You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Illumination estimation is often used in mixed reality to re-render a scene from another point of view, to change the color texture of an object, or to insert a virtual object consistently lit into a real video or photograph. Specifically, the estimation of a point light source is required for the shadows cast by the inserted object to be consistent with the real scene. We tackle the problem of illumination retrieval given an RGBD image of the scene as an inverse problem: we aim to find the illumination that minimizes the photometric error between the rendered image and the observation. In particular we propose a novel differentiable renderer based on the Blinn-Phong model with cast shadows. We compare our differentiable renderer to state-of-the-art methods and demonstrate its robustness to an incorrect reflectance estimation.

Cited Abstract(s):
[1]: Faithful manipulation of shape, material, and illumination in 2D Internet images would greatly benefit from a reliable factorization of appearance into material (i.e., diffuse and specular) and illumination (i.e., environment maps). On the one hand, current methods that produce very high fidelity results, typically require controlled settings, expensive devices, or significant manual effort. To the other hand, methods that are automatic and work on 'in the wild' Internet images, often extract only low-frequency lighting or diffuse materials. In this work, we propose to make use of a set of photographs in order to jointly estimate the non-diffuse materials and sharp lighting in an uncontrolled setting. Our key observation is that seeing multiple instances of the same material under different illumination (i.e., environment), and different materials under the same illumination provide valuable constraints that can be exploited to yield a high-quality solution (i.e., specular materials and environment illumination) for all the observed materials and environments. Similar constraints also arise when observing multiple materials in a single environment, or a single material across multiple environments. The core of this approach is an optimization procedure that uses two neural networks that are trained on synthetic images to predict good gradients in parametric space given observation of reflected light. We evaluate our method on a range of synthetic and real examples to generate high-quality estimates, qualitatively compare our results against state-of-the-art alternatives via a user study, and demonstrate photo-consistent image manipulation that is otherwise very challenging to achieve.

[2]: In this paper, we present a method that estimates reflectance and illumination information from a single image depicting a single-material specular object from a given class under natural illumination. We follow a data-driven, learning-based approach trained on a very large dataset, but in contrast to earlier work we do not assume one or more components (shape, reflectance, or illumination) to be known. We propose a two-step approach, where we first estimate the object’s reflectance map, and then further decompose it into reflectance and illumination. For the first step, we introduce a Convolutional Neural Network (CNN) that directly predicts a reflectance map from the input image itself, as well as an indirect scheme that uses additional supervision, first estimating surface orientation and afterwards inferring the reflectance map using a learning-based sparse data interpolation technique. For the second step, we suggest a CNN architecture to reconstruct both Phong reflectance parameters and high-resolution spherical illumination maps from the reflectance map. We also propose new datasets to train these CNNs. We demonstrate the effectiveness of our approach for both steps by extensive quantitative and qualitative evaluation in both synthetic and real data as well as through numerous applications, that show improvements over the state-of-the-art.

[3]: 

[4]: We present a CNN-based technique to estimate high-dynamic range outdoor illumination from a single low dynamic range image. To train the CNN, we leverage a large dataset of outdoor panoramas. We fit a low-dimensional physically-based outdoor illumination model to the skies in these panoramas giving us a compact set of parameters (including sun position, atmospheric conditions, and camera parameters). We extract limited field-of-view images from the panoramas, and train a CNN with this large set of input image--output lighting parameter pairs. Given a test image, this network can be used to infer illumination parameters that can, in turn, be used to reconstruct an outdoor illumination environment map. We demonstrate that our approach allows the recovery of plausible illumination conditions and enables photorealistic virtual object insertion from a single image. An extensive evaluation on both the panorama dataset and captured HDR environment maps shows that our technique significantly outperforms previous solutions to this problem.

[5]: We propose an automatic method to infer high dynamic range illumination from a single, limited field-of-view, low dynamic range photograph of an indoor scene. In contrast to previous work that relies on specialized image capture, user input, and or simple scene models, we train an end-to-end deep neural network that directly regresses a limited field-of-view photo to HDR illumination, without strong assumptions on scene geometry, material properties, or lighting. We show that this can be accomplished in a three step process: 1) we train a robust lighting classifier to automatically annotate the location of light sources in a large dataset of LDR environment maps, 2) we use these annotations to train a deep neural network that predicts the location of lights in a scene from a single limited field-of-view photo, and 3) we fine-tune this network using a small dataset of HDR environment maps to predict light intensities. This allows us to automatically recover high-quality HDR illumination estimates that significantly outperform previous state-of-the-art methods. Consequently, using our illumination estimates for applications like 3D object insertion, produces photo-realistic results that we validate via a perceptual user study.

[6]: This paper presents the first photometric registration pipeline for Mixed Reality based on high quality illumination estimation using convolutional neural networks (CNNs). For easy adaptation and deployment of the system, we train the CNNs using purely synthetic images and apply them to real image data. To keep the pipeline accurate and efficient, we propose to fuse the light estimation results from multiple CNN instances and show an approach for caching estimates over time. For optimal performance, we furthermore explore multiple strategies for the CNN training. Experimental results show that the proposed method yields highly accurate estimates for photo-realistic augmentations.
From a machine learning perspective, state-of-the-art techniques aim to estimate illumination (either indoor [5] or outdoor [4] ) by learning the weights of a neural network. To train such network, a supervised strategy is often adopted: the loss function is the error between some ground truth illumination and the illumination computed by the network fed with an example image. Rematas al [3] learn to estimate an intermediate representation that mixes illumination and a single material, called a "reflectance map". In [2] this architecture is combined with a CNN that decomposes the reflectance map into an environment map and a single material. In [1] a parametric model of illumination and material is fitted to a reflectance map, via a light transport operator that is approximated by two neural networks preliminary trained on synthetic data. Mandl al [6] try to estimate the illumination only, by training a CNN for every camera pose sampled around an object used as a light probe.