Estimation of Face Depths by Conditional Densities

Abstract

The expected value of missing data in a sample taken from a multivariate normal probability distribution is the mean of the conditional distribution of the missing dimensions given the known dimensions. We explain the derivation of this result, demonstrate its application to face image processing, then use it in a new method for recovering shape from image data. The context of our work is the use of 3D facial models to aid in recognition of human faces by humans. We explain the requirement for such models and review the practical possibilities for encoding depth information alongside photographs in identity documents like passports. The best alternative is to derive depths automatically from the photos, as this requires no side information. We show experimentally that conditional density estimation provides accurate face depth recovery, without recourse to explicit modelling of surface shape.

Covariance estimation in full- and reduced-dimensionality image classification

“…An objective function that matches the analysis task to be done may reasonably be expected to be superior to one that describes a class in isolation. For example, where conditional densities are used for recovering missing data, an appropriate objective function is the mean square error between recovered and actual values in training data [26]. Similarly, for classification, the estimator should follow RDA in adopting a classification error criterion.…”

A Novel Residual Electrical Endurance Prediction Method for Low-Voltage Electromagnetic Alternating Current Contactors

“…Conditional density estimation (CDE) [10], [11] is method that estimates unknown features according to known features of an observation by a pretrained estimation model, which is trained by the same type of data. Assume that there is an observation in a multidimensional distribution, and the features of the observation are partly known and the rest are unknown.…”

“…Define the lengths of X i and X j to be l i and l j , thus the size of i j is l i × l j . References [10] and [13] have described a derivation from (10)-(13) to the following equation:…”

“…To further investigate the relationship between REE and the arcing phenomenon, a method combining multiple characteristics for REE prediction is expected. Based on conditional density estimation (CDE) [10], [11], this paper proposes a novel prediction method that applies several arcing characteristics computed from electrical signals. The method is designed to not only recognize the failure condition of an ac contactor but also estimate the endurance condition throughout the entire lifetime.…”

3D and Infrared Face Reconstruction from RGB data using Canonical Correlation Analysis

“…In statistical approaches [3,1,2,14] the relationship of shape and intensity is learned by training from a set of examples, i.e. intensity images with corresponding shapes.…”