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I am wondering how to calculate the size of a 3d object in an image without knowing the focal length of the camera but the distance from the camera to the object.

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I am wondering how to calculate the size of a 3d object in an image without knowing the focal length of the camera but the distance from the camera to the object.

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There are hundred of papers on this task some older than I am! Normally this is done by trying to form a box shape around the image than estimate the volume. This task is typically done with multiple images so the two can generate a more clear picture of the size of the object than one image alone. An object could be 'infinitely' large but its mass could be behind the surface you can see with the picture. With the height and length dimensions extracted from the image and with the distance from the camera calculating the size of said surface is fairly easy.

Frustum PointNets for 3D Object Detection From RGB-D Data (2018) By Charles R. Qi, Wei Liu, Chenxia Wu, Hao Su, Leonidas J. Guibas

From contours to 3D object detection and pose estimation (2017) By Nadia Payet Sinisa Todorovic