This paper describes two new methods for modeling the manifolds of digitized images of handwritten digits. The models allow a priori information about the structure of the manifolds to be combined with empirical data. Accurate modeling of the manifolds allows digits to be discriminated using the relative probability densities under the alternative models. One of the methods is grounded in principal components analysis, the other in factor analysis. Both methods are based on locally linear low-dimensional approximations to the underlying data manifold. Links with other methods that model the manifold are discussed.

We describe a method of recognizing handwritten digits by fitting generative models that are built from deformable Bsplines 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.

In infants under the age of 6 mo respiratory inductive plethysmograph (RIP)-calculated tidal volumes (VT) were compared with simultaneously measured volumes using a pneumotachograph (PNT) to 1) assess whether using multiple points (MP) along the inspiratory profile of a breath is superior to using only VT when calculating volume-motion (VM) coefficients, 2) verify the assumption of independent contributions of the abdomen and rib cage to VT, which was accomplished by extending the normal RIP model to include a term representing interaction between these two compartments, and 3) investigate whether VM coefficients are sleep-state dependent. Neither use of multiple points nor inclusion of the interacting term improved the performance of the RIP over that observed using a simple two-compartment model with VT measurements. However, VM coefficients obtained during quiet sleep (QS) were not reliable when used during rapid-eye-movement (REM) sleep, suggesting that coefficients obtained during one sleep state may not be applicable to another state where there is a substantial change in the relative abdominal/rib cage contributions to VT.

Calibration of the respiratory inductive plethysmograph (RIP) was performed in premature infants weighing less than 1,500 g. In only 25% of the studies was an acceptable calibration achieved, as assessed by statistical comparison of simultaneously measured pneumotachygraph and RIP tidal volumes. In 6 infants, dead space loading or air injection was performed in an attempt to alter abdominal and rib cage volume contributions and thereby improve the calibration. Neither of these maneuvers resulted in an improvement of the accuracy of the RIP calibration coefficient. We conclude that, when calibrated by the least squares technique, the reliability of inductive plethysmography in measuring tidal volume in small infants is low. This is presumably because they have very small tidal volumes and highly compliant rib cages.

A model of automatic neonatal respiratory control has been constructed as an aid in the investigation of a possible maturation in respiratory control loops during the newborn period. The primary objective was to provide a framework for investigating this hypothesis without the need for external stimuli or invasive measurements. Spontaneous sighs provide a physiological disturbance to the respiratory system by transiently altering the levels of the blood gases. The dynamic ventilatory response following such a disturbance was modeled. A change from a highly damped to less damped pattern was found when model parameter values were varied to mimic maturation in the neonatal period. A perturbation model analysis demonstrated the dynamic ventilatory response is most sensitive to factors affecting the gain of the peripheral chemoreflex loop. It is concluded that the model provides valuable insight into the hypothesis that the peripheral chemoreflex matures during the neonatal period and provides a viable method for testing this in the human infant.