Maximum a posteriori estimation

About: Maximum a posteriori estimation is a research topic. Over the lifetime, 7486 publications have been published within this topic receiving 222291 citations. The topic is also known as: Maximum a posteriori, MAP & maximum a posteriori probability.

User authentication via adapted statistical models of face images

Abstract: It has been previously demonstrated that systems based on local features and relatively complex statistical models, namely, one-dimensional (1-D) hidden Markov models (HMMs) and pseudo-two-dimensional (2-D) HMMs, are suitable for face recognition. Recently, a simpler statistical model, namely, the Gaussian mixture model (GMM), was also shown to perform well. In much of the literature devoted to these models, the experiments were performed with controlled images (manual face localization, controlled lighting, background, pose, etc). However, a practical recognition system has to be robust to more challenging conditions. In this article we evaluate, on the relatively difficult BANCA database, the performance, robustness and complexity of GMM and HMM-based approaches, using both manual and automatic face localization. We extend the GMM approach through the use of local features with embedded positional information, increasing performance without sacrificing its low complexity. Furthermore, we show that the traditionally used maximum likelihood (ML) training approach has problems estimating robust model parameters when there is only a few training images available. Considerably more precise models can be obtained through the use of Maximum a posteriori probability (MAP) training. We also show that face recognition techniques which obtain good performance on manually located faces do not necessarily obtain good performance on automatically located faces, indicating that recognition techniques must be designed from the ground up to handle imperfect localization. Finally, we show that while the pseudo-2-D HMM approach has the best overall performance, authentication time on current hardware makes it impractical. The best tradeoff in terms of authentication time, robustness and discrimination performance is achieved by the extended GMM approach.

Amortised MAP Inference for Image Super-resolution

Abstract: Image super-resolution (SR) is an underdetermined inverse problem, where a large number of plausible high-resolution images can explain the same downsampled image. Most current single image SR methods use empirical risk minimisation, often with a pixel-wise mean squared error (MSE) loss. However, the outputs from such methods tend to be blurry, over-smoothed and generally appear implausible. A more desirable approach would employ Maximum a Posteriori (MAP) inference, preferring solutions that always have a high probability under the image prior, and thus appear more plausible. Direct MAP estimation for SR is non-trivial, as it requires us to build a model for the image prior from samples. Furthermore, MAP inference is often performed via optimisation-based iterative algorithms which don't compare well with the efficiency of neural-network-based alternatives. Here we introduce new methods for amortised MAP inference whereby we calculate the MAP estimate directly using a convolutional neural network. We first introduce a novel neural network architecture that performs a projection to the affine subspace of valid SR solutions ensuring that the high resolution output of the network is always consistent with the low resolution input. We show that, using this architecture, the amortised MAP inference problem reduces to minimising the cross-entropy between two distributions, similar to training generative models. We propose three methods to solve this optimisation problem: (1) Generative Adversarial Networks (GAN) (2) denoiser-guided SR which backpropagates gradient-estimates from denoising to train the network, and (3) a baseline method using a maximum-likelihood-trained image prior. Our experiments show that the GAN based approach performs best on real image data. Lastly, we establish a connection between GANs and amortised variational inference as in e.g. variational autoencoders.