Cuboid

Abstract: The derivation of a closed expression is presented to calculate the vertical component of the gravitational attraction of a right rectangular prism, with sides parallel to the coordinate axis. As any configuration can be expressed as the sum of prisms of various sizes and densities, the computation of the total gravitational effect of bodies of arbitrary shapes at any point outside of or on the boundary of the bodies is straightforward. To calculate the gravitational effect of the “unit” building element a subroutine called Prism has been developed, tested, and incorporated, in one program to calculate terrain corrections, and in another program for three‐dimensional analysis of a gravity field.

Abstract: Local spatio-temporal interest points (STIPs) and the resulting features from RGB videos have been proven successful at activity recognition that can handle cluttered backgrounds and partial occlusions. In this paper, we propose its counterpart in depth video and show its efficacy on activity recognition. We present a filtering method to extract STIPs from depth videos (called DSTIP) that effectively suppress the noisy measurements. Further, we build a novel depth cuboid similarity feature (DCSF) to describe the local 3D depth cuboid around the DSTIPs with an adaptable supporting size. We test this feature on activity recognition application using the public MSRAction3D, MSRDailyActivity3D datasets and our own dataset. Experimental evaluation shows that the proposed approach outperforms state-of-the-art activity recognition algorithms on depth videos, and the framework is more widely applicable than existing approaches. We also give detailed comparisons with other features and analysis of choice of parameters as a guidance for applications.

Abstract: An implant for the intervertebral space consists of an essentially cuboid body with a device for gripping by a tool.

Abstract: This paper addresses the problem of category-level 3D object detection. Given a monocular image, our aim is to localize the objects in 3D by enclosing them with tight oriented 3D bounding boxes. We propose a novel approach that extends the well-acclaimed deformable part-based model [1] to reason in 3D. Our model represents an object class as a deformable 3D cuboid composed of faces and parts, which are both allowed to deform with respect to their anchors on the 3D box. We model the appearance of each face in fronto-parallel coordinates, thus effectively factoring out the appearance variation induced by viewpoint. Our model reasons about face visibility patters called aspects. We train the cuboid model jointly and discriminatively and share weights across all aspects to attain efficiency. Inference then entails sliding and rotating the box in 3D and scoring object hypotheses. While for inference we discretize the search space, the variables are continuous in our model. We demonstrate the effectiveness of our approach in indoor and outdoor scenarios, and show that our approach significantly outperforms the state-of-the-art in both 2D [1] and 3D object detection [2].

Abstract: The aim was to compare kinematic data from an experimental foot model comprising four segments ((i) heel, (ii) navicular/cuboid (iii) medial forefoot, (iv) lateral forefoot), to the kinematics of the individual bones comprising each segment. The foot model was represented using two different marker attachment protocols: (a) markers attached directly to the skin; (b) markers attached to rigid plates mounted on the skin. Bone data were collected for the tibia, talus, calcaneus, navicular, cuboid, medial cuneiform and first and fifth metatarsals (n=6). Based on the mean differences between the three data sets during stance, the differences between any two of the three kinematic protocols (i.e. bone vs skin, bone vs plate, skin vs plate) were >3° in only 35% of the data and >5° in only 3.5% of the data. However, the maximum difference between any two of the three protocols during stance was >3° in 100% of the data, >5° in 73% of the data and >8° in 23% of the data. Differences were greatest for motion of the combined navicular/cuboid relative to the calcaneus and the medial forefoot segment relative to the navicular/cuboid. The differences between the data from the skin and plate protocols were consistently smaller than differences between either protocol and the kinematic data for each bone comprising the segment. The pattern of differences between skin and plate protocols and the actual bone motion showed no systematic pattern. It is unlikely that one rigid body foot model and marker attachment approach is always preferable over another.