Learning Separable Filters | EPFL Graph Search

Learning filters to produce sparse image representations in terms of overcomplete dictionaries has emerged as a powerful way to create image features for many different purposes. Unfortunately, these filters are usually both numerous and non-separable, making their use computationally expensive. In this paper, we show that such filters can be computed as linear combinations of a smaller number of separable ones, thus greatly reducing the computational complexity at no cost in terms of performance. This makes filter learning approaches practical even for large images or 3D volumes, and we show that we significantly outperform state-of-the-art methods on the tubular structure extraction task, in terms of both accuracy and speed. Moreover, our approach is general and can be used on generic convolutional filter banks to reduce the complexity of the feature extraction step.

Binaural Audio Signal Processing Using Interaural Coherence Matching

Fritz Menzer

Binaural room impulse responses (BRIRs) characterize the transfer of sound from a source in a room to the left and right ear entrances of a listener. Applying BRIRs to sound source signals enables headphone listening with the perception of a three dimensional auditory image. BRIRs are usually linear filters of several hundred milliseconds to several seconds length. The waveforms of the BRIRs contain therefore a vast amount of information. This thesis studies the modeling of BRIRs with a reduced set of parameters. It is shown that late BRIR tails can be modeled perceptually accurately by considering only the time-frequency energy decay relief and frequency dependent interaural coherence (IC). This insight on BRIR modeling enables a number of algorithms with advantages over the previous state of the art. Three such algorithms are proposed: The first algorithm makes it possible to obtain BRIRs by measuring room properties and listener properties separately, vastly reducing the number of measurements necessary to measure listener-specific BRIRs for a number of listeners and rooms. The listener properties are measured as a head related transfer function (HRTF) set and the room properties are measured as a B-format1 room impulse response (RIR). It is shown how to combine the HRTF set of the listener with a B-format RIR to obtain BRIRs for that room individualized for the listener. This technique uses the insight on BRIR perception by computing the BRIR tail as a frequency dependent, linear combination of B-format channels, designed to obtain the desired energy decay relief and interaural coherence. A serious problem related to convolving sound source signals with BRIRs is the computational complexity of implementing long BRIRs as finite impulse response (FIR) filters. Inspired by the perceptual experiments on BRIR tails, a modified Jot reverberator is proposed, simulating BRIR tails with the desired frequency dependent interaural coherence, requiring significantly less computational power than direct application of BRIRs. Also inspired by the perception of BRIRs, an extension of this reverberator is proposed, modeling efficiently the reverberation tail with the correct coherence and also distinct early reflections using two parallel feedback delay networks. If stereo signals are played back using headphones, unnatural binaural cues are given to the listener, e.g. interaural level difference (ILD) changes not accompanied by corresponding interaural time difference (ITD) changes or diffuse sound with unnatural IC. In order to simulate stereo listening in a room and to avoid these unnatural cues, BRIRs can be applied to the left and right stereo channels. Besides the computational complexity associated with applying the BRIR filters, this technique has a number of disadvantages. The room associated with the used BRIRs is imposed on the stereo signal, which usually already contains reverberation and applying BRIRs leads to a change in reverberation time and to coloration. A technique is proposed in which the direct sound is rendered using data extracted from HRTFs and the ambient sound contained in the stereo signal is modified such that its coherence is matched to the coherence of a binaural recording of diffuse sound, without modifying its spectrum. Implementations of reverberators based on general feedback-delay networks (e.g. Jot reverberators) can require a high number of operations for implementing the so-called feedback matrix. For certain applications where the number of channels needs to be high, such as decorrelators, this can pose a real problem. Special types of matrices are known which can be implemented efficiently due to matrix elements having the same magnitude. However, the complexity can also be reduced by introducing many zero elements. Different types of such sparse feedback matrices are proposed and tested for their suitability in Jot reverberators. A highly efficient feedback matrix is obtained by combining both approaches, choosing the nonzero elements of a sparse matrix from efficiently implementable Hadamard matrices. ______________________________ 1 B-format refers to a 4-channel signal recorded with four coincident microphones: one omni and three dipole microphones pointing in orthogonal directions.

