When Computer Vision Gazes at Cognition

Joint attention is a core, early-developing form of social interaction. It is based on our ability to discriminate the third party objects that other people are looking at. While it has been shown that people can accurately determine whether another person is looking directly at them versus away, little is known about human ability to discriminate a third person gaze directed towards objects that are further away, especially in unconstraint cases where the looker can move her head and eyes freely. In this paper we address this question by jointly exploring human psychophysics and a cognitively motivated computer vision model, which can detect the 3D direction of gaze from 2D face images. The synthesis of behavioral study and computer vision yields several interesting discoveries. (1) Human accuracy of discriminating targets 8{\deg}-10{\deg} of visual angle apart is around 40% in a free looking gaze task; (2) The ability to interpret gaze of different lookers vary dramatically; (3) This variance can be captured by the computational model; (4) Human outperforms the current model significantly. These results collectively show that the acuity of human joint attention is indeed highly impressive, given the computational challenge of the natural looking task. Moreover, the gap between human and model performance, as well as the variability of gaze interpretation across different lookers, require further understanding of the underlying mechanisms utilized by humans for this challenging task.Comment: Tao Gao and Daniel Harari contributed equally to this wor

Invariant Jordan curves of Sierpiski carpet rational maps

In this paper, we prove that if $R\colon\widehat{\mathbb{C}}\to\widehat{\mathbb{C}}$ is a postcritically finite rational map with Julia set homeomorphic to the Sierpi\'nski carpet, then there is an integer $n_0$, such that, for any $n\ge n_0$, there exists an $R^n$-invariant Jordan curve $\Gamma$ containing the postcritical set of $R$.Comment: 16 pages, 1 figu

LDSO: Direct Sparse Odometry with Loop Closure

In this paper we present an extension of Direct Sparse Odometry (DSO) to a monocular visual SLAM system with loop closure detection and pose-graph optimization (LDSO). As a direct technique, DSO can utilize any image pixel with sufficient intensity gradient, which makes it robust even in featureless areas. LDSO retains this robustness, while at the same time ensuring repeatability of some of these points by favoring corner features in the tracking frontend. This repeatability allows to reliably detect loop closure candidates with a conventional feature-based bag-of-words (BoW) approach. Loop closure candidates are verified geometrically and Sim(3) relative pose constraints are estimated by jointly minimizing 2D and 3D geometric error terms. These constraints are fused with a co-visibility graph of relative poses extracted from DSO's sliding window optimization. Our evaluation on publicly available datasets demonstrates that the modified point selection strategy retains the tracking accuracy and robustness, and the integrated pose-graph optimization significantly reduces the accumulated rotation-, translation- and scale-drift, resulting in an overall performance comparable to state-of-the-art feature-based systems, even without global bundle adjustment