Differential Features for Pedestrian Detection: A Taylor Series Perspective

Differential features are popularly used in computer vision tasks, such as object detection. In this paper, we revisit these features from a functional approximation perspective. In particular, we view an image as a 2-D functional and investigate its Taylor series approximation. Differential features are derived from the approximation coefficients and, therefore, are naturally collected for appearance representation. Thus motivated, we propose to use the zeroth-, first-, and second-order differential features for pedestrian detection and call such features Taylor feature transform (TAFT). In practice, the TAFT features are computed by discrete sampling to address scale issues and meanwhile achieve computational efficiency. In addition, orientation insensitivity is handled by using directional versions of differentials. When applied to pedestrian detection, the TAFT is sampled on grid pixels and calculated from multiple channels following previous solutions. In our extensive experiments on the INRIA, Caltech, TUD-Brussel, and KITTI data sets, the TAFT achieves state-of-the-art results. It outperforms all handcrafted features and performs on par with many deep-learning solutions. Moreover, when a low false-positive rate is requested, the TAFT generates results that are better than or comparable to the state-of-the-art deep learning-based methods. Meanwhile, our implementation runs at 33 fps for $640\times 480$ images without GPU, making TAFT favorable in many practical scenarios.