Continuous Direct Sparse Visual Odometry from RGB-D Images (1904.02266v3)

Abstract: This paper reports on a novel formulation and evaluation of visual odometry from RGB-D images. Assuming a static scene, the developed theoretical framework generalizes the widely used direct energy formulation (photometric error minimization) technique for obtaining a rigid body transformation that aligns two overlapping RGB-D images to a continuous formulation. The continuity is achieved through functional treatment of the problem and representing the process models over RGB-D images in a reproducing kernel Hilbert space; consequently, the registration is not limited to the specific image resolution and the framework is fully analytical with a closed-form derivation of the gradient. We solve the problem by maximizing the inner product between two functions defined over RGB-D images, while the continuous action of the rigid body motion Lie group is captured through the integration of the flow in the corresponding Lie algebra. Energy-based approaches have been extremely successful and the developed framework in this paper shares many of their desired properties such as the parallel structure on both CPUs and GPUs, sparsity, semi-dense tracking, avoiding explicit data association which is computationally expensive, and possible extensions to the simultaneous localization and mapping frameworks. The evaluations on experimental data and comparison with the equivalent energy-based formulation of the problem confirm the effectiveness of the proposed technique, especially, when the lack of structure and texture in the environment is evident.

• The paper introduces a continuous visual odometry model that reformulates photometric error minimization using a Lie group framework.
• The paper derives a closed-form gradient through reproducing kernel Hilbert spaces, bypassing traditional numerical differentiation methods.
• The paper demonstrates robust SLAM integration and reduced computational costs, validated by experiments on benchmark RGB-D datasets.

An Analytical Approach to Continuous Direct Sparse Visual Odometry from RGB-D Images

The paper entitled "Continuous Direct Sparse Visual Odometry from RGB-D Images" delineates a novel approach to visual odometry using RGB-D data, presenting a theoretical framework that extends direct energy minimization techniques into a continuous domain. The approach offers a comprehensive understanding of photometric error minimization strategies prevalent in visual odometry, but with a focus on continuous rather than discrete functions. This formulation leverages reproducing kernel Hilbert spaces (RKHS) to provide a functional representation of RGB-D image registration, managing to bypass the constraints of image resolution and achieve an analytical derivation of the gradient.

Methodology and Theoretical Foundations

The authors propose a framework that harnesses the power of Lie groups and algebras to represent rigid body transformations. The transformation updates are computed within a Lie algebra, ensuring smooth transitions and transformations. The process involves the maximization of an inner product between functions defined over RGB-D images, encapsulating the rigid body motion within the continuous action of a Lie group. This step is crucial since it creates the potential for parallel processing on both CPUs and GPUs while maintaining a high computational performance due to the intrinsic sparse structure of the representation.

Key contributions one must highlight include:

• Continuity and Lie Group Utilization: The paper introduces an analytical approach to RGB-D image registration that encompasses any image resolution, achieved through a continuous Lie group framework.
• Gradient Derivation: Distinct from the traditional numerical differentiation methods, this framework offers a complete closed-form expression for the gradient, which is critical for efficient computation.
• Simultaneous Localization and Mapping (SLAM) Integration: The structure of this framework is naturally extendable to SLAM, showcasing the versatility and potential applicability in more complex robotic and navigational tasks.

Experimental Validation and Observations

The methodology is supported by empirical evaluations using real-world RGB-D data, with experiments conducted on benchmark datasets. The results demonstrate the framework's effectiveness compared to traditional energy-based formulations, especially in environments with minimal scene structure and texture. The significant reduction in computational expenses through bypassing explicit data association further illustrates the practical strengths of the proposed approach.

Noteworthy, the evaluations provide cumulative distribution functions of the position and orientation errors, underscoring the algorithm's robustness in various scenarios. The work indicates a substantial improvement when dealing with environments lacking distinct features, which typically pose challenges for visual odometry systems.

Implications and Future Directions

The approach delineated in this paper carries substantial implications for robotic perception and autonomous navigation systems. The theoretical underpinning in using RKHS and Lie group motion formulation offers a promising direction for addressing the complexities in real-time tracking and mapping. Moreover, the potential to integrate the method into visual SLAM systems suggests broader applications and enhancements in AI and robotics.

Future research could explore further refinement of the framework's integration with IMU data to enhance the robustness and accuracy of pose tracking. Another area of potential exploration is the extension of this continuous framework to handle dynamic scenes and non-static environments, which remain a challenging aspect in the field of visual odometry.

In summary, the paper presents a methodologically sound advancement in the domain of visual odometry with strong theoretical justifications and promising experimental results that pave the way for further enhancements and applications in real-world scenarios.