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This paper presents a novel architecture for simultaneous estimation of highly accurate optical flows and rigid scene transformations for difficult scenarios where the brightness assumption is violated by strong shading changes. In the case of rotating objects or moving light sources, such as those encountered for driving cars in the dark, the scene appearance often changes significantly from one view to the next. Unfortunately, standard methods for calculating optical flows or poses are based on the expectation that the appearance of features in the scene remain constant between views. These methods may fail frequently in the investigated cases. The presented method fuses texture and geometry information by combining image, vertex and normal data to compute an illumination-invariant optical flow. By using a coarse-to-fine strategy, globally anchored optical flows are learned, reducing the impact of erroneous shading-based pseudo-correspondences. Based on the learned optical flows, a second architecture is proposed that predicts robust rigid transformations from the warped vertex and normal maps. Particular attention is payed to situations with strong rotations, which often cause such shading changes. Therefore a 3-step procedure is proposed that profitably exploits correlations between the normals and vertices. The method has been evaluated on a newly created dataset containing both synthetic and real data with strong rotations and shading effects. This data represents the typical use case in 3D reconstruction, where the object often rotates in large steps between the partial reconstructions. Additionally, we apply the method to the well-known Kitti Odometry dataset. Even if, due to fulfillment of the brighness assumption, this is not the typical use case of the method, the applicability to standard situations and the relation to other methods is therefore established.