Steerable Functions Research Articles

DEVELOPMENT OF A NOVEL STEERABLE BOUGIE

Background: This paper describes the development of a new airway device that will improve the speed and safety of endotracheal intubation in anaesthesia and critical care. Case of need, design specification and fabrication of the steerable bougie mechanism is discussed. Aims: Identify the need for a novel steerable bougie whilst considering technology readiness levels associated with medical device design. Analyse and produce suitable mechanisms utilising smart materials to increase device functionality aiding successful patient intubation procedures. Methods: This work describes the total design activity that contributes to the successful development of medical devices, from case of need, to smart material actuation mechanisms. Research focuses on identifying a suitable control mechanism to allow a steerable tip to be integrated into a bougie with a control device attached to the laryngoscope. Results: Data collected from a user group survey supported the development of a novel bougie, with better shape retention, variable rigidity within the tip, and an integrated steerable function. Analysis of several mechanisms, artificial muscles, and smart materials identified a cost-effective steerable mechanism that can be incorporated into a bougie. Conclusion: Users have defined a need for an improved bougie. Controlling smart materials and mechanisms, within the predefined dimensions, identified strengths and weaknesses associated with steerable functions. The performance of the selected mechanism for incorporation requires a high level of control to accurately steer a device within the human airway.

Exact reconstruction with directional wavelets on the sphere

A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of a previously developed wavelet formalism developed by Antoine & Vandergheynst and Wiaux et al. The translations of the wavelets at any point on the sphere and their proper rotations are still defined through the continuous three-dimensional rotations. The dilations of the wavelets are directly defined in harmonic space through a new kernel dilation, which is a modification of an existing harmonic dilation. A family of factorized steerable functions with compact harmonic support which are suitable for this kernel dilation are first identified. A scale-discretized wavelet formalism is then derived, relying on this dilation. The discrete nature of the analysis scales allows the exact reconstruction of band-limited signals. A corresponding exact multi-resolution algorithm is finally described and an implementation is tested. The formalism is of interest notably for the denoising or the deconvolution of signals on the sphere with a sparse expansion in wavelets. In astrophysics, it finds a particular application for the identification of localized directional features in the cosmic microwave background data, such as the imprint of topological defects, in particular, cosmic strings, and for their reconstruction after separation from the other signal components.

Design of steerable filters for feature detection using canny-like criteria

We propose a general approach for the design of 2D feature detectors from a class of steerable functions based on the optimization of a Canny-like criterion. In contrast with previous computational designs, our approach is truly 2D and provides filters that have closed-form expressions. It also yields operators that have a better orientation selectivity than the classical gradient or Hessian-based detectors. We illustrate the method with the design of operators for edge and ridge detection. We present some experimental results that demonstrate the performance improvement of these new feature detectors. We propose computationally efficient local optimization algorithms for the estimation of feature orientation. We also introduce the notion of shape-adaptable feature detection and use it for the detection of image corners.

Lie generators for computing steerable functions

We present a computational, group-theoretic approach to steerable functions. The approach is group-theoretic in that the treatment involves continuous transformation groups for which elementary Lie group theory may be applied. The approach is computational in that the theory is constructive and leads directly to a procedural implementation. For functions that are steerable with n basis functions under a k-parameter group, the procedure is efficient in that at most nk+1 iterations of the procedure are needed to compute all the basis functions. Furthermore, the procedure is guaranteed to return the minimum number of basis functions. If the function is not steerable, a numerical implementation of the procedure could be used to compute basis functions that approximately steer the function over a range of transformation parameters. Examples of both applications are described.

Canonical decomposition of steerable functions

Steerable functions find application in numerous problems in image processing, computer vision and computer graphics. As such, it is important to develop the appropriate mathematical tools to analyze them. In this paper, we introduce the mathematics of Lie group theory in the context of steerable functions and present a canonical decomposition of these functions under any transformation group. The theory presented in this paper can be applied and extended in various ways.