Geometry-Consistent Neural Shape Representation with Implicit Displacement Fields

We present implicit displacement fields, a novel representation for detailed 3D geometry. Inspired by a classic surface deformation technique, displacement mapping, our method represents a complex surface as a smooth base surface plus a displacement along the base's normal directions, resulting in a frequency-based shape decomposition, where the high frequency signal is constrained geometrically by the low frequency signal. Importantly, this disentanglement is unsupervised thanks to a tailored architectural design that has an innate frequency hierarchy by construction. We explore implicit displacement field surface reconstruction and detail transfer and demonstrate superior representational power, training stability and generalizability.

Studying Invariances of Trained Convolutional Neural Networks

Convolutional Neural Networks (CNNs) define an exceptionally powerful class of models for image classification, but the theoretical background and the understanding of how invariances to certain transformations are learned is limited. In a large scale screening with images modified by different affine and nonaffine transformations of varying magnitude, we analyzed the behavior of the CNN architectures AlexNet and ResNet. If the magnitude of different transformations does not exceed a class- and transformation dependent threshold, both architectures show invariant behavior. In this work we furthermore introduce a new learnable module, the Invariant Transformer Net, which enables us to learn differentiable parameters for a set of affine transformations. This allows us to extract the space of transformations to which the CNN is invariant and its class prediction robust.