  In this study, we propose a novel approach to predict the distances of the
detected objects in an observed scene. The proposed approach modifies the
recently proposed Convolutional Support Estimator Networks (CSENs). CSENs are
designed to compute a direct mapping for the Support Estimation (SE) task in a
representation-based classification problem. We further propose and demonstrate
that representation-based methods (sparse or collaborative representation) can
be used in well-designed regression problems. To the best of our knowledge,
this is the first representation-based method proposed for performing a
regression task by utilizing the modified CSENs; and hence, we name this novel
approach as Representation-based Regression (RbR). The initial version of CSENs
has a proxy mapping stage (i.e., a coarse estimation for the support set) that
is required for the input. In this study, we improve the CSEN model by
proposing Compressive Learning CSEN (CL-CSEN) that has the ability to jointly
optimize the so-called proxy mapping stage along with convolutional layers. The
experimental evaluations using the KITTI 3D Object Detection distance
estimation dataset show that the proposed method can achieve a significantly
improved distance estimation performance over all competing methods. Finally,
the software implementations of the methods are publicly shared at
https://github.com/meteahishali/CSENDistance.
