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It is well-known that any sum of squares (SOS) program can be cast as a semidefinite program (SDP) of a particular structure and that therein lies the computational bottleneck for SOS programs, as the SDPs generated by this procedure are…
Due to large variations in shape, appearance, and viewing conditions, object recognition is a key precursory challenge in the fields of object manipulation and robotic/AI visual reasoning in general. Recognizing object categories,…
We consider the problem of finding exact sums of squares (SOS) decompositions for certain classes of non-negative multivariate polynomials, relying on semidefinite programming (SDP) solvers. We start by providing a hybrid numeric-symbolic…
Self-supervised learning (SSL) has emerged as a powerful technique for learning visual representations. While recent SSL approaches achieve strong results in global image understanding, they are limited in capturing the structured…
Compared to 2D object bounding-box labeling, it is very difficult for humans to annotate 3D object poses, especially when depth images of scenes are unavailable. This paper investigates whether we can estimate the object poses effectively…
Enabling robots to understand the world in terms of objects is a critical building block towards higher level autonomy. The success of foundation models in vision has created the ability to segment and identify nearly all objects in the…
With the human pursuit of knowledge, open-set object detection (OSOD) has been designed to identify unknown objects in a dynamic world. However, an issue with the current setting is that all the predicted unknown objects share the same…
Sequential manipulation tasks require a robot to perceive the state of an environment and plan a sequence of actions leading to a desired goal state. In such tasks, the ability to reason about spatial relations among object entities from…
The second-order cone (SOC) is a class of simple convex cones and optimizing over them can be done more efficiently than with semidefinite programming. It is interesting both in theory and in practice to investigate which convex cones admit…
Object detection is a critical part of visual scene understanding. The representation of the object in the detection task has important implications on the efficiency and feasibility of annotation, robustness to occlusion, pose, lighting,…
In this work, we tackle the task of estimating the 6D pose of an object from point cloud data. While recent learning-based approaches to addressing this task have shown great success on synthetic datasets, we have observed them to fail in…
Sum of squares (SOS) optimization is a powerful technique for solving problems where the positivity of a polynomials must be enforced. The common approach to solve an SOS problem is by relaxation to a Semidefinite Program (SDP). The main…
This paper presents the initial stages in the development of a deep learning classifier for generalised Resident Space Object (RSO) characterisation that combines high-fidelity simulated light curves with transfer learning to improve the…
If a robot is supposed to roam an environment and interact with objects, it is often necessary to know all possible objects in advance, so that a database with models of all objects can be generated for visual identification. However, this…
We study sum of squares (SOS) relaxations to optimize polynomial functions over a set $V\cap R^n$, where $V$ is a complex algebraic variety. We propose a new methodology that, rather than relying on some algebraic description, represents…
We propose a framework to continuously learn object-centric representations for visual learning and understanding. Existing object-centric representations either rely on supervisions that individualize objects in the scene, or perform…
A widely used method for solving SOS (Sum Of Squares) decomposition problem is to reduce it to the problem of semi-definite programs (SDPs) which can be efficiently solved in theory. In practice, although many SDP solvers can work out some…
Recognizing precise geometrical configurations of groups of objects is a key capability of human spatial cognition, yet little studied in the deep learning literature so far. In particular, a fundamental problem is how a machine can learn…
We address the problem of inferring self-supervised dense semantic correspondences between objects in multi-object scenes. The method introduces learning of class-aware dense object descriptors by providing either unsupervised discrete…
A polynomial that is a sum of squares (SOS) of other polynomials is evidently positive. The converse is not true, there are positive polynomials which are not SOS. This note focuses on the problem of certifying, in exact arithmetic, that a…