interpolation problems, such as the interpolation of optical flow on video in [PERSON] et al. [3]. The origins of this interpolator trace back to the foundational work of [PERSON] et al. [18]. The authors applied an axiomatic approach to data interpolation, stating a set of properties that a well-behaved interpolator should hold. One of the interpolators holding the full set of axioms was the infinity Laplacian. More recently, [PERSON] et al. [19] also proposed a practical implementation of the infinity Laplacian and the biased infinity Laplacian models. One of the most relevant contributions was the proposal of a Euclidean metric that included a spatial and a color term. The infinity Laplacian provided the best results for upsampling images in the context of the Middlebury data set. In addition to the infinity Laplacian, there is a panoply of computationally efficient techniques in the literature. For instance, in [20], the authors segmented the reference color image using superpixels and the SLIC algorithm. A 2D linear interpolation approach was used to generate a depth-value plane using the depth information in each superpixel. The model incorporated heuristics and simple rules to tackle depth estimation when segmentation errors occurred. The results outperformed the bilateral filtering approach. A more recent and interesting approach is the work by [PERSON] et al. [21]. The authors proposed a real-time algorithm capable of estimating up to 111 depth maps per second. Unfortunately, the estimated depth maps presented missing or low-confidence data. Table 1 summarizes the number of parameters, GPUs, and images in the training set reported in the literature of cited methods. Table 1 shows that most models use thousands of images for training and more than one GPU, and two report thousands of parameters to be estimated. Last but not least, it is important to mention that some consensus has been reached by the depth completion community regarding performance evaluation. Researchers used well-established data sets, which include clear evaluation protocols, to benchmark their solutions. This article will use two popular data sets: KITTI [5] and NYU_V2 [25].