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June 25, 2022 07:32
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Hu moments in Latex
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| M_{ij}=\sum\limits_{x}\sum\limits_{y}x^iy^iI(x,y)\\ | |
| \eta_{pq}=\sum\limits_{x}\sum\limits_{y}(x-\bar x)^p(y- \bar y)^qI(x,y)\\ | |
| \bar x=\frac{M_{10}}{M_{00}}, \bar y=\frac{M_{01}}{M_{00}}\\ | |
| \mu_{pq}=\frac{\eta_{pq}}{\eta_{00}^\gamma},\gamma=\frac{p+q}{2}\\ | |
| H_{1} = \mu_{20} + \mu_{02}\\ | |
| H_{2} = (\mu_{20} - \mu_{02})^2 + 4(\mu_{11})^2\\ | |
| H_{3} = (\mu_{30} - 3\mu_{12})^2 + (\mu_{03} - 3\mu_{21})^2\\ | |
| H_{4} = (\mu_{30} + \mu_{12})^2 + (\mu_{03} + \mu_{21})^2\\ | |
| H_{5} = (\mu_{30} - 3\mu_{12})(\mu_{30} + \mu_{12})((\mu_{30} + \mu_{12})^2 - 3(\mu_{21} + \mu_{03})^2) + (3\mu_{21} - \mu_{03})(\mu_{21} + \mu_{03})(3(\mu_{30} + \mu_{12})^2 - (\mu_{03} + \mu_{21})^2)\\ | |
| H_{6} = (\mu_{20} - \mu_{02})((\mu_{30} + \mu_{12})^2 - (\mu_{21} + \mu_{03})^2) + 4\mu_{11}(\mu_{30} + \mu_{12})(\mu_{21} + \mu_{03})\\ | |
| H_{7} = (3\mu_{21} - \mu_{03})(\mu_{30} + \mu_{12})((\mu_{30} + \mu_{12})^2 - 3(\mu_{21} + \mu_{03})^2) + (\mu_{30} - 3\mu_{12})(\mu_{21} + \mu_{03})(3(\mu_{30} + \mu_{12})^2 - (\mu_{03} + \mu_{21})^2) | |
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