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Figure 114: Patterns oflight are projected onto a surface to create interesting points on an otherwise smooth surface
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In addition to the stereo imaging method described above, numerous other methods known as shape from X techniques have been developed for extracting shape information from intensity images Many of these methods estimate local surface orientation rather than absolute depth at each point If the actual depth to at least one point on each object is known, then the depth at other points on the same object can be computed by integrating the local surface orientation Hence these methods are called indirect methods for depth computation We briefly describe some of these methods here and provide pointers to other chapters where they are described in more detail Photometric Stereo
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In the photometric stereo method, three images of the same scene are obtained using light sources from three different directions Both camera and objects in the scene are required to be stationary during the acquisition of the three images By knowing the surface reflectance properties of the objects in the scene, the local surface orientation at points illuminated by all
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three light sources can be computed This method is described in detail in 9 One of the important advantages of the photometric stereo method is that the points in all three images are perfectly registered with one another since both camera and scene are stationary Thus, this method does not suffer from the correspondence problem The primary disadvantages of this method are that it is an indirect method and it may not be practical to employ an imaging system in which the illumination is so carefully controlled Shape from Shading Shape from shading methods exploit the changes in the image intensity (shading) to recover surface shape information This is done by calculating the orientation of the scene surface corresponding to each point (X', y') in the image In addition to the constraint imposed by the radiometric principles, shape from shading methods assume that the surfaces are smooth in order to calculate surface orientation parameters This method is described in detail in 9 Clearly, shape from shading is an indirect method for depth computation Furthermore, the smoothness constraint is not satisfied at all points and the surface reflectance properties are not always known accurately, resulting in inaccurate reconstructions Shape from Texture Image plane variations in the texture properties such as density, size, and orientation are the cues exploited by shape from texture algorithms For example, the texture gradient, defined as the magnitude and direction of maximum change in the primitive size of the texture elements, determines the orientation of the surface Quantifying the changes in the shape of texture elements (eg, circles appearing as ellipses) is also useful to determine surface orientation From images of surfaces with textures made up of regular grids of lines, possibly due to structured lighting (described in the following section), orientation may be uniquely determined by finding the vanishing points Besides being indirect methods for depth computation, shape from texture methods also suffer from difficulties in accurately locating and quantifying texture primitives and their properties Shape from texture techniques are described in 7
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Shape from Focus Due to the finite depth offield of optical systems (see 8), only objects which are at a proper distance appear focused in the image whereas those at other depths are blurred in proportion to their distances Algorithms to exploit this blurring effect have been developed The image is modeled as a convolution of focused images with a point spread function determined by the camera parameters and the distance of the object from the camera The depth is recovered by estimating the amount of blur in the image and using the known or estimated line spread function Such reconstruction problems are mathematically ill posed However, in some applications, especially those requiring qualitative depth information, depth from focus methods are useful Shape from Motion When images of a stationary scene are acquired using a moving camera, the displacement of the image plane coordinate of a scene point from one frame to another depends on the distance of the scene point from the camera This is thus similar to the stereo imaging described in earlier sections Alternatively, a moving object also produces motion disparity in image sequences captured by a stationary camera Such a disparity also depends upon the position and velocity of the object point Methods for recovering structure and motion of objects are described in detail in 14
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