Akiko Nakashima

Error correcting memorization learning for noisy training examples

In order to avoid overfitting, we propose error correcting memorization learning. This method is derived from minimization of error between outputs of a trained neural network and correct values for noisy training examples, although the correct values are unknown. We show that noise is adequately suppressed by error correcting memorization learning. The noise suppression mechanism is theoretically clarified. It is found that redundancy plays an essential role for noise suppression and depends on a set of training inputs. We give the condition for the training inputs to provide the redundancy. Moreover, by clarifying the relationships between the proposed method and the weighted least squares estimation with the Mahalanobis norm, we reveal effectiveness of the weighted least squares estimation on noise suppression.

Constructing Illumination Image Basis from Object Motion

We propose to construct a 3D linear image basis which spans an image space of arbitrary illumination conditions, from images of a moving object observed under a static lighting condition. The key advance is to utilize the object motion which causes illumination variance on the object surface, rather than varying the lighting, and thereby simplifies the environment for acquiring the input images. Since we then need to re-align the pixels of the images so that the same view of the object can be seen, the correspondence between input images must be solved despite the illumination variance. In order to overcome the problem, we adapt the recently introduced geotensity constraint that accurately governs the relationship between four or more images of a moving object. Through experiments we demonstrate that equivalent 3D image basis is indeed computable and available for recognition or image rendering.

How to design a regularization term for improving generalization

In supervised learning, the regularization method is often used for improving the level of generalization. We give a necessary and sufficient condition of an optimal regularization term, i.e., a regularization operator and parameter. The optimality is discussed based on the projection learning criterion in which the minimization of a generalization error is explicitly considered. We suggest how to design the optimal regularization term so as to satisfy the obtained condition.

Mimicking video: real-time morphable 3D model fitting

This paper presents a new automatic scheme for tracking a 3D non-rigid object surface such as a human face in a real-time video sequence. We introduce a coordinate-oriented error minimization method for estimating the tracking parameters, whereas we base our algorithm on a morphable 3D model consisting of a combination of 3D linear bases, and show that it is extremely well suited to the task of fitting the 3D model to the target object in real time. The algorithm is straightforward, allowing the parameters of an objects pose and non-rigid motion to be computed in an integrated manner. Also, it is found that the illumination variability on the object surface, for instance due to the target motion, can be handled easily. Through the experiments we not only show that on-line tracking is indeed possible, but also demonstrate the effect of our technique of video mimicking.

Noise suppression in training examples for improving generalization capability

For the supervised learning problem, error correcting memorization learning was proposed in order to suppress noise in teacher signals. In this paper, generalization capability of the learning method is discussed. Generalization capability is evaluated based on the projection learning criterion. We give a necessary and sufficient condition for error correcting memorization learning to provide the same level of generalization as projection learning, and suggest how to choose a training set so as to satisfy the obtained condition. Moreover, it is revealed that noise suppression based on the error correcting memorization learning criterion always has a good effect on improving generalization to the level of projection learning.

Noise suppression in training data for improving generalization

Multilayer feedforward neural networks are trained using the error backpropagation (BP) algorithm. This algorithm minimizes the error between outputs of a neural network (NN) and training data. Hence, in the case of noisy training data, a trained network memorizes noisy outputs for given inputs. Such learning is called rote memorization learning (RML). In this paper we propose error correcting memorization learning (CML). It can suppress noise in training data. In order to evaluate generalization ability of CML, it is compared with the projection learning (PL) criterion. It is theoretically proved that although CML merely suppresses noise in training data, it provides the same generalization as PL under some necessary and sufficient condition.

Synthesizing pose and lighting variation from object motion

We present a novel method to synthesize images of a 3D object in arbitrary poses illuminated from arbitrary directions, given a few images of the object in unknown motion under static lighting. Our scheme is underpinned by the notion of illumination image basis which spans an image space of arbitrary lighting, and we propose to generate it by a recursive search for the correspondence between input images and by subsequent realignment of their pixels. Using the 3D surface of the object that also becomes available in this procedure, we synthesize images of the object in arbitrary poses while arbitrarily varying the direction of lighting by combination of the illumination basis images. The effectiveness of the entire algorithm is shown through experiments.