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Fig. 10. Schematic of variables pertinent to the semi-automated blurring algorithm. Here, the image surface is equivalent to the monitor surface, and v and 1 are in units of pixels. o indicates the angle between the ground plane’s surface normal and the imaging system’s optical axis. Refer to Al- gorithm | for details on how each value can be calculated from an input image. (Adapted from Okatani and Deguchi [2007]) Fig. 9. Determining the most likely focal distance from blur and perspective. Intended focal distance was 0.06m. Each panel plots estimated focal distance as a function of relative distance. The left, middle, and right panels show the estimates for consistent blur, vertical blur gradient, and horizontal blur gradient, respectively. The first step in the analysis is to extract the relative-distance and blur information from several points in the image. The values for each point are then used with Eq. (2) to estimate the focal distance. Each estimate is represented by a point. Then all of the focal distance estimates are accumulated to form a marginal distribution of estimates (shown on the right of each panel). The data from a consistent-blur rendering most closely matches the selected curve, resulting in extremely low variance. Though the vertical blur gradient incorrectly blurs several pixels, it is well correlated with the relative distances in the scene, so it too produces a marginal distribution with low variance. The blur applied by the horizontal gradient is mostly uncorrelated with relative distance, resulting in a marginal distribution with large variance and therefore the least reliable estimate.

Figure 10 Schematic of variables pertinent to the semi-automated blurring algorithm. Here, the image surface is equivalent to the monitor surface, and v and 1 are in units of pixels. o indicates the angle between the ground plane’s surface normal and the imaging system’s optical axis. Refer to Al- gorithm | for details on how each value can be calculated from an input image. (Adapted from Okatani and Deguchi [2007]) Fig. 9. Determining the most likely focal distance from blur and perspective. Intended focal distance was 0.06m. Each panel plots estimated focal distance as a function of relative distance. The left, middle, and right panels show the estimates for consistent blur, vertical blur gradient, and horizontal blur gradient, respectively. The first step in the analysis is to extract the relative-distance and blur information from several points in the image. The values for each point are then used with Eq. (2) to estimate the focal distance. Each estimate is represented by a point. Then all of the focal distance estimates are accumulated to form a marginal distribution of estimates (shown on the right of each panel). The data from a consistent-blur rendering most closely matches the selected curve, resulting in extremely low variance. Though the vertical blur gradient incorrectly blurs several pixels, it is well correlated with the relative distances in the scene, so it too produces a marginal distribution with low variance. The blur applied by the horizontal gradient is mostly uncorrelated with relative distance, resulting in a marginal distribution with large variance and therefore the least reliable estimate.

Related Figures (14)

