Adaptive Real-Time Numerical Differentiation with Variable-Rate Forgetting and Exponential Resetting

Digital PID control requires a differencing operation to implement the D gain. In order to suppress the effects of noisy data, the traditional approach is to filter the data, where the frequency response of the filter is adjusted manually based on the characteristics of the sensor noise. The present paper considers the case where the characteristics of the sensor noise change over time in an unknown way. This problem is addressed by applying adaptive real-time numerical differentiation based on adaptive input and state estimation (AISE). The contribution of this paper is to extend AISE to include variable-rate forgetting with exponential resetting, which allows AISE to more rapidly respond to changing noise characteristics while enforcing the boundedness of the covariance matrix used in recursive least squares.

Generalized Forgetting Recursive Least Squares: Stability and Robustness Guarantees

This work present generalized forgetting recursive least squares (GF-RLS), a generalization of recursive least squares (RLS) that encompasses many extensions of RLS as special cases. First, sufficient conditions are presented for the 1) Lyapunov stability, 2) uniform Lyapunov stability, 3) global asymptotic stability, and 4) global uniform exponential stability of parameter estimation error in GF-RLS when estimating fixed parameters without noise. Second, robustness guarantees are derived for the estimation of time-varying parameters in the presence of measurement noise and regressor noise. These robustness guarantees are presented in terms of global uniform ultimate boundedness of the parameter estimation error. A specialization of this result gives a bound to the asymptotic bias of least squares estimators in the errors-in-variables problem. Lastly, a survey is presented to show how GF-RLS can be used to analyze various extensions of RLS from the literature.

Time-Supervised Primary Object Segmentation

We describe an unsupervised method to detect and segment portions of live scenes that, at some point in time, are seen moving as a coherent whole, which we refer to as primary objects. Our method first segments motions by minimizing the mutual information between partitions of the image domain, which bootstraps a static object detection model that takes a single image as input. The two models are mutually reinforced within a feedback loop, enabling extrapolation to previously unseen classes of objects. Our method requires video for training, but can be used on either static images or videos at inference time. As the volume of our training sets grows, more and more objects are seen moving, thus turning our method into unsupervised (or time-supervised) training to segment primary objects. The resulting system outperforms the state-of-the-art in both video object segmentation and salient object detection benchmarks, even when compared to methods that use explicit manual annotation.

ErrorNet: Learning error representations from limited data to improve vascular segmentation

Deep convolutional neural networks have proved effective in segmenting lesions and anatomies in various medical imaging modalities. However, in the presence of small sample size and domain shift problems, these models often produce masks with non-intuitive segmentation mistakes. In this paper, we propose a segmentation framework called ErrorNet, which learns to correct these segmentation mistakes through the repeated process of injecting systematic segmentation errors to a segmentation mask based on a learned shape prior, followed by attempting to predict the injected error. During inference, ErrorNet corrects the segmentation mistakes by adding the predicted error map to the initial segmentation mask. ErrorNet has advantages over alternatives based on domain adaptation or CRF-based post processing, because it requires neither domain-specific parameter tuning nor any data from the target domains. We have evaluated ErrorNet using five public datasets for the task of retinal vessel segmentation. The selected datasets differ in size and patient population, allowing us to evaluate the effectiveness of ErrorNet in handling small sample size and domain shift problems. Our experiments demonstrate that ErrorNet outperforms a base segmentation model, a CRF-based post processing scheme, and a domain adaptation method, with a greater performance gain in the presence of dataset limitations above.