In the following work object detection approaches with Convolutional Neural Networks (CNNs), which have provable characteristics regarding translational robustness, are proposed, evaluated in an application scenario, and compared to state of the art approaches. The provable characteristics are achieved by transferring theoretical results from wavelet theory and scattering networks to common CNNs used for classification. Therefore first a CNN is modeled as a scattering network. Needed parameters are estimated with data relevant for application scenarios. With the obtained information first the best feature extractor for a given application scenario is chosen. Afterward, the theory is extended to cover object detection networks. The proposed approaches are trained on simulated and real datasets and evaluated on real datasets.