Using generative models for handwritten digit recognition

We describe a method of recognizing handwritten digits by fitting generative models that are built from deformable B-splines with Gaussian ``ink generators'' spaced along the length of the spline. The splines are adjusted using a novel elastic matching procedure based on the Expectation Maximization (EM) algorithm that maximizes the likelihood of the model generating the data. This approach has many advantages. (1) After identifying the model most likely to have generated the data, the system not only produces a classification of the digit but also a rich description of the instantiation parameters which can yield information such as the writing style. (2) During the process of explaining the image, generative models can perform recognition driven segmentation. (3) The method involves a relatively small number of parameters and hence training is relatively easy and fast. (4) Unlike many other recognition schemes it does not rely on some form of pre-normalization of input images, but can handle arbitrary scalings, translations and a limited degree of image rotation. We have demonstrated our method of fitting models to images does not get trapped in poor local minima. The main disadvantage of the method is it requires much more computation than more standard OCR techniques.

Perceiving edge contrast

We have shown previously that a template model for edge perception successfully predicts perceived blur for a variety of edge profiles (Georgeson, 2001 Journal of Vision 1 438a; Barbieri-Hesse and Georgeson, 2002 Perception 31 Supplement, 54). This study concerns the perceived contrast of edges. Our model spatially differentiates the luminance profile, half-wave rectifies this first derivative, and then differentiates again to create the edge's 'signature'. The spatial scale of the signature is evaluated by filtering it with a set of Gaussian derivative operators. This process finds the correlation between the signature and each operator kernel at each position. These kernels therefore act as templates, and the position and scale of the best-fitting template indicate the position and blur of the edge. Our previous finding, that reducing edge contrast reduces perceived blur, can be explained by replacing the half-wave rectifier with a smooth, biased rectifier function (May and Georgeson, 2003 Perception 32 388; May and Georgeson, 2003 Perception 32 Supplement, 46). With the half-wave rectifier, the peak template response R to a Gaussian edge with contrast C and scale s is given by: R=Cp-1/4s-3/2. Hence, edge contrast can be estimated from response magnitude and blur: C=Rp1/4s3/2. Use of this equation with the modified rectifier predicts that perceived contrast will decrease with increasing blur, particularly at low contrasts. Contrast-matching experiments supported this prediction. In addition, the model correctly predicts the perceived contrast of Gaussian edges modified either by spatial truncation or by the addition of a ramp.

Perceiving edge blur: Gaussian-derivative filtering and a rectifying nonlinearity

We studied the visual mechanisms that encode edge blur in images. Our previous work suggested that the visual system spatially differentiates the luminance profile twice to create the `signature' of the edge, and then evaluates the spatial scale of this signature profile by applying Gaussian derivative templates of different sizes. The scale of the best-fitting template indicates the blur of the edge. In blur-matching experiments, a staircase procedure was used to adjust the blur of a comparison edge (40% contrast, 0.3 s duration) until it appeared to match the blur of test edges at different contrasts (5% - 40%) and blurs (6 - 32 min of arc). Results showed that lower-contrast edges looked progressively sharper. We also added a linear luminance gradient to blurred test edges. When the added gradient was of opposite polarity to the edge gradient, it made the edge look progressively sharper. Both effects can be explained quantitatively by the action of a half-wave rectifying nonlinearity that sits between the first and second (linear) differentiating stages. This rectifier was introduced to account for a range of other effects on perceived blur (Barbieri-Hesse and Georgeson, 2002 Perception 31 Supplement, 54), but it readily predicts the influence of the negative ramp. The effect of contrast arises because the rectifier has a threshold: it not only suppresses negative values but also small positive values. At low contrasts, more of the gradient profile falls below threshold and its effective spatial scale shrinks in size, leading to perceived sharpening.

Perceiving edge blur: linear filtering and a rectifying nonlinearity

We studied the visual mechanisms that encode edge blur in images. Our previous work suggested that the visual system spatially differentiates the luminance profile twice to create the 'signature' of the edge, and then evaluates the spatial scale of this signature profile by applying Gaussian derivative templates of different sizes. The scale of the best-fitting template indicates the blur of the edge. In blur-matching experiments, a staircase procedure was used to adjust the blur of a comparison edge (40% contrast, 0.3 s duration) until it appeared to match the blur of test edges at different contrasts (5% - 40%) and blurs (6 - 32 min of arc). Results showed that lower-contrast edges looked progressively sharper.We also added a linear luminance gradient to blurred test edges. When the added gradient was of opposite polarity to the edge gradient, it made the edge look progressively sharper. Both effects can be explained quantitatively by the action of a half-wave rectifying nonlinearity that sits between the first and second (linear) differentiating stages. This rectifier was introduced to account for a range of other effects on perceived blur (Barbieri-Hesse and Georgeson, 2002 Perception 31 Supplement, 54), but it readily predicts the influence of the negative ramp. The effect of contrast arises because the rectifier has a threshold: it not only suppresses negative values but also small positive values. At low contrasts, more of the gradient profile falls below threshold and its effective spatial scale shrinks in size, leading to perceived sharpening.

Template model for blur coding: the role of early nonlinearity in edge segmentation

We describe a template model for perception of edge blur and identify a crucial early nonlinearity in this process. The main principle is to spatially filter the edge image to produce a 'signature', and then find which of a set of templates best fits that signature. Psychophysical blur-matching data strongly support the use of a second-derivative signature, coupled to Gaussian first-derivative templates. The spatial scale of the best-fitting template signals the edge blur. This model predicts blur-matching data accurately for a wide variety of Gaussian and non-Gaussian edges, but it suffers a bias when edges of opposite sign come close together in sine-wave gratings and other periodic images. This anomaly suggests a second general principle: the region of an image that 'belongs' to a given edge should have a consistent sign or direction of luminance gradient. Segmentation of the gradient profile into regions of common sign is achieved by implementing the second-derivative 'signature' operator as two first-derivative operators separated by a half-wave rectifier. This multiscale system of nonlinear filters predicts perceived blur accurately for periodic and aperiodic waveforms. We also outline its extension to 2-D images and infer the 2-D shape of the receptive fields.

Molecularly imprinted polymers in the drug discovery process

Since molecularly imprinted polymers (MIPs) are designed to have a memory for their molecular templates it is easy to draw parallels with the affinity between biological receptors and their substrates. Could MIPs take the place of natural receptors in the selection of potential drug molecules from synthetic compound libraries? To answer that question this review discusses the results of MIP studies which attempt to emulate natural receptors. In addition the possible use of MIPs to guide a compound library synthesis towards a desired biological activity is highlighted. © 2005 Elsevier B.V. All rights reserved.