Splines minimizing rotation-invariant semi-norms in Sobolev spaces

1977 ◽  
pp. 85-100 ◽  
Author(s):  
Jean Duchon
Keyword(s):  
Sobolev Spaces ◽  
Rotation Invariant

Rotation Invariant Neural Network-Based Face Detection

1997 ◽  
Author(s):  
Henry A. Rowley ◽  
Shumeet Baluja ◽  
Takeo Kanade
Keyword(s):  
Neural Network ◽  
Face Detection ◽  
Rotation Invariant

Sobolev Spaces

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Sobolev Spaces ◽  
Embedding Theorems ◽  
Approximation Numbers ◽  
Selection Of

This chapter presents a selection of some of the most important results in the theory of Sobolev spacesn. Special emphasis is placed on embedding theorems and the question as to whether an embedding map is compact or not. Some results concerning the k-set contraction nature of certain embedding maps are given, for both bounded and unbounded space domains: also the approximation numbers of embedding maps are estimated and these estimates used to classify the embeddings.

scholarly journals SACN: A Novel Rotating Face Detector Based on Architecture Search

Electronics ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 558
Author(s):  
Anping Song ◽  
Xiaokang Xu ◽  
Xinyi Zhai
Keyword(s):  
Face Detection ◽  
Human Face ◽  
Angle Error ◽  
Rotation Invariant ◽  
Convolutional Network ◽  
Data Set ◽  
Practical Applications ◽  
Model Size ◽  
Average Angle ◽  
Face Detector

Rotation-Invariant Face Detection (RIPD) has been widely used in practical applications; however, the problem of the adjusting of the rotation-in-plane (RIP) angle of the human face still remains. Recently, several methods based on neural networks have been proposed to solve the RIP angle problem. However, these methods have various limitations, including low detecting speed, model size, and detecting accuracy. To solve the aforementioned problems, we propose a new network, called the Searching Architecture Calibration Network (SACN), which utilizes architecture search, fully convolutional network (FCN) and bounding box center cluster (CC). SACN was tested on the challenging Multi-Oriented Face Detection Data Set and Benchmark (MOFDDB) and achieved a higher detecting accuracy and almost the same speed as existing detectors. Moreover, the average angle error is optimized from the current 12.6° to 10.5°.

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