Visibility Graphs for Image Processing

Abstract

The family of image visibility graphs (IVGs) have been recently introduced as simple algorithms by which scalar fields can be mapped into graphs. Here we explore the usefulness of such operator in the scenario of image processing and image classification. We demonstrate that the link architecture of the image visibility graphs encapsulates relevant information on the structure of the images and we explore their potential as image filters and compressors. We introduce several graph features, including the novel concept of Visibility Patches, and show through several examples that these features are highly informative, computationally efficient and universally applicable for general pattern recognition and image classification tasks.

Shopper intent prediction from clickstream e-commerce data with minimal browsing information

“…6 (see 21 for a convexity criterion that generates ‘natural’ visibility graphs instead). As noted above, visibility graphs and horizontal visibility graphs were introduced with the aims of using the tools of Graph Theory and Network Science 24 to describe the structure of time series and their underlying dynamics from a combinatorial perspective (other proposals for graph-theoretical time series analysis can be found in 25 , 26 and references therein and the extension of visibility graphs to image processing can be found in 27 ). Research on this methodology has been primarily theoretical, elaborating on mathematical methods 28 – 31 to extract rigorous results on the properties of these graphs when associated to canonical models of complex dynamics, including stochastic processes with and without correlations or chaotic processes 32 – 35 .…”

Detection and recognition of LPI radar signals using visibility graphs

“…The weighting algorithm [26] is to use the following equation for all adjacent edges of a vertex in a complex network, it can be expressed as…”

“…The average clustering coefficient reflects the clustering of the connection nodes, and its definition [26,27] can be written as…”

Automatic LPI Radar Signal Sensing Method Using Visibility Graphs

“…VG and HVG meet three criteria: 1) each vertex connecting to at least the adjacent vertex, 2) all vertices are undirected, it can be summarized as shown in Table 2. Consider the case of three vertices, and so on for multiple vertices, and 3) change the horizontal or vertical scale of all vertices at the same time, and the connection mode is unchanged [24]. The traditional power spectrum algorithm, that is, performing fast Fourier transform (FFT) on the autocorrelation signal, this method cannot be used for phase modulation signals, because it cannot distinguish the bandwidth itself.…”