text: Terahertz (THz) sensing is a promising imaging technology for a wide variety of different applications. Extracting the interpretable and physically meaningful parameters for such applications, however, requires solving an inverse problem in which a model function determined by these parameters needs to be fitted to the measured data. Since the underlying optimization problem is nonconvex and very costly to solve, we propose learning the prediction of suitable parameters from the measured data directly. More precisely, we develop a model-based autoencoder in which the encoder network predicts suitable parameters and the decoder is fixed to a physically meaningful model function, such that we can train the encoding network in an unsupervised way. We illustrate numerically that the resulting network is more than 140 times faster than classical optimization techniques while making predictions with only slightly higher objective values. Using such predictions as starting points of local optimization techniques allows us to converge to better local minima about twice as fast as optimization without the network-based initialization.
  @cite_9: In this work we propose a novel model-based deep convolutional autoencoder that addresses the highly challenging problem of reconstructing a 3D human face from a single in-the-wild color image. To this end, we combine a convolutional encoder network with an expert-designed generative model that serves as decoder. The core innovation is the differentiable parametric decoder that encapsulates image formation analytically based on a generative model. Our decoder takes as input a code vector with exactly defined semantic meaning that encodes detailed face pose, shape, expression, skin reflectance and scene illumination. Due to this new way of combining CNN-based with model-based face reconstruction, the CNN-based encoder learns to extract semantically meaningful parameters from a single monocular input image. For the first time, a CNN encoder and an expert-designed generative model can be trained end-to-end in an unsupervised manner, which renders training on very large (unlabeled) real world data feasible. The obtained reconstructions compare favorably to current state-of-the-art approaches in terms of quality and richness of representation.
  @cite_23: In this paper, a new technique for modeling textured 3D faces is introduced. 3D faces can either be generated automatically from one or more photographs, or modeled directly through an intuitive user interface. Users are assisted in two key problems of computer aided face modeling. First, new face images or new 3D face models can be registered automatically by computing dense one-to-one correspondence to an internal face model. Second, the approach regulates the naturalness of modeled faces avoiding faces with an “unlikely” appearance. Starting from an example set of 3D face models, we derive a morphable face model by transforming the shape and texture of the examples into a vector space representation. New faces and expressions can be modeled by forming linear combinations of the prototypes. Shape and texture constraints derived from the statistics of our example faces are used to guide manual modeling or automated matching algorithms. We show 3D face reconstructions from single images and their applications for photo-realistic image manipulations. We also demonstrate face manipulations according to complex parameters such as gender, fullness of a face or its distinctiveness.
summary: The most related prior work is the 3D face reconstruction network from Tewari al @cite_9 . They aimed at finding a semantic code vector from a given facial image such that feeding this code vector into a rending engine yields an image similar to the input image itself. While this problem had been addressed using optimization algorithms a long time ago @cite_23 (also known under the name of analysis-by-synthesis approaches), the Tewari al @cite_9 replaced the optimizer with a neural network and kept the original cost function to train the network in an unsupervised way. The resulting structure resembles an AE in which the decoder fixed to the forward model and was therefore coined model-based AE. As we will discuss in the next section, the idea of model-based AEs generalizes far beyond 3D face reconstruction and can be used to boost the THz parameter identification problem significantly.