Representation Based Regression for Object Distance Estimation

TL;DR

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 and can achieve a significantly improved distance estimation performance over all competing methods.

Abstract

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.

Figures (9)

• Figure 1: The proposed framework for the object distance estimation is based on representation-based classification methodologies including Sparse Representation-based Classification (SRC) and Collaborative Representation-based Classification (CRC). The output class estimation yields the quantized estimated distance.
• Figure 2: To form the representative dictionary $\mathbf{D}$, samples are collected with the increasing order of the distances. Then, they are resized and fed to the feature extractor. Next, after additional dimensional reduction operation with the matrix $\mathbf{A}$, they are stacked in such a way that the first-class category corresponds to 1m and the $C^{\text{th}}$ class to $C$ meters.
• Figure 3: The proposed framework for the object distance estimation based on Convolutional Support Estimator Networks (CSEN). The modified CSEN performs regression over the estimated support sets using the reshaped proxy signal $\mathbf{\Tilde{x}} = \mathbf{By}$ where $\mathbf{B}=\left( \mathbf{D}^T\mathbf{D}+\lambda\mathbf{I} \right)^{-1}\mathbf{D}^T$.
• Figure 4: Conventional dictionary design versus the proposed dictionary design for the CSEN. In the conventional dictionary design, samples are collected with the increasing order of the distances. The first, second, third class categories correspond to 1m, 2m, 3m, respectively, and the $C^{\text{th}}$ class corresponds to $C$ meters.
• Figure 5: The proposed Compressive Learning CSEN (CL-CSEN) framework that jointly optimizes proxy mapping with support estimation and regression parts during the training.