Image Sampling with Quasicrystals

We investigate the use of quasicrystals in image sampling. Quasicrystals produce space-filling, non-periodic point sets that are uniformly discrete and relatively dense, thereby ensuring the sample sites are evenly spread out throughout the sampled image. Their self-similar structure can be attractive for creating sampling patterns endowed with a decorative symmetry. We present a brief general overview of the algebraic theory of cut-and-project quasicrystals based on the geometry of the golden ratio. To assess the practical utility of quasicrystal sampling, we evaluate the visual effects of a variety of non-adaptive image sampling strategies on photorealistic image reconstruction and non-photorealistic image rendering used in multiresolution image representations. For computer visualization of point sets used in image sampling, we introduce a mosaic rendering technique.Comment: For a full resolution version of this paper, along with supplementary materials, please visit at http://www.Eyemaginary.com/Portfolio/Publications.htm

Image Sampling with Quasicrystals

We investigate the use of quasicrystals in image sampling. Quasicrystals produce space-filling, non-periodic point sets that are uniformly discrete and relatively dense, thereby ensuring the sample sites are evenly spread out throughout the sampled image. Their self-similar structure can be attractive for creating sampling patterns endowed with a decorative symmetry. We present a brief general overview of the algebraic theory of cut-and-project quasicrystals based on the geometry of the golden ratio. To assess the practical utility of quasicrystal sampling, we evaluate the visual effects of a variety of non-adaptive image sampling strategies on photorealistic image reconstruction and non-photorealistic image rendering used in multiresolution image representations. For computer visualization of point sets used in image sampling, we introduce a mosaic rendering technique

Colour videos with depth : acquisition, processing and evaluation

The human visual system lets us perceive the world around us in three dimensions by integrating evidence from depth cues into a coherent visual model of the world. The equivalent in computer vision and computer graphics are geometric models, which provide a wealth of information about represented objects, such as depth and surface normals. Videos do not contain this information, but only provide per-pixel colour information. In this dissertation, I hence investigate a combination of videos and geometric models: videos with per-pixel depth (also known as RGBZ videos). I consider the full life cycle of these videos: from their acquisition, via filtering and processing, to stereoscopic display. I propose two approaches to capture videos with depth. The first is a spatiotemporal stereo matching approach based on the dual-cross-bilateral grid – a novel real-time technique derived by accelerating a reformulation of an existing stereo matching approach. This is the basis for an extension which incorporates temporal evidence in real time, resulting in increased temporal coherence of disparity maps – particularly in the presence of image noise. The second acquisition approach is a sensor fusion system which combines data from a noisy, low-resolution time-of-flight camera and a high-resolution colour video camera into a coherent, noise-free video with depth. The system consists of a three-step pipeline that aligns the video streams, efficiently removes and fills invalid and noisy geometry, and finally uses a spatiotemporal filter to increase the spatial resolution of the depth data and strongly reduce depth measurement noise. I show that these videos with depth empower a range of video processing effects that are not achievable using colour video alone. These effects critically rely on the geometric information, like a proposed video relighting technique which requires high-quality surface normals to produce plausible results. In addition, I demonstrate enhanced non-photorealistic rendering techniques and the ability to synthesise stereoscopic videos, which allows these effects to be applied stereoscopically. These stereoscopic renderings inspired me to study stereoscopic viewing discomfort. The result of this is a surprisingly simple computational model that predicts the visual comfort of stereoscopic images. I validated this model using a perceptual study, which showed that it correlates strongly with human comfort ratings. This makes it ideal for automatic comfort assessment, without the need for costly and lengthy perceptual studies