Pruned Continuous Haar Transform of 2D Polygonal Patterns with Application to VLSI Layouts

We introduce an algorithm for the efficient computation of the continuous Haar transform of 2D patterns that can be described by polygons. These patterns are ubiquitous in VLSI processes where they are used to describe design and mask layouts. There, speed is of paramount importance due to the magnitude of the problems to be solved and hence very fast algorithms are needed. We show that by techniques borrowed from computational geometry we are not only able to compute the continuous Haar transform directly, but also to do it quickly. This is achieved by massively pruning the transform tree and thus dramatically decreasing the computational load when the number of vertices is small, as is the case for VLSI layouts. We call this new algorithm the pruned continuous Haar transform. We implement this algorithm and show that for patterns found in VLSI layouts the proposed algorithm was in the worst case as fast as its discrete counterpart and up to 12 times faster.Comment: 4 pages, 5 figures, 1 algorith

Pruned Continuous Haar Transform of 2D Polygonal Patterns with Application to VLSI Layouts

We introduce an algorithm for the efficient computation of the continuous Haar transform of 2D patterns that can be described by polygons. These patterns are ubiquitous in VLSI processes where they are used to describe design and mask layouts. There speed is of paramount importance due to the magnitude of the problems to be solved and hence very fast algorithms are needed. We show that by techniques borrowed from computational geometry we are not only able to compute the continuous Haar transform directly, but also to do it quickly. This is achieved by massively pruning the transform tree and thus dramatically decreasing the computational load when the number of vertices is small, as is the case for VLSI layouts. We call this new algorithm the pruned continuous Haar transform. We implement this algorithm and show that for patterns found in VLSI layouts the proposed algorithm was in the worst case as fast as its discrete counterpart and up to 12 times faster

Rake, Peel, Sketch:The Signal Processing Pipeline Revisited

The prototypical signal processing pipeline can be divided into four blocks. Representation of the signal in a basis suitable for processing. Enhancement of the meaningful part of the signal and noise reduction. Estimation of important statistical properties of the signal. Adaptive processing to track and adapt to changes in the signal statistics. This thesis revisits each of these blocks and proposes new algorithms, borrowing ideas from information theory, theoretical computer science, or communications. First, we revisit the Walsh-Hadamard transform (WHT) for the case of a signal sparse in the transformed domain, namely that has only K †N non-zero coefficients. We show that an efficient algorithm exists that can compute these coefficients in O(K log2(K) log2(N/K)) and using only O(K log2(N/K)) samples. This algorithm relies on a fast hashing procedure that computes small linear combinations of transformed domain coefficients. A bipartite graph is formed with linear combinations on one side, and non-zero coefficients on the other. A peeling decoder is then used to recover the non-zero coefficients one by one. A detailed analysis of the algorithm based on error correcting codes over the binary erasure channel is given. The second chapter is about beamforming. Inspired by the rake receiver from wireless communications, we recognize that echoes in a room are an important source of extra signal diversity. We extend several classic beamforming algorithms to take advantage of echoes and also propose new optimal formulations. We explore formulations both in time and frequency domains. We show theoretically and in numerical simulations that the signal-to-interference-and-noise ratio increases proportionally to the number of echoes used. Finally, beyond objective measures, we show that echoes also directly improve speech intelligibility as measured by the perceptual evaluation of speech quality (PESQ) metric. Next, we attack the problem of direction of arrival of acoustic sources, to which we apply a robust finite rate of innovation reconstruction framework. FRIDA â the resulting algorithm â exploits wideband information coherently, works at very low signal-to-noise ratio, and can resolve very close sources. The algorithm can use either raw microphone signals or their cross- correlations. While the former lets us work with correlated sources, the latter creates a quadratic number of measurements that allows to locate many sources with few microphones. Thorough experiments on simulated and recorded data shows that FRIDA compares favorably with the state-of-the-art. We continue by revisiting the classic recursive least squares (RLS) adaptive filter with ideas borrowed from recent results on sketching least squares problems. The exact update of RLS is replaced by a few steps of conjugate gradient descent. We propose then two different precondi- tioners, obtained by sketching the data, to accelerate the convergence of the gradient descent. Experiments on artificial as well as natural signals show that the proposed algorithm has a performance very close to that of RLS at a lower computational burden. The fifth and final chapter is dedicated to the software and hardware tools developed for this thesis. We describe the pyroomacoustics Python package that contains routines for the evaluation of audio processing algorithms and reference implementations of popular algorithms. We then give an overview of the microphone arrays developed

Advancements in multi-view processing for reconstruction, registration and visualization.

The ever-increasing diffusion of digital cameras and the advancements in computer vision, image processing and storage capabilities have lead, in the latest years, to the wide diffusion of digital image collections. A set of digital images is usually referred as a multi-view images set when the pictures cover different views of the same physical object or location. In multi-view datasets, correlations between images are exploited in many different ways to increase our capability to gather enhanced understanding and information on a scene. For example, a collection can be enhanced leveraging on the camera position and orientation, or with information about the 3D structure of the scene. The range of applications of multi-view data is really wide, encompassing diverse fields such as image-based reconstruction, image-based localization, navigation of virtual environments, collective photographic retouching, computational photography, object recognition, etc. For all these reasons, the development of new algorithms to effectively create, process, and visualize this type of data is an active research trend. The thesis will present four different advancements related to different aspects of the multi-view data processing: - Image-based 3D reconstruction: we present a pre-processing algorithm, that is a special color-to-gray conversion. This was developed with the aim to improve the accuracy of image-based reconstruction algorithms. In particular, we show how different dense stereo matching results can be enhanced by application of a domain separation approach that pre-computes a single optimized numerical value for each image location. - Image-based appearance reconstruction: we present a multi-view processing algorithm, this can enhance the quality of the color transfer from multi-view images to a geo-referenced 3D model of a location of interest. The proposed approach computes virtual shadows and allows to automatically segment shadowed regions from the input images preventing to use those pixels in subsequent texture synthesis. - 2D to 3D registration: we present an unsupervised localization and registration system. This system can recognize a site that has been framed in a multi-view data and calibrate it on a pre-existing 3D representation. The system has a very high accuracy and it can validate the result in a completely unsupervised manner. The system accuracy is enough to seamlessly view input images correctly super-imposed on the 3D location of interest. - Visualization: we present PhotoCloud, a real-time client-server system for interactive exploration of high resolution 3D models and up to several thousand photographs aligned over this 3D data. PhotoCloud supports any 3D models that can be rendered in a depth-coherent way and arbitrary multi-view image collections. Moreover, it tolerates 2D-to-2D and 2D-to-3D misalignments, and it provides scalable visualization of generic integrated 2D and 3D datasets by exploiting data duality. A set of effective 3D navigation controls, tightly integrated with innovative thumbnail bars, enhances the user navigation. These advancements have been developed in tourism and cultural heritage application contexts, but they are not limited to these

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum