Properties of the Shannon entropy vectors are instrumental for analyzing the limits of reliable communication for various communication models. However, the set of all Shannon entropy vectors is not yet known even for three random variables. Often, there are constraints on the entropy vectors of random variables due to the underlying communication model, e.g., functional dependence, independence, and Markov chain constraints. Moreover, the entropy vectors may be constrained to belong to a specific class for a given model, e.g., belonging to the class of quasi-uniform entropy vectors due to code design constraints. This paper presents distribution construction approaches and converse results for such constrained entropy vectors. We present three approaches for constructing distributions such that corresponding entropy vectors satisfy given constraints: (i) by exploiting functional dependence constraints, (ii) by quasiuniform constructions, and (iii) by using independent random vectors. In particular, these approaches are utilized to show the looseness of the known inner bounds for constrained entropy vectors for three random variables. We also present converse results for entropy vectors constrained by basic equalities and quasi-uniformity.

Despite the recent progress in deep learning-based face image colorization techniques, there is still much room for improvement. One of the significant challenges is the bias toward specific skin color. Moreover, the conventional face colorization approaches aim to produce colored 2D face images, whereas the generation of colored 3D faces from monocular achromatic (gray-scale) images is beyond the scope of these methods despite having immense potential applications. To address these issues, we propose Self-Supervised COoperative COlorizaTion of Achromatic Faces (COCOTA) framework that contains chromatic and achromatic pipelines to jointly estimate the color and shape of 3D faces using monocular achromatic face images without inducing any specific color bias. On the challenging CelebA test dataset, COCOTA out-performs the current state-of-the-art method by a large margin (e.g., for 3D color-based error, a reduction from 5.12 ± 0.13 to 3.09 ± 0.08 leading to an improvement of 39.6%), demonstrating the effectiveness of the proposed method.

Recent 3D face reconstruction methods show encouraging results in retrieving 3D face shape and texture from monocular face images. However, these approaches pose several dependencies during testing, such as the requirement of facial landmark coordinates. Moreover, a large testing time presents a challenge for real-time applications. To address these issues, we propose REduced Dependency Fast UnsuperviSEd 3D Face Reconstruction (RED-FUSE) framework, which uses unprocessed face images to estimate reliable 3D face shape and texture, thus eliminating the need for prior land-mark knowledge, and considerable prediction time during testing. RED-FUSE outperforms the current state-of-the-art method on CelebA dataset e.g., for 3D shape and color-based errors, a reduction from 5.84 ± 0.16 to 3.14 ± 0.11 and from 3.50 ± 0.14 to 2.97 ± 0.09 is observed, leading to an improvement of 46.2% and 15.1%, respectively. In addition, the testing time reduces from 7.30 msec to 1.85 msec per face, showing the effectiveness of our method.

3D face reconstruction from a monocular face image is a mathematically ill-posed problem. Recently, we observed a surge of interest in deep learning-based approaches to address the issue. These methods possess extreme sensitivity towards occlusions. Thus, in this paper, we present a novel context-learning-based distillation approach to tackle the occlusions in the face images. Our training pipeline focuses on distilling the knowledge from a pre-trained occlusion-sensitive deep network. The proposed model learns the context of the target occluded face image. Hence our approach uses a weak model (unsuitable for occluded face images) to train a highly robust network towards partially and fully-occluded face images. We obtain a landmark accuracy of 0.77 against 5.84 of recent state-of-the-art-method for real-life challenging facial occlusions. Also, we propose a novel end-to-end training pipeline to reconstruct 3D faces from multiple variations of the target image per identity to emphasize the significance of visible facial features during learning. For this purpose, we leverage a novel composite multi-occlusion loss function. Our multi-occlusion per identity model shows a dip in the landmark error by a large margin of 6.67 in comparison to a recent state-of-the-art method. We deploy the occluded variations of the CelebA validation dataset and AFLW2000-3D face dataset: naturally-occluded and artificially occluded, for the comparisons. We comprehensively compare our results with the other approaches concerning the accuracy of the reconstructed 3D face mesh for occluded face images.

The entropy region is a fundamental object in information theory. An outer bound for the entropy region is defined by a minimal set of Shannon-type inequalities called elemental inequalities also referred to as the Shannon region. This paper focuses on characterization of the entropic points at the boundary of the Shannon region for three random variables. The proper faces of the Shannon region form its boundary. We give new outer bounds for the entropy region in certain faces and show by explicit construction of distributions that the existing inner bounds for the entropy region in certain faces are not tight.