![]() Thus, representing the film's scale explicitly would be redundant it is captured by the focal length. If instead, you double the film size and not the focal length, it is equivalent to doubling both (a no-op) and then halving the focal length. What about scaling? It should be obvious that doubling all camera dimensions (film size and focal length) has no effect on the captured scene. Rotating the film around any other fixed point \(x\) is equivalent to rotating around the pinhole \(P\), then translating by \((x-P)\). Rotating the film around the pinhole is equivalent to rotating the camera itself, which is handled by the extrinsic matrix. There must be other ways to transform the camera, right? What about rotating or scaling the film? The focal length and principal point offset amount to simple translations of the film relative to the pinhole. As far as I know, there isn't any analogue to axis skew a true pinhole camera, but apparently some digitization processes can cause nonzero skew. Axis Skew, \(s\)Īxis skew causes shear distortion in the projected image. Notice that the box surrounding the camera is irrelevant, only the pinhole's position relative to the film matters. This is equivalent to shifting the film to the left and leaving the pinhole unchanged. Increasing \(x_0\) shifts the pinhole to the right: The exact definition depends on which convention is used for the location of the origin the illustration below assumes it's at the bottom-left of the film. The "principal point offset" is the location of the principal point relative to the film's origin. Its itersection with the image plane is referred to as the "principal point," illustrated below. The camera's "principal axis" is the line perpendicular to the image plane that passes through the pinhole. focal length) from distortion (aspect ratio). Such a parameterization nicely separates the camera geometry (i.e. Forsyth and Ponce) use a single focal length and an "aspect ratio" that describes the amount of deviation from a perfectly square pixel. Having two different focal lengths isn't terribly intuitive, so some texts (e.g. In all of these cases, the resulting image has non-square pixels. The camera uses an anamorphic format, where the lens compresses a widescreen scene into a standard-sized sensor.The camera's lens introduces unintentional distortion.The image has been non-uniformly scaled in post-processing.In practice, \(f_x\) and \(f_y\) can differ for a number of reasons: In a true pinhole camera, both \(f_x\) and \(f_y\) have the same value, which is illustrated as \(f\) below. For reasons we'll discuss later, the focal length is measured in pixels. The focal length is the distance between the pinhole and the film (a.k.a. Let's examine each of these properties in detail. The intrinsic matrix is parameterized by Hartley and Zisserman asĮach intrinsic parameter describes a geometric property of the camera. This perspective projection is modeled by the ideal pinhole camera, illustrated below. The intrinsic matrix transforms 3D camera cooordinates to 2D homogeneous image coordinates. If you're not interested in delving into the theory and just want to use your intrinsic matrix with OpenGL, check out the articles Calibrated Cameras in OpenGL without glFrustum and Calibrated Cameras and gluPerspective.Īll of these articles are part of the series " The Perspective Camera, an Interactive Tour." To read the other entries in the series, head over to the table of contents. Afterward, you'll see an interactive demo illustrating both interpretations. Today we'll give the same treatment to the intrinsic matrix, examining two equivalent interpretations: as a description of the virtual camera's geometry and as a sequence of simple 2D transformations. The second article examined the extrinsic matrix in greater detail, looking into several different interpretations of its 3D rotations and translations. ![]() Today we'll study the intrinsic camera matrix in our third and final chapter in the trilogy "Dissecting the Camera Matrix." In the first article, we learned how to split the full camera matrix into the intrinsic and extrinsic matrices and how to properly handle ambiguities that arise in that process.
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