Christopher K. I. Williams

The Pascal Visual Object Classes (VOC) Challenge

The Pascal Visual Object Classes (VOC) challenge is a benchmark in visual object category recognition and detection, providing the vision and machine learning communities with a standard dataset of images and annotation, and standard evaluation procedures. Organised annually from 2005 to present, the challenge and its associated dataset has become accepted as the benchmark for object detection.This paper describes the dataset and evaluation procedure. We review the state-of-the-art in evaluated methods for both classification and detection, analyse whether the methods are statistically different, what they are learning from the images (e.g. the object or its context), and what the methods find easy or confuse. The paper concludes with lessons learnt in the three year history of the challenge, and proposes directions for future improvement and extension.

GTM: the generative topographic mapping

Latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. A familiar example is factor analysis, which is based on a linear transformation between the latent space and the data space. In this article, we introduce a form of nonlinear latent variable model called the generative topographic mapping, for which the parameters of the model can be determined using the expectation-maximization algorithm. GTM provides a principled alternative to the widely used self-organizing map (SOM) of Kohonen (1982) and overcomes most of the significant limitations of the SOM. We demonstrate the performance of the GTM algorithm on a toy problem and on simulated data from flow diagnostics for a multiphase oil pipeline.

Bayesian classification with Gaussian processes

We consider the problem of assigning an input vector to one of m classes by predicting P(c|x) for c=1,...,m. For a two-class problem, the probability of class one given x is estimated by /spl sigma/(y(x)), where /spl sigma/(y)=1/(1+e/sup -y/). A Gaussian process prior is placed on y(x), and is combined with the training data to obtain predictions for new x points. We provide a Bayesian treatment, integrating over uncertainty in y and in the parameters that control the Gaussian process prior the necessary integration over y is carried out using Laplaces approximation. The method is generalized to multiclass problems (m>2) using the softmax function. We demonstrate the effectiveness of the method on a number of datasets.

Using Machine Learning to Focus Iterative Optimization

Iterative compiler optimization has been shown to outperform static approaches. This, however, is at the cost of large numbers of evaluations of the program. This paper develops a new methodology to reduce this number and hence speed up iterative optimization. It uses predictive modelling from the domain of machine learning to automatically focus search on those areas likely to give greatest performance. This approach is independent of search algorithm, search space or compiler infrastructure and scales gracefully with the compiler optimization space size. Off-line, a training set of programs is iteratively evaluated and the shape of the spaces and program features are modelled. These models are learnt and used to focus the iterative optimization of a new program. We evaluate two learnt models, an independent and Markov model, and evaluate their worth on two embedded platforms, the Texas Instrument C67I3 and the AMD Au1500. We show that such learnt models can speed up iterative search on large spaces by an order of magnitude. This translates into an average speedup of 1.22 on the TI C6713 and 1.27 on the AMD Au1500 in just 2 evaluations.

The 2005 PASCAL visual object classes challenge

The PASCAL Visual Object Classes Challenge ran from February to March 2005. The goal of the challenge was to recognize objects from a number of visual object classes in realistic scenes (i.e. not pre-segmented objects). Four object classes were selected: motorbikes, bicycles, cars and people. Twelve teams entered the challenge. In this chapter we provide details of the datasets, algorithms used by the teams, evaluation criteria, and results achieved.

Learning generative texture models with extended Fields-of-Experts

We evaluate the ability of the popular Field-of-Experts (FoE) to model structure in images. As a test case we focus on modeling synthetic and natural textures. We find that even for modeling single textures, the FoE provides insufficient flexibility to learn good generative models ‐ it does not perform any better than the much simpler Gaussian FoE. We propose an extended version of the FoE (allowing for bimodal potentials) and demonstrate that this novel formulation, when trained with a better approximation of the likelihood gradient, gives rise to a more powerful generative model of specific visual structure that produces significantly better results for the texture task.

On a Connection between Kernel PCA and Metric Multidimensional Scaling

In this note we show that the kernel PCA algorithm of Schölkopf, Smola, and Müller (Neural Computation, 10, 1299–1319.) can be interpreted as a form of metric multidimensional scaling (MDS) when the kernel function k(x, y) is isotropic, i.e. it depends only on ‖x − y‖. This leads to a metric MDS algorithm where the desired configuration of points is found via the solution of an eigenproblem rather than through the iterative optimization of the stress objective function. The question of kernel choice is also discussed.

Developments of the generative topographic mapping

The generative topographic mapping (GTM) model was introduced by Bishop et al. (1998, Neural Comput. 10(1), 215-234) as a probabilistic re- formulation of the self-organizing map (SOM). It offers a number of advantages compared with the standard SOM, and has already been used in a variety of applications. In this paper we report on several extensions of the GTM, including an incremental version of the EM algorithm for estimating the model parameters, the use of local subspace models, extensions to mixed discrete and continuous data, semi-linear models which permit the use of high-dimensional manifolds whilst avoiding computational intractability, Bayesian inference applied to hyper-parameters, and an alternative framework for the GTM based on Gaussian processes. All of these developments directly exploit the probabilistic structure of the GTM, thereby allowing the underlying modelling assumptions to be made explicit. They also highlight the advantages of adopting a consistent probabilistic framework for the formulation of pattern recognition algorithms.

Dataset Issues in Object Recognition

Appropriate datasets are required at all stages of object recognition research, including learning visual models of object and scene categories, detecting and localizing instances of these models in images, and evaluating the performance of recognition algorithms. Current datasets are lacking in several respects, and this paper discusses some of the lessons learned from existing efforts, as well as innovative ways to obtain very large and diverse annotated datasets. It also suggests a few criteria for gathering future datasets.

Unsupervised learning of multiple aspects of moving objects from video

A popular framework for the interpretation of image sequences is based on the layered model; see e.g. Wang and Adelson [8], Irani et al. [2]. Jojic and Frey [3] provide a generative probabilistic model framework for this task. However, this layered models do not explicitly account for variation due to changes in the pose and self occlusion. In this paper we show that if the motion of the object is large so that different aspects (or views) of the object are visible at different times in the sequence, we can learn appearance models of the different aspects using a mixture modelling approach.