Diffuse Optical Tomography (DOT) is a well-known imaging technique for detecting the optical properties of an object in order to detect anomalies, such as diffusive or absorptive targets. More specifically, DOT has many applications in medical imaging including breast cancer screening. It is an affordable and noninvasive method to recover the optical properties of a body using photon density measurements from applying laser sources placed at its surface. Mathematically, the reconstruction of the internal absorption or scattering is a severely ill-posed inverse problem and yields a poor quality image reconstruction. Studying coefficient inverse problems in a stochastic setting has increasingly gained in prominence in the past couple of decades. In this work, we will show convergence and optimality for a Bayesian estimator for the absorption coefficient built from the noisy data obtained in a simplified DOT Model. We establish the rate of convergence of such an estimator in the supremum norm loss and show that it is optimal. We also present numerical experiments in support of our theoretical findings.

Implicit representations of 3D objects have recently achieved impressive results on learning-based 3D reconstruction tasks. While existing works use simple texture models to represent object appearance, photo-realistic image synthesis requires reasoning about the complex interplay of light, geometry and surface properties. In this work, we propose a novel implicit representation for capturing the visual appearance of an object in terms of its surface light field. In contrast to existing representations, our implicit model represents surface light fields in a continuous fashion and independent of the geometry. Moreover, we condition the surface light field with respect to the location and color of a small light source. Compared to traditional surface light field models, this allows us to manipulate the light source and relight the object using environment maps. We further demonstrate the capabilities of our model to predict the visual appearance of an unseen object from a single real RGB image and corresponding 3D shape information. As evidenced by our experiments, our model is able to infer rich visual appearance including shadows and specular reflections. Finally, we show that the proposed representation can be embedded into a variational auto-encoder for generating novel appearances that conform to the specified illumination conditions.

In recent years, substantial progress has been achieved in learning-based reconstruction of 3D objects. At the same time, generative models were proposed that can generate highly realistic images. However, despite this success in these closely related tasks, texture reconstruction of 3D objects has received little attention from the research community and state-of-the-art methods are either limited to comparably low resolution or constrained experimental setups. A major reason for these limitations is that common representations of texture are inefficient or hard to interface for modern deep learning techniques. In this paper, we propose Texture Fields, a novel texture representation which is based on regressing a continuous 3D function parameterized with a neural network. Our approach circumvents limiting factors like shape discretization and parameterization, as the proposed texture representation is independent of the shape representation of the 3D object. We show that Texture Fields are able to represent high frequency texture and naturally blend with modern deep learning techniques. Experimentally, we find that Texture Fields compare favorably to state-of-the-art methods for conditional texture reconstruction of 3D objects and enable learning of probabilistic generative models for texturing unseen 3D models. We believe that Texture Fields will become an important building block for the next generation of generative 3D models.