Diffusion maps for exploring electro-optical synthetic vehicle image data

In this work, we explore low-dimensional representations of high-dimensional data derived from electro-optical synthetic vehicle images. The collection of vehicle images consists of four different vehicle models: Toyota Camry, Toyota Avalon, Toyota Tacoma, and Nissan Sentra. This data contains 3,601 160 × 213 gray-scale vehicle images sampled uniformly over a camera view hemisphere. We use the non-linear manifold learning technique of diffusion maps with Gaussian kernel to explore low-dimensional structure the high-dimensional cloud of vehicle image observations. Diffusion maps have been shown to be a valuable tool in the analysis of high-dimensional data and the technique is able to extract an approximation for the underlying structure inherent to the data. Our analysis includes examining how the diffusion time and kernel width leads to different low-dimensional representations and we present a novel technique to relate the kernel width to the distribution of data in the observation space. In addition, we present initial results for multi-class vehicle classification through low-dimensional embedding coordinates and the out-of-sample extension of unlabeled vehicle images.