From CNNs to Shift-Invariant Twin Models Based on Complex Wavelets

We propose a novel antialiasing method to increase shift invariance and prediction accuracy in convolutional neural networks. Specifically, we replace the first-layer combination "real-valued convolutions + max pooling" ($\mathbb{R}$Max) by "complex-valued convolutions + modulus" ($\mathbb{C}$Mod), which is stable to translations. To justify our approach, we claim that $\mathbb{C}$Mod and $\mathbb{R}$Max produce comparable outputs when the convolution kernel is band-pass and oriented (Gabor-like filter). In this context, $\mathbb{C}$Mod can be considered as a stable alternative to $\mathbb{R}$Max. Thus, prior to antialiasing, we force the convolution kernels to adopt such a Gabor-like structure. The corresponding architecture is called mathematical twin, because it employs a well-defined mathematical operator to mimic the behavior of the original, freely-trained model. Our antialiasing approach achieves superior accuracy on ImageNet and CIFAR-10 classification tasks, compared to prior methods based on low-pass filtering. Arguably, our approach's emphasis on retaining high-frequency details contributes to a better balance between shift invariance and information preservation, resulting in improved performance. Furthermore, it has a lower computational cost and memory footprint than concurrent work, making it a promising solution for practical implementation

The Robotic Visual Information Processing System Based on Wavelet Transformation and Photoelectric Hybrid

Non

Anisotropic noise

Programmable graphics hardware makes it possible to generate procedural noise textures on the fly for interactive rendering. However, filtering and antialiasing procedural noise involves a tradeoff between aliasing artifacts and loss of detail. In this paper we present a technique, targeted at interactive applications, that provides high-quality anisotropic filtering for noise textures. We generate noise tiles directly in the frequency domain by partitioning the frequency domain into oriented subbands. We then compute weighted sums of the subband textures to accurately approximate noise with a desired spectrum. This allows us to achieve high-quality anisotropic filtering. Our approach is based solely on 2D textures, avoiding the memory overhead of techniques based on 3D noise tiles. We devise a technique to compensate for texture distortions to generate uniform noise on arbitrary meshes. We develop a GPU-based implementation of our technique that achieves similar rendering performance as state-of-the-art algorithms for procedural noise. In addition, it provides anisotropic filtering and achieves superior image quality.National Science Foundation (U.S.) (CAREER Award 0447561)Microsoft Research (New Faculty Fellowship)Alfred P. Sloan Foundation (Fellowship

Dictionary Learning for Deblurring and Digital Zoom

This paper proposes a novel approach to image deblurring and digital zooming using sparse local models of image appearance. These models, where small image patches are represented as linear combinations of a few elements drawn from some large set (dictionary) of candidates, have proven well adapted to several image restoration tasks. A key to their success has been to learn dictionaries adapted to the reconstruction of small image patches. In contrast, recent works have proposed instead to learn dictionaries which are not only adapted to data reconstruction, but also tuned for a specific task. We introduce here such an approach to deblurring and digital zoom, using pairs of blurry/sharp (or low-/high-resolution) images for training, as well as an effective stochastic gradient algorithm for solving the corresponding optimization task. Although this learning problem is not convex, once the dictionaries have been learned, the sharp/high-resolution image can be recovered via convex optimization at test time. Experiments with synthetic and real data demonstrate the effectiveness of the proposed approach, leading to state-of-the-art performance for non-blind image deblurring and digital zoom

Applications of Antialiasing in an Image Processing Framework Setting

Compression of certain low bit-depth images are studied for the most common image formats. The images studied con-sist of both vector and raster content, and are processed with an image processing framework supporting antialias-ing. It is studied how antialiasing can be applied with the most common image formats, in particular JPEG2000, and how image format specific parameters can affect compres-sion rates for our images. 1

Optimization techniques for computationally expensive rendering algorithms

Realistic rendering in computer graphics simulates the interactions of light and surfaces. While many accurate models for surface reflection and lighting, including solid surfaces and participating media have been described; most of them rely on intensive computation. Common practices such as adding constraints and assumptions can increase performance. However, they may compromise the quality of the resulting images or the variety of phenomena that can be accurately represented. In this thesis, we will focus on rendering methods that require high amounts of computational resources. Our intention is to consider several conceptually different approaches capable of reducing these requirements with only limited implications in the quality of the results. The first part of this work will study rendering of time-­¿varying participating media. Examples of this type of matter are smoke, optically thick gases and any material that, unlike the vacuum, scatters and absorbs the light that travels through it. We will focus on a subset of algorithms that approximate realistic illumination using images of real world scenes. Starting from the traditional ray marching algorithm, we will suggest and implement different optimizations that will allow performing the computation at interactive frame rates. This thesis will also analyze two different aspects of the generation of anti-­¿aliased images. One targeted to the rendering of screen-­¿space anti-­¿aliased images and the reduction of the artifacts generated in rasterized lines and edges. We expect to describe an implementation that, working as a post process, it is efficient enough to be added to existing rendering pipelines with reduced performance impact. A third method will take advantage of the limitations of the human visual system (HVS) to reduce the resources required to render temporally antialiased images. While film and digital cameras naturally produce motion blur, rendering pipelines need to explicitly simulate it. This process is known to be one of the most important burdens for every rendering pipeline. Motivated by this, we plan to run a series of psychophysical experiments targeted at identifying groups of motion-­¿blurred images that are perceptually equivalent. A possible outcome is the proposal of criteria that may lead to reductions of the rendering budgets

EWA Splatting

In this paper, we present a framework for high quality splatting based on elliptical Gaussian kernels. To avoid aliasing artifacts, we introduce the concept of a resampling filter, combining a reconstruction kernel with a low-pass filter. Because of the similarity to Heckbert's EWA (elliptical weighted average) filter for texture mapping, we call our technique EWA splatting. Our framework allows us to derive EWA splat primitives for volume data and for point-sampled surface data. It provides high image quality without aliasing artifacts or excessive blurring for volume data and, additionally, features anisotropic texture filtering for point-sampled surfaces. It also handles nonspherical volume kernels efficiently; hence, it is suitable for regular, rectilinear, and irregular volume datasets. Moreover, our framework introduces a novel approach to compute the footprint function, facilitating efficient perspective projection of arbitrary elliptical kernels at very little additional cost. Finally, we show that EWA volume reconstruction kernels can be reduced to surface reconstruction kernels. This makes our splat primitive universal in rendering surface and volume data.Engineering and Applied Science