## 1 Introduction
They further perform a contour recognition for each sign using a linear regression model based on a raster image. [PERSON] et al. [9] utilize prior information to eliminate ground and building points. They then segment the remaining data to different categories based on local descriptor histogram (LDH), spin images, and geometrical features. [PERSON] et al. [10] detect high elevated objects located on top or border of the road in MLS point cloud and cluster these high elevated objects to traffic sign and light pole classes. They further introduce a modified seeded region growing algorithm to remove noisy points and incorporate shape information to filter out false objects from both classes. These aforementioned methods use the 3-dimensional information or reflectiveness of traffic signs to detect various objects. However, their detection efficiency and effectiveness on airborne LiDAR data is degraded due to its low quality resulted from a large number of outliers and different angles of view. To achieve the maximum level of accuracy and completeness, we propose to develop a data fusion approach that utilizes both aerial LiDAR and aerial imagery data to address the limitations of both image-based and LiDAR-based methods. Unlike other methods [9; 10], which detect traffic signs using high resolution MLS data, the proposed method detects traffic sign candidates in airborne LiDAR data, which tend to be more noisy than MLS data and easier and faster to collect. It also represents traffic sign candidates in a convex optimization model in color imagery data to classify candidates as traffic or non-traffic signs at a higher accuracy. Specifically, we first segment the airborne color images to road and non-road segments by integrating various local features in an inequality constraint quadratic optimization model. Next, we find the corresponding road regions in LiDAR data and use the height information to extract high elevated objects above the road. We then use Euclidean distance-based clustering to segment extracted objects into traffic sign candidate regions. Finally, we find the corresponding traffic sign candidate regions in color images and extract their convolutional neural network (CNN) features in a new convex optimization framework to classify them as traffic signs or non-traffic signs. The main contributions of the paper are as follows:* Incorporating various local features extracted from color imagery data in an inequality constraint quadratic optimization model and numerically solving the model using the accelerated proximal gradient (APG) method. * Adopting Euclidean distance-based clustering to classify high elevated objects in LiDAR data to several object candidates. * Developing a convex optimization model in color imagery data to classify object candidates as traffic or non-traffic signs. * Seamlessly combining the CNN features of local patches of each object candidate with a group-sparsity regularization term to encourage the classifier to sparsely select appropriate local patches of the same subset of templates. * Designing a fast and parallel numerical algorithm by deriving the augmented Lagrangian of the optimization model into two close-form problems: the quadratic problem and the Euclidean norm projection onto probability simplex constraints problem. The remainder of this paper is organized as follows: Section 2 describes the three main components of the proposed method in detail. These three components are road extraction, traffic sign candidate detection, and traffic sign classification. Section 3 presents experimental results and demonstrates the effectiveness of the proposed method to utilize information captured from geo-referenced color images and noisy airborne LiDAR data provided by Utah State University (USU) for Utah DOT (UDOT) along I-15 highway. Section 4 draws the conclusions.