Page 8 - Rapid Learning in Robotics
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4.3 The Best-Match Search . . . . . . . . . . . . . . . . . . . . . . 51
4.4 Learning Phases . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.5 Basis Function Sets, Choice and Implementation Aspects . . 56
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5 Characteristic Properties by Examples 63
5.1 Illustrated Mappings – Constructed From a Small Number
of Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.2 Map Learning with Unregularly Sampled Training Points . . 66
5.3 Topological Order Introduces Model Bias . . . . . . . . . . . 68
5.4 “Topological Defects” . . . . . . . . . . . . . . . . . . . . . . . 70
5.5 Extrapolation Aspects . . . . . . . . . . . . . . . . . . . . . . 71
5.6 Continuity Aspects . . . . . . . . . . . . . . . . . . . . . . . . 72
5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6 Extensions to the Standard PSOM Algorithm 75
6.1 The “Multi-Start Technique” . . . . . . . . . . . . . . . . . . . 76
6.2 Optimization Constraints by Modulating the Cost Function 77
6.3 The Local-PSOM . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.3.1 Approximation Example: The Gaussian Bell . . . . . 80
6.3.2 Continuity Aspects: Odd Sub-Grid Sizes n Give Op-
tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.3.3 Comparison to Splines . . . . . . . . . . . . . . . . . . 82
6.4 Chebyshev Spaced PSOMs . . . . . . . . . . . . . . . . . . . . 83
6.5 Comparison Examples: The Gaussian Bell . . . . . . . . . . . 84
6.5.1 Various PSOM Architectures . . . . . . . . . . . . . . 85
6.5.2 LLM Based Networks . . . . . . . . . . . . . . . . . . 87
6.6 RLC-Circuit Example . . . . . . . . . . . . . . . . . . . . . . . 88
6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7 Application Examples in the Vision Domain 95
7.1 2 D Image Completion . . . . . . . . . . . . . . . . . . . . . . 95
7.2 Sensor Fusion and 3 D Object Pose Identification . . . . . . . 97
7.2.1 Reconstruct the Object Orientation and Depth . . . . 97
7.2.2 Noise Rejection by Sensor Fusion . . . . . . . . . . . . 99
7.3 Low Level Vision Domain: a Finger Tip Location Finder . . . 102
