The goal of multi-objective optimisation is to identify the Pareto front surface which is the set obtained by connecting the best trade-off points. Typically this surface is computed by evaluating the objectives at different points and then interpolating between the subset of the best evaluated trade-off points. In this work, we propose to parameterise the Pareto front surface using polar coordinates. More precisely, we show that any Pareto front surface can be equivalently represented using a scalar-valued length function which returns the projected length along any positive radial direction. We then use this representation in order to rigorously develop the theory and applications of stochastic Pareto front surfaces. In particular, we derive many Pareto front surface statistics of interest such as the expectation, covariance and quantiles. We then discuss how these can be used in practice within a design of experiments setting, where the goal is to both infer and use the Pareto front surface distribution in order to make effective decisions. Our framework allows for clear uncertainty quantification and we also develop advanced visualisation techniques for this purpose. Finally we discuss the applicability of our ideas within multivariate extreme value theory and illustrate our methodology in a variety of numerical examples, including a case study with a real-world air pollution data set.

In this paper, we propose a method for calculating the three-dimensional (3D) position and orientation of a pallet placed on a shelf on the side of a forklift truck using a 360-degree camera. By using a 360-degree camera mounted on the forklift truck, it is possible to observe both the pallet at the side of the forklift and one several meters ahead. However, the pallet on the obtained image is observed with different distortion depending on its 3D position, so that it is difficult to extract the pallet from the image. To solve this problem, a method [1] has been proposed for detecting a pallet by projecting a 360-degree image on a vertical plane that coincides with the front of the shelf to calculate an image similar to the image seen from the front of the shelf. At the same time as the detection, the approximate position and orientation of the detected pallet can be obtained, but the accuracy is not sufficient for automatic control of the forklift truck. In this paper, we propose a method for accurately detecting the yaw angle, which is the angle of the front surface of the pallet in the horizontal plane, by projecting the 360-degree image on a horizontal plane including the boundary line of the front surface of the detected pallet. The position of the pallet is also determined by moving the vertical plane having the detected yaw angle back and forth, and finding the position at which the degree of coincidence between the projection image on the vertical plane and the actual size of the front surface of the pallet is maximized. Experiments using real images taken in a laboratory and an actual warehouse have confirmed that the proposed method can calculate the position and orientation of a pallet within a reasonable calculation time and with the accuracy necessary for inserting the fork into the hole in the front of the pallet.

At the end of the month, Barcelona will traditionally host the annual Mobile World Congress and Doogee plans to introduce three new ("futuristic" as they say) smartphones during the show. The first one is the Dogee V, which has a full-screen front design with an in-display fingerprint sensor and an AMOLED display with a U-shaped notch. The second is Doogee Mix 3, which will have a side-mounted fingerprint sensor and... Doogee V is known for featuring an in-display fingerprint sensor, 8GB of RAM, 128GB of RAM and almost an all-screen front. The new unnamed smartphone resembles the V in many ways - it has the same U-shaped notch, 3D curved back, but instead of having an in-display fingerprint sensor, it has a thin chin... While Doogee BL12000's hot pre-sale is currently going on, the DoogeeSlide Full-screen Concept Phone appears on a third-party video.