SDICP: Semi-Dense Tracking based on Iterative Closest Points

The paper addresses the problem of camera tracking, which denotes the continuous image-based computation of a camera’s position and orientation with respect to a reference frame. The method aims at regular cameras, which means that 3D-3D registration methods applicable to RGB-D cameras are not an option. The tracked frame contains only 2D information, thus requiring a solution to the absolute pose or 2D-3D registration problem. While traditional solutions to camera tracking [3] rely on sparse feature correspondences, the community has recently seen a number of direct photometric registration methods such as Newcombe et al. [8] and Engel et al. [1]. [1] is conceptually similar to [8], however gains computational efficiency by reducing the computation from dense to semi-dense regions that correspond to a thresholded edge-map of the image. Photometric methods have the more general advantage of compensating for appearance variations caused by perspective view-point changes, whereas classical sparse methods often rely on static feature descriptors only (providing at most rotation and scale invariant properties [5, 6]). However, photometric registration techniques inherently suffer from the disability to overcome large disparities, where large sometimes means even just a couple of pixels [7]. Many photometric registration techniques therefore depend on pyramidal subsampling schemes in order to alleviate this problem. The goal of the present paper is a novel 2D-3D registration paradigm for semi-dense depth maps that relies on the Iterative Closest Point (ICP) technique, and thus a reintroduction of geometric error minimization as a valid alternative for real-time monocular camera tracking in the case of semi-dense features. An example semi-dense depth map is indicated in Figure 1. In comparison to photometric registration techniques, our ICP technique has the conceptual advantage of requiring neither isotropic enlargement of the employed semi-dense regions, nor pyramidal subsampling. The work is in line with Feldmar et al. [2], Tomono [9], and Klein and Murray [4], which already attempt curve or edge registration in 2D using ICP. Based on a hypothesized relative pose, the basic idea consists of warping a reference curve into the tracked image based on a prior 3D model or depth (in our case semi-dense) inside a reference frame. From a mathematical point of view, our idea may be formulated as follows. Let