Abstract We propose a new method to correct distortions in equirectangular images, i.e., images that use the longitude/latitude representation to describe the full spherical field of view around a given viewpoint. We show that Mobius transformations are the correct mathematical tool to deal with the conflicting distortions in this setting: they are conformal, are able to rectify lines, perform rotations, translations and scales on the sphere and are bijective. Multiple transformations are specified through points, lines and cages on the sphere. We associate three points that uniquely define a Mobius transformation to each one of these geometric handles. Linear blend skinning with bounded biharmonic weights combine the different transformations into a single full spherical modified image. We present a collection of results in challenging settings and show that our method is more flexible and produces higher quality results when compared to previous methods.

中文翻译：

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用于灵活全向图像校正的莫比乌斯变换的有界双调和混合

摘要 我们提出了一种校正等距柱状图图像失真的新方法，即使用经度/纬度表示来描述给定视点周围全球面视场的图像。我们表明，莫比乌斯变换是处理此设置中冲突失真的正确数学工具：它们是共形的，能够校正直线，在球体上执行旋转、平移和缩放，并且是双射的。通过球体上的点、线和笼指定多个变换。我们将三个唯一定义莫比乌斯变换的点与这些几何手柄中的每一个相关联。具有有界双调和权重的线性混合蒙皮将不同的变换组合成一个完整的球形修改图像。