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32 lines
1.2 KiB
TeX
32 lines
1.2 KiB
TeX
\subsection{Keypoints}
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\bi{Corner det.} $SSD(\Delta x, \Delta y) \approx [\Delta_x \; \Delta_y] \mat{M} [\Delta_x \; \Delta_y]^\top$
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$\lambda_i$ E.V. of $M$; $\kappa$ const 0.04-0.15;
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$\mat{R} = \det(M) - \kappa \cdot \text{TR}(M)^2 = \lambda_1\lambda_2 - \kappa(\lambda_1 + \lambda_2)^2$;\\
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$\mat{M} = \sum_{x, y \in P}
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{\scriptsize
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\begin{bmatrix}
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I_x^2 & I_x I_y \\
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I_x I_y & I_y^2
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\end{bmatrix}
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=
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R^\top
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\begin{bmatrix}
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\lambda_1 & 0 \\
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0 & \lambda_2
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\end{bmatrix}
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R
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}$
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\shade{gray}{Blob Detection} ($I$ is the image)
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\bi{Laplacian of Gaussian} (LoG): $L = g(x, y, t) * I(x, y)$.
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Then apply Laplacian Operator $\nabla_\text{norm}^2 L = t\left( \frac{\partial^2 L}{\partial x^2} + \frac{\partial^2 L}{\partial y^2} \right)$
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\bi{Diff. of Gaussians} (DoG): $\Delta L = L(x, y, t) - L(x, y, kt)$
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\bi{SIFT Detector} \bi{(1)} Subsample + Blur \bi{(2)} DoG on each res. image \bi{(3)} Keypoints extrema in DoG pyramid
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\bi{BRISK} / binary descriptors: Compare pixel intensities at fixed sampling pattern around keypoint. Match by Hamming distance (very fast),
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\bi{SuperPoint}: CNN learns detector + descriptor
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