Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

STV-based Video Feature Processing for Action Recognition

In comparison to still image-based processes, video features can provide rich and intuitive information about dynamic events occurred over a period of time, such as human actions, crowd behaviours, and other subject pattern changes. Although substantial progresses have been made in the last decade on image processing and seen its successful applications in face matching and object recognition, video-based event detection still remains one of the most difficult challenges in computer vision research due to its complex continuous or discrete input signals, arbitrary dynamic feature definitions, and the often ambiguous analytical methods. In this paper, a Spatio-Temporal Volume (STV) and region intersection (RI) based 3D shape-matching method has been proposed to facilitate the definition and recognition of human actions recorded in videos. The distinctive characteristics and the performance gain of the devised approach stemmed from a coefficient factor-boosted 3D region intersection and matching mechanism developed in this research. This paper also reported the investigation into techniques for efficient STV data filtering to reduce the amount of voxels (volumetric-pixels) that need to be processed in each operational cycle in the implemented system. The encouraging features and improvements on the operational performance registered in the experiments have been discussed at the end

A framework for digital sunken relief generation based on 3D geometric models

Sunken relief is a special art form of sculpture whereby the depicted shapes are sunk into a given surface. This is traditionally created by laboriously carving materials such as stone. Sunken reliefs often utilize the engraved lines or strokes to strengthen the impressions of a 3D presence and to highlight the features which otherwise are unrevealed. In other types of reliefs, smooth surfaces and their shadows convey such information in a coherent manner. Existing methods for relief generation are focused on forming a smooth surface with a shallow depth which provides the presence of 3D figures. Such methods unfortunately do not help the art form of sunken reliefs as they omit the presence of feature lines. We propose a framework to produce sunken reliefs from a known 3D geometry, which transforms the 3D objects into three layers of input to incorporate the contour lines seamlessly with the smooth surfaces. The three input layers take the advantages of the geometric information and the visual cues to assist the relief generation. This framework alters existing techniques in line drawings and relief generation, and then combines them organically for this particular purpose

Extracting 3D parametric curves from 2D images of Helical objects

Helical objects occur in medicine, biology, cosmetics, nanotechnology, and engineering. Extracting a 3D parametric curve from a 2D image of a helical object has many practical applications, in particular being able to extract metrics such as tortuosity, frequency, and pitch. We present a method that is able to straighten the image object and derive a robust 3D helical curve from peaks in the object boundary. The algorithm has a small number of stable parameters that require little tuning, and the curve is validated against both synthetic and real-world data. The results show that the extracted 3D curve comes within close Hausdorff distance to the ground truth, and has near identical tortuosity for helical objects with a circular profile. Parameter insensitivity and robustness against high levels of image noise are demonstrated thoroughly and quantitatively