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• In a denoising problem, the correct location of a point also depends on the color attribute and not only the geometry of the neighboring points, and the correct color also depends on the geometry of the neighbors. • Graph-based convex optimization enforces smoothness on the graph signal to perform the denoising task. • Several different tasks, i.e., denoising of color-only noise, geometry-only noise, and both of them jointly, an be addressed employing the same algorithm by simply adapting the parameters to each denoising scenario. • Tikhonov regularization performs better than Total variation in all the denoising scenarios. • The algorithm is robust to different noise distributions and intensities. A point cloud is a representation of a 3D scene as a discrete collection of geometry plus other attributes such as color, normal, transparency associated with each point. The traditional acquisition process of a 3D point cloud, e.g. using depth information acquired directly by active sensors or indirectly from multi-viewpoint images, suffers from a significant amount of noise. Hence, the problem of point cloud denoising has recently received a lot of attention. However, most existing techniques attempt to denoise only the geometry of each point, based on the geometry information of the neighboring points; there are very few works at all considering the problem of denoising the color attributes of a point cloud. In this paper, we move beyond the state of the art and we propose a novel technique employing graph-based optimization, taking advantage of the correlation between geometry and color, and using it as a powerful tool for several different tasks, i.e. color denoising, geometry denoising, and combined geometry and color denoising. The proposed method is based on the notion that the correct location of a point also depends on the color attribute and not only the geometry of the neighboring points, and the correct color also depends on the geometry of the neighbors. The proposed method constructs a suitable k -NN graph from geometry and color and applies graph-based convex optimization to obtain the denoised point cloud. Extensive simulation results on both real-world and synthetic point clouds show that the proposed denoising technique outperforms state-of-the-art methods using both subjective and objective quality metrics. [ABSTRACT FROM AUTHOR]