## Very rough draft |

The appearance models encompass both shape and texture which are coded in a single vector. The means of finding correlation between the two is eigen-analysis of the covariance matrix where Principal Component analysis gives encouraging results and can reduce the dimensionality of the data considerably well while still accounting for much of the variation (but not all of it of course). There is a significant improportion between the space required (hence speed) and the loss that Principal Component analysis imposes. What is seen in practice that the components in the analysis quickly shrink, that is, they have a very small discriminatory power and when values become almost negligible they can be discarded. That, of course, will depend on the requirments of the system. For industrial inspection where quality is crucial or in medical image analysis, low error rates are usually required and the presence of abnormality is difficult to spot. On the contrary, if real-time object tracing in a video sequence is required, subsequent framed can compensate for incorrect location and efficiency is at a premium.

Throughout the process of PCA, dimensionality reduction is initially performed to make the shape representation more compact, but secondly to reduce the dimensionality of the vector describing texture variation (with the mean shape available for normalisation) in the observed (training) data.

To obtain a model that accounts for both the above variations, namely shape

A linear PCA is used to recursively find the direction in which the variation of some data is maximal. Sometimes (for a manageable number of dimensions) we can visualise all vectorised data in space so that an imaginary cloud of points is formed. PCA is able to identify the component whose removal would be the most harmful to classification of that data, i.e. the direction that distinguishes different data instances most effectively. The eigenvalues corresponding to the data in hand indicate how significant each eignevector is with respect to data discrimination. Hence, not all existing eigenvectors (which are linearly dependent on the data dimensionality) are equally useful in some new, more succinct vector representation. Some of them can be found to be 0 in which case they can be fully ignored and dimesionality reduction that is not lossy becomes available.

The allowed range of values for each parameter in the resulting appearance model indicates a general variability property. The modes of variation, that is, the collection of

Extensions to appearance models span a large range of applications and purposes. Some work of Cootes

To traverse image structures, the models produced are usually stretched to fit an image under a standard optimisation routine where image differences (pairwise difference) is first and foremost taken into account. It is not the most attractive feature of this novel technique, but uses of this ability begin to emerge. Interpretation of gestures through the variables

A somewhat detailed and irrelevant aspect of AAM search is to do with optimisations, off-line training and speed-up. To allow quick and reliable convergence between a model and an image, the relationship between parameter values and the effects they have on the error measure (inferred from image differences) is learned before searching takes place. Not only parameters are taken into account, but also rigid transformations that are vital for matching, let us say, if we know very little about the size of a target object in an image.

To achieve the above a long sequence of alterations to the models is applied and the effects on intensities is learned and recorded in some matrix

Good initialisation is normally required when it comes to the placement of a model in some image. The search will inspect nearby pixels more than distant ones and if nearby pixels show little potential (for fitting), if any at all, then the algorithm will converge in some local minima (or run forever, or maximum number of iterations will be reached). To allow for robust performance, different resolutions of the image as well as scaled models of appearance can be used. Gaussian averaging is normally used to produce such analogous simpler (coarser) elements of the original data. The assumption is that given a coarse scale the problem is simplified and something can be learned and passed forward to the later iterations that deal with finer image resolutions.

- Project Description (PDF)

This page was last modified on October 25th, 2003 | Maintained by Roy Schestowitz |