Assuming the camera model is pinhole, according to Brown's distortion model, there are two types of common distortions: radial distortion and tangential distortion.

Radial distortion

  • The most commonly encountered distortions are radially symmetric, due to the symmetry of a photographic lens. These radial distortions can be classified as either barrel distortions or pincushion distortions.

    • Barrel distortion: image magnification decreases with distance from the optical axis.

    • Pincushion distortion: image magnification increases with distance from the optical axis.

  • Mathematically, barrel and pincushion distortion are quadratic, meaning they increase as the square of distance from the center. We can model it with three parameters: k1,k2,k3k_1, k_2, k_3.

xdistorted =x(1+k1r2+k2r4+k3r6)ydistorted =y(1+k1r2+k2r4+k3r6)x_{\text {distorted }}=x\left(1+k_{1} r^{2}+k_{2} r^{4}+k_{3} r^{6}\right) \\ y_{\text {distorted }}=y\left(1+k_{1} r^{2}+k_{2} r^{4}+k_{3} r^{6}\right)

Tangential distortion

  • Tangential distortion can happen when the lens is not fully parallel to the image plane.

  • Mathematically, we can model this distortion with two parameters: p1,p2p_1, p_2.

xdistorted =x+2p1xy+p2(r2+2x2)ydistorted =y+p1(r2+2y2)+2p2xyx_{\text {distorted }}=x+2 p_{1} x y+p_{2}\left(r^{2}+2 x^{2}\right) \\ y_{\text {distorted }}=y+p_{1}\left(r^{2}+2 y^{2}\right)+2 p_{2} x y


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