EPFL2010

Learning Reach-to-Grasp Motions From Human Demonstrations

Ashwini Shukla

Reaching over to grasp an item is arguably the most commonly used motor skill by humans. Even under sudden perturbations, humans seem to react rapidly and adapt their motion to guarantee success. Despite the apparent ease and frequency with which we use this ability, a complete understanding of the underlying mechanisms cannot be claimed. It is partly due to such incomplete knowledge that adaptive robot motion for reaching and grasping under perturbations is not perfectly achieved. In this thesis, we take the discriminative approach for modelling trajectories of reach-to-grasp motion from expert demonstrations. Throughout this thesis, we will employ time-independent (autonomous) flow based representations to learn reactive motion controllers which can then be ported onto robots. This thesis is divided into three main parts. The first part is dedicated to biologically inspired modelling of reach-to-grasp motions with respect to the hand-arm coupling. We build upon previous work in motion modelling using autonomous dynamical systems (DS) and present a coupled dynamical system (CDS) model of these two subsystems. The coupled model ensures satisfaction of the constraints between the hand and the arm subsystems which are critical to the success of a reach-to-grasp task. Moreover, it reduces the complexity of the overall motion planning problem as compared to considering a combined problem for the hand and the arm motion. In the second part we extend the CDS approach to incorporate multiple grasping points. Such a model is beneficial due to the fact that many daily life objects afford multiple grasping locations on their surface. We combine a DS based approach with energy-function learning to learn a multiple attractor dynamical system where the attractors are mapped to the desired grasping points. We present the Augmented-SVM (ASVM) model that combines the classical SVM formulation with gradient constraints arising from the energy function to learn the desired dynamical function for motion generation. In the last part of this thesis, we address the problem of inverse-kinematics and obstacle avoidance by combining our flow-based motion generator with global configuration-space planners. We claim that the two techniques complement each other. On one hand, the fast reactive nature of our flow based motion generator can used to guide the search of a randomly exploring random tree (RRT) based global planner. On the other hand, global planners can efficiently handle arbitrary obstacles and avoid local minima present in the dynamical function learned from demonstrations. We show that combining the information from demonstrations with global planning in the form of a energy-map considerably decreases the computational complexity of state-of-the-art sampling based planners. We believe that this thesis has the following contributions to Robotics and Machine Learning. First, we have developed algorithms for fast and adaptive motion generation for reach-grasp motions. Second, we formulated an extension to the classical SVM formulation that takes into account the gradient information from data. We showed that instead of being limited as a classifier or a regressor, the SVM framework can be used as a more general function approximation technique. Lastly, we have combined our local methods with global approaches for planning to achieve arbitrary obstacle avoidance and considerable reduction in the computation complexity of the global planners.

EPFL2014

Multiscale Centerline Extraction Based on Regression and Projection onto the Set of Elongated Structures

Amos Sironi

Automatically extracting linear structures from images is a fundamental low-level vision problem with numerous applications in different domains. Centerline detection and radial estimation are the first crucial steps in most Computer Vision pipelines aiming to reconstruct linear structures. Existing techniques rely either on hand-crafted filters, designed to respond to ideal profiles of the linear structure, or on classification-based approaches, which automatically learn to detect centerline points from data. Hand-crafted methods are the most accurate when the content of the image fulfills the ideal model they rely on. However, they lose accuracy in the presence of noise or when the linear structures are irregular and deviate from the ideal case. Machine learning techniques can alleviate this problem. However, they are mainly based on a classification framework. In this thesis, we show that classification is not the best formalism to solve the centerline detection problem. In fact, since the appearance of a centerline point is very similar to the points immediately next to it, the output of a classifier trained to detect centerlines presents low localization accuracy and double responses on the body of the linear structure. To solve this problem, we propose a regression-based formulation for centerline detection. We rely on the distance transform of the centerlines to automatically learn a function whose local maxima correspond to centerline points. The output of our method can be used to directly estimate the location of the centerline, by a simple Non-Maximum Suppression operation, or it can be used as input to a tracing pipeline to reconstruct the graph of the linear structure. In both cases, our method gives more accurate results than state-of-the-art techniques on challenging 2D and 3D datasets. Our method relies on features extracted by means of convolutional filters. In order to process large amount of data efficiently, we introduce a general filter bank approximation scheme. In particular, we show that a generic filter bank can be approximated by a linear combination of a smaller set of separable filters. Thanks to this method, we can greatly reduce the computation time of the convolutions, without loss of accuracy. Our approach is general, and we demonstrate its effectiveness by applying it to different Computer Vision problems, such as linear structure detection and image classification with Convolutional Neural Networks. We further improve our regression-based method for centerline detection by taking advantage of contextual image information. We adopt a multiscale iterative regression approach to efficiently include a large image context in our algorithm. Compared to previous approaches, we use context both in the spatial domain and in the radial one. In this way, our method is also able to return an accurate estimation of the radii of the linear structures. The idea of using regression can also be beneficial for solving other related Computer Vision problems. For example, we show an improvement compared to previous works when applying it to boundary and membrane detection. Finally, we focus on the particular geometric properties of the linear structures. We observe that most methods for detecting them treat each pixel independently and do not model the strong relation that exists between neighboring pixels. As a consequence, their output is geometrically inconsistent. In this thesis, we address this problem by considering the projection of the score map returned by our regressor onto the set of all geometrically admissible ground truth images. We propose an efficient patch-wise approximation scheme to compute the projection. Moreover, we provide conditions under which the projection is exact. We demonstrate the advantage of our method by applying it to four different problems.

EPFL2016