Regularization Theory, Radial Basis Functions and Networks

Abstract Path planning has been widely investigated by many researchers and engineers for its extensive applications in the real world. In this paper, a biharmonic radial basis potential function (BRBPF) representation is proposed to construct navigation fields in 2D maps with obstacles, and it therefore can guide and design a path joining given start and goal positions with obstacle avoidance. We construct BRBPF by solving a biharmonic equation associated with distance-related boundary conditions using radial basis functions (RBFs). In this way, invalid gradients calculated by finite difference methods in large size grids can be preventable. Furthermore, paths constructed by BRBPF are smoother than paths constructed by harmonic potential functions and other methods, and plenty of experimental results demonstrate that the proposed method is valid and effective.

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Efficient mesh deformation using radial basis functions with a grouping-circular-based greedy algorithm

Journal of Computational Physics ◽

10.1016/j.jcp.2021.110200 ◽

2021 ◽

Vol 433 ◽

pp. 110200

Author(s):

Hong Fang ◽

He Zhang ◽

Fanli Shan ◽

Ming Tie ◽

Xing Zhang ◽

...

Keyword(s):

Greedy Algorithm ◽

Radial Basis Functions ◽

Basis Functions ◽

Mesh Deformation ◽

Radial Basis

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EYE DETECTION USING OPTIMAL WAVELET PACKETS AND RADIAL BASIS FUNCTIONS (RBFs)

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001499000562 ◽

1999 ◽

Vol 13 (07) ◽

pp. 1009-1025 ◽

Cited By ~ 62

Author(s):

JEFFREY HUANG ◽

HARRY WECHSLER

Keyword(s):

Radial Basis Functions ◽

Detection Task ◽

Basis Functions ◽

Wavelet Packets ◽

Eye Detection ◽

Robust Performance ◽

Image Normalization ◽

Entropy Minimization ◽

Novel Approach ◽

Radial Basis

The eyes are important facial landmarks, both for image normalization due to their relatively constant interocular distance, and for post processing due to the anchoring on model-based schemes. This paper introduces a novel approach for the eye detection task using optimal wavelet packets for eye representation and Radial Basis Functions (RBFs) for subsequent classification ("labeling") of facial areas as eye versus non-eye regions. Entropy minimization is the driving force behind the derivation of optimal wavelet packets. It decreases the degree of data dispersion and it thus facilitates clustering ("prototyping") and capturing the most significant characteristics of the underlying (eye regions) data. Entropy minimization is thus functionally compatible with the first operational stage of the RBF classifier, that of clustering, and this explains the improved RBF performance on eye detection. Our experiments on the eye detection task prove the merit of this approach as they show that eye images compressed using optimal wavelet packets lead to improved and robust performance of the RBF classifier compared to the case where original raw images are used by the RBF classifier.

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