# A Cascaded Ensemble of Sparse-and-Dense Dictionaries for Vehicle Detection
## 3 Training of CESDD
### Downstream AdaBoost Classifier Learning  
Even though the proposed cascade of SDD ensemble achieved pretty good classification performance, the situation of in-the-wild vehicle detection is still very complex in terms of image appearances. In this case, classification accuracy, especially for vehicle category, deserves more emphasis, since it is critical to the robustness of vehicle detection. The fact of the existence of ensemble of SDDs in the proposed CESDD-based classifier provides a chance to cooperate with ensemble learning models, like AdaBoost. Specifically, every SDD from vehicle category and every other SDD from background category could be coupled to act as a weak vehicle/background classifier (a micro ESDD-based classifier with ensemble size as two). In this way, many such couples of SDDs could be constructed as such kind of weak classifiers, creating the possibility of applying AdaBoost process. These SDD couples are not independent from each other, since there exists couples sharing common SDDs, while AdaBoost algorithm requires independent weak classifiers that are learned incrementally. To bridge this gap, instead of directly using the SDD couples as weak classifiers, additional machine learning models could be adopted as the weak classifiers which take the reconstruction residues from the SDD couples as inputs. With this adaptation, AdaBoost process could be carried out to learn these weak classifiers and corresponding aggregation weights. The steps in CESDD training and CESDD-based detection where this downstream AdaBoost mechanism is involved are illustrated as portions of Figure 1a,b; note that each weak classifier is learned from the training samples' reconstruction residues produced by the corresponding SDD couple only.  
In the case of cascaded SDD ensemble, weak classifiers learned from SDD couples purely consisting of Level 1 SDDs are evaluated for all incoming test samples to generate initial classifications, while weak classifiers learned from SDD couples consisting of Level 2 VP type SDDs and Level 1 vehicle category (FV or PO) SDDs are only evaluated for initial positive classifications, and weak classifiers learned from SDD couples consisting of Level 2 LO vehicle type SDDs and Level 1 background category SDDs are to be evaluated only for initial negative classifications. For an input sample, classifications from all evaluated weak classifiers are aggregated to form the final classification; the detailed procedure is illustrated in Figure 7. The effectiveness of this downstream AdaBoost process could be observed in subsequent experimental results, and the enhancement in classification accuracy of vehicle category is noticeable.  
Figure 5: Two kinds of subcategory divisions in SDD ensemble and corresponding classification workflows: (**a**) no subcategory; (**b**) multiple subcategories in each category.  
Figure 6: Quantitative ablation evaluation results of CESDD classifier on KITTI2017. (**a**) multiple subcategories vs. no subcategory; (**b**) with cascade vs. without cascade; (**c**) with AdaBoost vs. without AdaBoost; (**d**) comparison of features; (**e**) with vs. without feature selection; (**f**) CESDD classifier vs. other classifiers.