# On-Board Flickering Pixel Dynamic Suppression Method Based on Multi-Feature Fusion
## 2 Methodology
### Visual Feature Extraction Based on Facet Model  
A point target is a target whose actual image area on the surface of the detector is smaller than one pixel of the detector [20]. However, the imaging process of the practical optical system is influenced by diffraction and aberration. Therefore, IRPT imaging is not an ideal point but a speckle. Conversely, blind pixels are mainly caused by the limitations of the sensor, and their image is entirely unrelated to the optical system. Hence, blind pixels appear as bright or dark points in the infrared focal plane array (IRFPA). From the above results and analysis, we propose a visual feature extraction method based on the facet model using the result of IRPT detection as input to distinguish blind pixels from suspected IRPT. The facet model was proposed by [PERSON] [21]. This model considers the discrete pixel response as surface, and a polynomial function is used to estimate the surface in a small neighborhood [22]. Therefore, the spatial domain of the image can be partitioned into connected smooth regions called facets. Obviously, the blind pixels cannot be estimated by the facet model accurately because of its pulse shape. On the contrary, the intensity of IRPT decreased gradually from the center to the edge, which could be estimated more accurately by using the facet model. Therefore, we regard the detected IRPTs as potential blind pixels, and estimate them based on the facet model. Then, the estimation error of the facet model is segmented by the threshold to extract blind pixels. A detailed description of the steps is provided bellow. Firstly, we use a bivariate cubic function f in canonical form as Equation (1) to fit the \(3\times 3\) neighborhood. \[f(r,c)=\sum_{i=1}^{8}k_{i}p_{i}, \tag{1}\]  
where, \((r,c)\in R\times C\), \(R,C=\{-1,0,1\}\) are symmetric index sets of row and column respectively. \(p_{i}\in\left\{1,r,c,r^{2}-2/3,rc,c^{2}-2/3,r\big{(}c^{2}-2/3\big{)},c\big{(}r ^{2}-2/3\big{)}\right\}\) are 2-D discrete  
Figure 1: The block diagram of proposed algorithm. orthogonal Chebyshev polynomials, and \(k_{i}\) is the fitting coefficient which could be deduced by the least-squares algorithm as shown in Equation (2). \[k_{i}=\frac{\sum_{(r,c)\in R\times C}P_{i}(r,c)I(r,c)}{\sum_{(r,c)\in R\times C}P_ {i}^{2}(r,c)}, \tag{2}\]  
where \(I(r,c)\) is the response intensity of pixel \((r,c)\). Obviously, \(I(r,c)\) is independent of the remainder in Equation (2). Therefore, we can define this remainder as fixed filters \(\omega_{i}\) in Equation (3) so that \(k_{i}\) could be calculated by convolution. \[\omega_{i}=\frac{P_{i}(r,c)}{\sum_{(r,c)\in R\times C}P_{i}^{2}(r,c)}, \tag{3}\]  
Then, the estimation of the facet model can be deduced through Equations (1) and (2) as follows:  
\[f_{facet}(i,j)=k_{1}-\frac{2}{3}k_{4}-\frac{2}{3}k_{6}, \tag{4}\]  
where \((i,j)\) is the coordinate of potential blind pixels, and \(f_{facet}(i,j)\) is the estimation of the facet model. The non-zero fitting coefficients could be calculated by the Equation (3) as follows:  
\[\left\{ \begin{array}{c}\omega_{1}=\frac{1}{9}\left[\begin{array}{rrrr}1&1& 1\\ 1&1&1\\ 1&1&1\end{array}\right]\\ \omega_{4}=\frac{1}{6}\left[\begin{array}{rrrr}1&1&1\\ -2&-2&-2\\ 1&1&1\end{array}\right]\\ \omega_{6}=\omega_{4}7\end{array} \right., \tag{5}\]  
Up to now, we could estimate the response intensity of the 3 \(\times\) 3 neighborhood of potential blind pixels quickly. Figure 2 shows simulated blind pixel and IRPT and their estimation by the above-mentioned facet model. It can be clearly seen that the estimation of IRPT is more accurate. Figure 2: The estimation of facet model (**a**) simulated blind pixel, (**b**) estimation of blind pixel by facet model, (**c**) simulated IRPT, (**d**) estimation of IRPT by facet model.