Fourier Domain Object Detection via Point-Wise Multiplication
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Solution Overview
Problem
Current linear object detection methods are computationally slow due to the high number of linear filters required, which increases error when acceleration techniques are applied.
Innovation Solution
Performing object detection in the Fourier space through point-wise multiplication and summation of Fourier feature and filter matrices, followed by an inverse Fourier transform, reduces computational time while maintaining accuracy by efficiently computing the Fourier transform and minimizing the number of inverse transforms needed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a large number of linear filters are used to detect objects from different viewpoints, then detection accuracy is improved, but computational time increases significantly
Solution Approach 1:
The patent replaces the mechanical convolution operation in spatial domain with mathematical Fourier transform-based multiplication in frequency domain. This substitution transforms the computationally intensive filter application process into a more efficient operation that can be parallelized, thereby maintaining detection accuracy while significantly reducing computational time
Solution Approach 2:
The patent changes the domain parameter from spatial domain to frequency domain by applying Fourier transform. This parameter transformation allows the same detection task to be performed with different computational characteristics, enabling faster processing while preserving the accuracy of detecting objects from multiple viewpoints
2Loss of time
If acceleration techniques such as cascades are applied to speed up detection, then computational time is reduced, but detection error increases and requires parameter tuning
Solution Approach 1:
The patent substitutes the cascade acceleration approach with a direct Fourier-domain computation method. This replacement eliminates the need for approximate cascade stages and parameter tuning, achieving speedup without introducing the detection errors and reliability issues that plague cascade-based acceleration techniques
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach accelerates object detection by a factor of 2, reducing computation time by 10 times compared to traditional methods without increasing error, as the convolution in the frequency space is mathematically equivalent to the position space convolution.
Implementation Method 1
A Fourier transform of the plurality of feature matrices is performed which yields a plurality of Fourier feature matrices
Implementation Method 2
The Fourier score matrix is then transformed back by an inverse Fourier transform to a score matrix
Data Source
AI summary
Object detection receives an input image to detect an object of interest. It determines feature matrices based on the received image, wherein each matrix represents a feature of the received image. The plurality of matrices are Fourier transformed to Fourier feature matrices. Fourier filter matrices are provided, each representing a feature of an object transformed in Fourier space. Each filter matrix is point-wise multiplied with one of the feature matrices corresponding to the same feature. The plurality of matrices are summed, resulting by point-wise multiplying each Fourier filter matrix with the corresponding Fourier feature matrix to obtain a Fourier score matrix. An inverse Fourier transform of the Fourier score matrix is performed, resulting in a score matrix, which is used to detect the object in the input image.