ROTATION-INVARIANT OBJECT RECOGNITION USING EDGE PROFILE CLUSTERS

This paper introduces a new method to recognize objects at any rotation using clusters that represent edge profiles. These clusters are calculated from the Interlevel Product (ILP) of complex wavelets whose phases represent the level of “edginess” vs “ridginess ” of a feature, a quantity that is invariant to basic affine transformations. These clusters represent areas where ILP coefficients are large and of similar phase; these are two properties which indicate that a stable, coarse-level feature with a consistent edge profile exists at the indicated locations. We calculate these clusters for a small target image, and then seek these clusters within a larger search image, regardless of their rotation angle. We compare our method against SIFT for the task of rotation-invariant matching in the presence of heavy Gaussian noise, where our method is shown to be more noise-robust. This improvement is a direct result of our new edge-profile clusters ’ broad spatial support and stable relationship to coarse-level image content. 1

Uses of Complex Wavelets in Deep Convolutional Neural Networks

Image understanding has long been a goal for computer vision. It has proved to be an exceptionally difficult task due to the large amounts of variability that are inherent to objects in a scene. Recent advances in supervised learning methods, particularly convolutional neural networks (CNNs), have pushed forth the frontier of what we have been able to train computers to do. Despite their successes, the mechanics of how these networks are able to recognize objects are little understood, and the networks themselves are often very difficult and time-consuming to train. It is very important that we improve our current approaches in every way possible. A CNN is built from connecting many learned convolutional layers in series. These convolutional layers are fairly crude in terms of signal processing - they are arbitrary taps of a finite impulse response filter, learned through stochastic gradient descent from random initial conditions. We believe that if we reformulate the problem, we may achieve many insights and benefits in training CNNs. Noting that modern CNNs are mostly viewed from and analyzed in the spatial domain, this thesis aims to view the convolutional layers in the frequency domain (viewing things in the frequency domain has proved useful in the past for denoising, filter design, compression and many other tasks). In particular, we use complex wavelets (rather than the Fourier transform or the discrete wavelet transform) as basis functions to reformulate image understanding with deep networks. In this thesis, we explore the most popular and well-developed form of using complex wavelets in deep learning, the ScatterNet from Stephane Mallat. We explore its current limitations by building a DeScatterNet and found that while it has many nice properties, it may not be sensitive to the most appropriate shapes for understanding natural images. We then develop a locally invariant convolutional layer, a combination of a complex wavelet transform, a modulus operation, and a learned mixing. To do this, we derive backpropagation equations and allow gradients to flow back through the (previously fixed) ScatterNet front end. Connecting several such locally invariant layers allows us to build learnable ScatterNet, a more flexible and general form of the ScatterNet (while still maintaining its desired properties). We show that the learnable ScatterNet can provide significant improvements over the regular ScatterNet when being used as a front end for a learning system. Additionally, we show that the locally invariant convolutional layer can directly replace convolutional layers in a deep CNN (and not just at the front-end). The locally invariant convolutional layers naturally downsample the input (because of the complex modulus) while increasing the channel dimension (because of the multiple wavelet orientations used). This is an operation that often happens in a CNN by a combination of a pooling and convolutional layer. It was at these locations in a CNN where the learnable ScatterNet performed best, implying it may be useful as learnable pooling layer. Finally, we develop a system to learn complex weights that act directly on the wavelet coefficients of signals, in place of a convolutional layer. We call this layer the wavelet gain layer and show it can be used alongside convolutional layers. The network designer may then choose to learn in the pixel or wavelet domains. This layer shows a lot of promise and affords more control over what regions of the frequency space we want our layer to learn from. Our experiments show that it can improve on learning in the pixel domain for early layers of a CNN

Contour and texture for visual recognition of object categories

The recognition of categories of objects in images has become a central topic in computer vision. Automatic visual recognition systems are rapidly becoming central to applications such as image search, robotics, vehicle safety systems, and image editing. This work addresses three sub-problems of recognition: image classification, object detection, and semantic segmentation. The task of classification is to determine whether an object of a particular category is present or not. Object detection aims to localize any objects of the category. Semantic segmentation is a more complete image understanding, whereby an image is partitioned into coherent regions that are assigned meaningful class labels. This thesis proposes novel discriminative learning approaches to these problems. Our primary contributions are threefold. Firstly, we demonstrate that the contours (the outline and interior edges) of an object are, alone, sufficient for accurate visual recognition. Secondly, we propose two powerful new feature types: (i) a learned codebook of contour fragments matched with an improved oriented chamfer distance, and (ii) a set of texture-based features that simultaneously exploit local appearance, approximate shape, and appearance context. The efficacy of these new features types is evaluated on a wide variety of datasets. Thirdly, we show how, in combination, these two largely orthogonal feature types can substantially improve recognition performance above that achieved by either alone