One of the fundamental tasks in visualization is to compare two or more visual elements. However, it is often difficult to visually differentiate graphical elements encoding a small difference in value, such as the heights of similar bars in bar chart or angles of similar sections in pie chart. Perceptual laws can be used in order to model when and how we perceive this difference. In this work, we model the perception of Just Noticeable Differences (JNDs), the minimum difference in visual attributes that allow faithfully comparing similar elements, in charts. Specifically, we explore the relation between JNDs and two major visual variables: the intensity of visual elements and the distance between them, and study it in three charts: bar chart, pie chart and bubble chart. Through an empirical study, we identify main effects on JND for distance in bar charts, intensity in pie charts, and both distance and intensity in bubble charts. By fitting a linear mixed effects model, we model JND and find that JND grows as the exponential function of variables. We highlight several usage scenarios that make use of the JND modeling in which elements below the fitted JND are detected and enhanced with secondary visual cues for better discrimination.

We introduce the first path-oriented drone trajectory planning algorithm, which performs continuous (i.e., dense ) image acquisition along an aerial path and explicitly factors path quality into an optimization along with scene reconstruction quality. Specifically, our method takes as input a rough 3D scene proxy and produces a drone trajectory and image capturing setup, which efficiently yields a high-quality reconstruction of the 3D scene based on three optimization objectives: one to maximize the amount of 3D scene information that can be acquired along the entirety of the trajectory, another to optimize the scene capturing efficiency by maximizing the scene information that can be acquired per unit length along the aerial path, and the last one to minimize the total turning angles along the aerial path, so as to reduce the number of sharp turns. Our search scheme is based on the rapidly-exploring random tree framework, resulting in a final trajectory as a single path through the search tree. Unlike state-of-the-art works, our joint optimization for view selection and path planning is performed in a single step. We comprehensively evaluate our method not only on benchmark virtual datasets as in existing works but also on several large-scale real urban scenes. We demonstrate that the continuous paths optimized by our method can effectively reduce onsite acquisition cost using drones, while achieving high-fidelity 3D reconstruction, compared to existing planning methods and oblique photography, a mature and popular industry solution.