On visual complexity of 3D shapes

We present an approach to compute the perceived complexity of a given 3D shape using the similarity between its views. Previous studies on 3D shape complexity relied on geometric and/or topological properties of the shape and are not appropriate for incorporating results from human shape perception which claim that humans perceive 3D shapes as organizations of 2D views. Therefore, we base our approach to computing 3D shape complexity on the (dis)similarity matrix of the shape's 2D views. To illustrate the application of our approach, we note that simple shapes lead to similar views whereas complex ones result in different, dissimilar views. This reflected in the View Similarity Graph (VSG) of a shape as tight clusters of points if the shape is simple and increasingly dispersed points as it gets more complex. To get a visual intuition of the VSG, we project it to 2D using Multi-Dimensional Scaling (MDS) and introduce measures to compute shape complexity through point dispersion in the resulting MDS plot. Experiments show that results obtained using our measures alleviate some of the drawbacks present in previous approaches.

Graphical AbstractAn overview of our approach. Views of a shape are captured and their boundary contours are extracted and compared with each other to yield a similarity matrix, S. The distances in S are represented as a 2D plot using SSA. Point positions in the plot are then used to compute complexity. (a) A shape to be analyzed. (b) The shape's view sphere (c) Some views of the shape. (d) Extracted boundary contours of the views. (e) Similarity matrix of boundary contours. (f) SSA plot corresponding to S.Figure optionsDownload high-quality image (39 K)Download as PowerPoint slideHighlights
► We introduce the View Similarity Graph (VSG) of a 3D shape.
► Point dispersion in a shape's VSG is used to compute its visual complexity.
► To obtain a visual intuition, the VSG is projected to 2D.
► Our approach alleviates some artifacts of previous methods.