text: In this paper we propose an edge-direct visual odometry algorithm that efficiently utilizes edge pixels to find the relative pose that minimizes the photometric error between images. Prior work on exploiting edge pixels instead treats edges as features and employ various techniques to match edge lines or pixels, which adds unnecessary complexity. Direct methods typically operate on all pixel intensities, which proves to be highly redundant. In contrast our method builds on direct visual odometry methods naturally with minimal added computation. It is not only more efficient than direct dense methods since we iterate with a fraction of the pixels, but also more accurate. We achieve high accuracy and efficiency by extracting edges from only one image, and utilize robust Gauss-Newton to minimize the photometric error of these edge pixels. This simultaneously finds the edge pixels in the reference image, as well as the relative camera pose that minimizes the photometric error. We test various edge detectors, including learned edges, and determine that the optimal edge detector for this method is the Canny edge detection algorithm using automatic thresholding. We highlight key differences between our edge direct method and direct dense methods, in particular how higher levels of image pyramids can lead to significant aliasing effects and result in incorrect solution convergence. We show experimentally that reducing the photometric error of edge pixels also reduces the photometric error of all pixels, and we show through an ablation study the increase in accuracy obtained by optimizing edge pixels only. We evaluate our method on the RGB-D TUM benchmark on which we achieve state-of-the-art performance.
  @cite_0: 
  @cite_18: In this work, we present a real-time robust edge-based visual odometry framework for RGBD sensors (REVO). Even though our method is independent of the edge detection algorithm, we show that the use of state-of-the-art machine-learned edges gives significant improvements in terms of robustness and accuracy compared to standard edge detection methods. In contrast to approaches that heavily rely on the photo-consistency assumption, edges are less influenced by lighting changes and the sparse edge representation offers a larger convergence basin while the pose estimates are also very fast to compute. Further, we introduce a measure for tracking quality, which we use to determine when to insert a new key frame. We show the feasibility of our system on real-world datasets and extensively evaluate on standard benchmark sequences to demonstrate the performance in a wide variety of scenes and camera motions. Our framework runs in real-time on the CPU of a laptop computer and is available online.
  @cite_10: Direct Sparse Odometry (DSO) is a visual odometry method based on a novel, highly accurate sparse and direct structure and motion formulation. It combines a fully direct probabilistic model (minimizing a photometric error) with consistent, joint optimization of all model parameters, including geometry-represented as inverse depth in a reference frame-and camera motion. This is achieved in real time by omitting the smoothness prior used in other direct methods and instead sampling pixels evenly throughout the images. Since our method does not depend on keypoint detectors or descriptors, it can naturally sample pixels from across all image regions that have intensity gradient, including edges or smooth intensity variations on essentially featureless walls. The proposed model integrates a full photometric calibration, accounting for exposure time, lens vignetting, and non-linear response functions. We thoroughly evaluate our method on three different datasets comprising several hours of video. The experiments show that the presented approach significantly outperforms state-of-the-art direct and indirect methods in a variety of real-world settings, both in terms of tracking accuracy and robustness.
summary: The extension of direct methods using edge pixels is a logical direction, yet to the best of our knowledge no work has solely used edge pixels in a direct method minimizing the photometric error. @cite_18 the authors reduce a Euclidean geometric error using the distance transform on edges which does not utilize all information available in the scene. @cite_0 the authors minimize a joint error function combining photometric error over all pixels along with geometric error over edge pixels. Minimizing a joint error function always suffers from the decision on how best to weight each function, and the weighting can have significant effect on the final converged solution. @cite_10 , the authors threshold by gradients, which does not guarantee edges due to noise. They additionally select texture-less regions as well.