# A Cascaded Ensemble of Sparse-and-Dense Dictionaries for Vehicle Detection
###### Abstract  
Vehicle detection as a special case of object detection has practical meaning but faces challenges, such as the difficulty of detecting vehicles of various orientations, the serious influence from occlusion, the clutter of background, etc. In addition, existing effective approaches, like deep-learning-based ones, demand a large amount of training time and data, which causes trouble for their application. In this work, we propose a dictionary-learning-based vehicle detection approach which explicitly addresses these problems. Specifically, an ensemble of sparse-and-dense dictionaries (ESDD) are learned through supervised low-rank decomposition; each pair of sparse-and-dense dictionaries (SDD) in the ensemble is trained to represent either a subcategory of vehicle (corresponding to certain orientation range or occlusion level) or a subcategory of background (corresponding to a cluster of background patterns) and only gives good reconstructions to samples of the corresponding subcategory, making the ESDD capable of classifying vehicles from background even though they exhibit various appearances. We further organize ESDD into a two-level cascade (CESDD) to perform coarse-to-fine two-stage classification for better performance and computation reduction. The CESDD is then coupled with a downstream AdaBoost process to generate robust classifications. The proposed CESDD model is used as a window classifier in a sliding-window scan process over image pyramids to produce multi-scale detections, and an adapted mean-shift-like non-maximum suppression process is adopted to remove duplicate detections. Our CESDD vehicle detection approach is evaluated on KITTI dataset and compared with other strong counterparts; the experimental results exhibit the effectiveness of CESDD-based classification and detection, and the training of CESDD only demands small amount of time and data. object detection; vehicle detection; dictionary learning; ensemble learning +
Footnote †: journal: Medical  
training-data-intensive and training-time-intensive characteristics cause troubles for their real-world application. In contrast, dictionary learning models have been successfully applied to recognition tasks through learning of dictionaries for discriminative coding, attaining good recognition ability with low demanding of training data and time [10; 11]. In the case of vehicle detection, vehicles and background exhibit various appearances which are hard to represent with a single dictionary, but are well represented with an ensemble of multiple dictionaries [12; 13]; furthermore, dictionaries could easily cooperate with additional machine learning models to attain strong recognition abilities, like [13; 14]. This paper presents a dictionary-learning-based sliding-window-styled vehicle detection approach. In general, the proposed approach learns an ensemble of dictionaries to represent both vehicle appearances and background patterns. Specifically, vehicle and background categories are further divided into several subcategories, each of which is easier to represent with a dictionary model; each subcategory of vehicle corresponds to certain orientation range (a sub-range in 0-2\(\pi\)) and certain occlusion level (fully visible/partly occluded/largely occluded); and each subcategory of background corresponds to a cluster of background patterns (the background pattern clusters are obtained by clustering algorithms like K-means). For each subcategory, we learn a pair of sparse-and-dense dictionaries (SDDs) to represent corresponding sample appearances; SDD is capable of capturing subcategory-specific intrinsic features with its sparse dictionary and absorbing non-subcategory-specific patterns (like noises and shadows) with its dense dictionary, so it is able to give good reconstructions to samples of the corresponding subcategory only but not for others; the desired SDD could be efficiently learned through the supervised low-rank (SLR) decomposition [11].