Andrew M. Wallace

Anis Hamadouche, Yun Wu, Andrew M. Wallace et al.

We analyse the convergence of the proximal gradient algorithm for convex composite problems in the presence of gradient and proximal computational inaccuracies. We derive new tighter deterministic and probabilistic bounds that we use to verify a simulated (MPC) and a synthetic (LASSO) optimization problems solved on a reduced-precision machine in combination with an inaccurate proximal operator. We also show how the probabilistic bounds are more robust for algorithm verification and more accurate for application performance guarantees. Under some statistical assumptions, we also prove that some cumulative error terms follow a martingale property. And conforming to observations, e.g., in \cite{schmidt2011convergence}, we also show how the acceleration of the algorithm amplifies the gradient and proximal computational errors.

Yining Ding, João F. C. Mota, Andrew M. Wallace et al.

We propose a method which, given a sequence of stereo foggy images, estimates the parameters of a fog model and updates them dynamically. In contrast with previous approaches, which estimate the parameters sequentially and thus are prone to error propagation, our algorithm estimates all the parameters simultaneously by solving a novel optimisation problem. By assuming that fog is only locally homogeneous, our method effectively handles real-world fog, which is often globally inhomogeneous. The proposed algorithm can be easily used as an add-on module in existing visual Simultaneous Localisation and Mapping (SLAM) or odometry systems in the presence of fog. In order to assess our method, we also created a new dataset, the Stereo Driving In Real Fog (SDIRF), consisting of high-quality, consecutive stereo frames of real, foggy road scenes under a variety of visibility conditions, totalling over 40 minutes and 34k frames. As a first-of-its-kind, SDIRF contains the camera's photometric parameters calibrated in a lab environment, which is a prerequisite for correctly applying the atmospheric scattering model to foggy images. The dataset also includes the counterpart clear data of the same routes recorded in overcast weather, which is useful for companion work in image defogging and depth reconstruction. We conducted extensive experiments using both synthetic foggy data and real foggy sequences from SDIRF to demonstrate the superiority of the proposed algorithm over prior methods. Our method not only produces the most accurate estimates on synthetic data, but also adapts better to real fog. We make our code and SDIRF publicly available\footnote{https://github.com/SenseRoboticsLab/estimating-fog-parameters} to the community with the aim of advancing the research on visual perception in fog.

Alireza Ahrabian, Joao F. C. Mota, Andrew M. Wallace

We propose a method that combines sparse depth (LiDAR) measurements with an intensity image and to produce a dense high-resolution depth image. As there are few, but accurate, depth measurements from the scene, our method infers the remaining depth values by incorporating information from the intensity image, namely the magnitudes and directions of the identified edges, and by assuming that the scene is composed mostly of flat surfaces. Such inference is achieved by solving a convex optimisation problem with properly weighted regularisers that are based on the `1-norm (specifically, on total variation). We solve the resulting problem with a computationally efficient ADMM-based algorithm. Using the SYNTHIA and KITTI datasets, our experiments show that the proposed method achieves a depth reconstruction performance comparable to or better than other model-based methods.