## 4 Practical Multidirectional MTF Measurement Method
### Modified Practical Edge Method  
Based on the modified strategies in 4.1-4.3, this paper proposes a practical multidirectional MTF modified edge method with an adaptive determination of OSR. The flow chart of the modified practical edge method is shown in Figure 16.  
The subpixel edge detection process is explained as follows: the actual image may not only contain edge features, so step 1.1 is to preliminarily extract the vertical or horizontal edge ROI from the actual image with edges. In order to facilitate the computation and processing, the horizontal edge should be rotated into the vertical edge. Step 1.2 is used to verify whether the extracted edge contrast (which should be greater than 0.1) and edge SNR (which should be greater than 10 dB) can guarantee the accuracy and validity of MTF measurement results. Step 1.3 is used to selectively perform inverse photoelectric conversion on actual images and multi-layer data fusion of color images. In step 1.4, the accuracy of edge angle determined by coarse and fine edge detection twice can meet the MTF measurement requirements in most imaging fields. Both coarse and fine edge detection are composed of three steps: filtering each row of ROI data, determining edge points by row difference, and performing least square linear fitting on edge points. The difference between the coarse and fine edge detection lies in the application of a symmetric Hamming window filter and an asymmetric Hamming window filter based on coarse positioning edge points. In step 1.5, firstly, calculate the minimum number of rows \(R_{min}(=\)1/tan(\(\theta\))) of effective ROI according to the edge angle, then calculate the maximum number \(X_{max}\)-\(R_{min}(=\)\(R/R_{min})\) of optional \(R_{min}\) according to the number of rows \(R\) of input edge ROI, and finally, extract multiple sub-ROIs with different sizes and different positions that meet the MTF measurement requirements according to the multi-ROI automatic extraction algorithm in Algorithm 1. The modified practical edge method in this paper constructs multiple ESF by automatically extracting multiple ROI and binning with multiple PS. In step 2.1, each ROI is projected along the edge to the direction perpendicular to the edge, and multidirectional projection data is obtained. In step 2.2, the OSR with stronger adaptability is determined by the variable OSR determination model proposed in Section 4.2, and the oversampled ESF is constructed according to ISO-cos binning scheme. In step 2.3, the number of binning PS is determined according to the model mentioned in Section 4.3, and the accuracy of the edge method is improved by constructing multi-PS oversampled ESF. To sum up, a plurality of ESFs will be obtained from multiple measurement states, i.e., multiple ROIs and multiple binning phases. Figure 16: The processing steps of modified practical edge method. It is found that the calculation rationality of spatial frequency (SF) and the accuracy of the correspondence between SF and MTF directly determine the accuracy and reliability of the edge method, but the relevant research shows little about the accurate calculation of SF. The calculation of SF and Nyquist frequency depends on edge image resolution _DPI_ (e.g., 300 dpi), edge angle \(\theta\) (e.g., 10 deg), the number of discrete LSF point \(L\) (even number) participating in FFT, and OSR (e.g., 1/tan(10) = 5.67). Assume that the pixel spacing of the edge image is _del_ (mm), the projection path spacing of adjacent pixels in each row is _delcorr_, the Nyquist frequency is _freNyq_, the number of valid data after FFT is _Num_, and the spatial frequency value to be calculated is _SF_. The _SF_ and _freNyq_ are calculated and deduced as follows:  
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