Fig. 1. (a) Rendering a cityscape with a pinhole aperture results in no perceptible blur. The scene looks large and far away. (b) Simulating a 60m- wide aperture produces blur consistent with a shallow depth of field, making the scene appear to be a miniature model. Original city images and data from GoogleEarth are copyright Terrametrics, SanBorn, and Google.
Fig. 1. (a) Rendering a cityscape with a pinhole aperture results in no perceptible blur. The scene looks large and far away. (b) Simulating a 60m- wide aperture produces blur consistent with a shallow depth of field, making the scene appear to be a miniature model. Original city images and data from GoogleEarth are copyright Terrametrics, SanBorn, and Google.
Fig. 4. The Scheimpflug Principle. Tilt-and-shift lenses cause the orienta- tion of the focal plane to shift and rotate relative to the image plane. As a result, the apparent depth of field in an image can be drastically changed and the photographer has greater control over which objects are in focus and which are blurred.
Fig. 4. The Scheimpflug Principle. Tilt-and-shift lenses cause the orienta- tion of the focal plane to shift and rotate relative to the image plane. As a result, the apparent depth of field in an image can be drastically changed and the photographer has greater control over which objects are in focus and which are blurred.
Fig. 5. Comparison of blur patterns produced by three rendering techniques: consistent blur (a), simulated tilt-and-shift lens (b), and linear blur gradient (c) The settings in (b) and (c) were chosen to equate the maximum blur-circle diameters with those in (a). The percent differences in blur-circle diameters betweer the images are plotted in (d), (e), and (f). Panels (d) and (e) show that the simulated tilt-and-shift lens and linear blur gradient do not closely approximate consistent blur rendering. The large differences are due to the buildings, which protrude from the ground plane. Panel (f) shows that the linear blur gradient provides essentially the same blur pattern as a simulated tilt-and-shift lens. Most of the differences in (f) are less than 7%; the only exceptions are in the banc near the center, where the blur diameters are less than one pixel and not detectable in the final images.
Fig. 5. Comparison of blur patterns produced by three rendering techniques: consistent blur (a), simulated tilt-and-shift lens (b), and linear blur gradient (c) The settings in (b) and (c) were chosen to equate the maximum blur-circle diameters with those in (a). The percent differences in blur-circle diameters betweer the images are plotted in (d), (e), and (f). Panels (d) and (e) show that the simulated tilt-and-shift lens and linear blur gradient do not closely approximate consistent blur rendering. The large differences are due to the buildings, which protrude from the ground plane. Panel (f) shows that the linear blur gradient provides essentially the same blur pattern as a simulated tilt-and-shift lens. Most of the differences in (f) are less than 7%; the only exceptions are in the banc near the center, where the blur diameters are less than one pixel and not detectable in the final images.
Here we see that we can achieve the same amount of blur as en- countered with a focal distance of 2) = m2zo by shooting the scene at distance z and setting the diameter of the camera aperture to A= A/m. The aperture must therefore be quite small to make a scene look much larger than it is and this limits the amount of available light, causing problems with signal-to-noise ratio, motion, and so forth. Likewise the aperture must be quite large to make the scene look much smaller than it actually is, and such large aper- tures might be difficult to achieve with a physical camera. Because of these limitations, it is quite attractive to be able to use a con-
Here we see that we can achieve the same amount of blur as en- countered with a focal distance of 2) = m2zo by shooting the scene at distance z and setting the diameter of the camera aperture to A= A/m. The aperture must therefore be quite small to make a scene look much larger than it is and this limits the amount of available light, causing problems with signal-to-noise ratio, motion, and so forth. Likewise the aperture must be quite large to make the scene look much smaller than it actually is, and such large aper- tures might be difficult to achieve with a physical camera. Because of these limitations, it is quite attractive to be able to use a con-
Fig. 6. Focal distance as a function of relative distance and retinal-image blur. Relative distance is defined as the ratio of the distance to an object and the distance to the focal plane. The three colored curves represent different amounts of image blur expressed as the diameter of the blur circle, c, in degrees. We use angular units because in those units, the image device’s fo- cal length drops out [Kingslake 1992]. The variance in the distribution was determined by assuming that pupil diameter is Gaussian distributed with a mean of 4.6mm and standard deviation of 1mm [Spring and Stiles 1948]. For a given amount of blur, it is impossible to recover the original focal distance without knowing the relative distance. Note that as the relative dis- tance approaches 1, the object moves closer to the focal plane. There is a singularity at a relative distance of 1 because the object is by definition completely in focus at that distance.
Fig. 6. Focal distance as a function of relative distance and retinal-image blur. Relative distance is defined as the ratio of the distance to an object and the distance to the focal plane. The three colored curves represent different amounts of image blur expressed as the diameter of the blur circle, c, in degrees. We use angular units because in those units, the image device’s fo- cal length drops out [Kingslake 1992]. The variance in the distribution was determined by assuming that pupil diameter is Gaussian distributed with a mean of 4.6mm and standard deviation of 1mm [Spring and Stiles 1948]. For a given amount of blur, it is impossible to recover the original focal distance without knowing the relative distance. Note that as the relative dis- tance approaches 1, the object moves closer to the focal plane. There is a singularity at a relative distance of 1 because the object is by definition completely in focus at that distance.
Fig. 7. Bayesian analysis of blur as cue to absolute distance. (a) The probability distribution P(z,,d|c) where c is the observed blur diameter in the image (in this case, 0.1°), zo is the focal distance, and d is the relative distance of another point in the scene. Measuring the blur produced by an object cannot reveal the absolute or relative distance to points in the scene. (b) The probability distribution P(zo,d|p) where p is the observed perspective. Perspective specifies the relative distance, but not the absolute distance: it is scale ambiguous. (c) The product of the distributions in (a) and (b). From this posterior distribution, the absolute and relative distances of points in the scene can be estimated.
Fig. 7. Bayesian analysis of blur as cue to absolute distance. (a) The probability distribution P(z,,d|c) where c is the observed blur diameter in the image (in this case, 0.1°), zo is the focal distance, and d is the relative distance of another point in the scene. Measuring the blur produced by an object cannot reveal the absolute or relative distance to points in the scene. (b) The probability distribution P(zo,d|p) where p is the observed perspective. Perspective specifies the relative distance, but not the absolute distance: it is scale ambiguous. (c) The product of the distributions in (a) and (b). From this posterior distribution, the absolute and relative distances of points in the scene can be estimated.
Fig. 8. The four types of blur used in the analysis and experiment: (a) no blur, (b-c) consistent blur, (d-e) linear vertical blur gradient, and (f-g) linear horizontal blur gradient. Simulated focal distances of 0.15m (b,d,f) and 0.06m (c,e,g) are shown. In approximating the blur produced by a short focal length, the consistent-blur condition produces the most accurate blur, followed by the vertical gradient, the horizontal gradient, and the no-blur condition. Original city images and data from GoogleEarth are copyright Terrametrics, SanBorn, and Google.
Fig. 8. The four types of blur used in the analysis and experiment: (a) no blur, (b-c) consistent blur, (d-e) linear vertical blur gradient, and (f-g) linear horizontal blur gradient. Simulated focal distances of 0.15m (b,d,f) and 0.06m (c,e,g) are shown. In approximating the blur produced by a short focal length, the consistent-blur condition produces the most accurate blur, followed by the vertical gradient, the horizontal gradient, and the no-blur condition. Original city images and data from GoogleEarth are copyright Terrametrics, SanBorn, and Google.
Figure 11(a), we use the technique in Algorithm 1, originally de- scribed by Okatani and DeGuchi [2007]. If the scene is uncarpen- tered, like the landscape in Figure 11(b), then a grid is displayed over the image. The viewer uses a mouse to rotate the grid until it appears to be parallel to the scene. The orientation of the grid yields o and 7. Parameters | and v (defined in Figure 10) are re- covered from the settings (in our case, from OpenGL) that were used to render the grid on-screen. Finally, Algorithm 2 determines the amount of blur assigned to each pixel, then creates the final image.
Figure 11(a), we use the technique in Algorithm 1, originally de- scribed by Okatani and DeGuchi [2007]. If the scene is uncarpen- tered, like the landscape in Figure 11(b), then a grid is displayed over the image. The viewer uses a mouse to rotate the grid until it appears to be parallel to the scene. The orientation of the grid yields o and 7. Parameters | and v (defined in Figure 10) are re- covered from the settings (in our case, from OpenGL) that were used to render the grid on-screen. Finally, Algorithm 2 determines the amount of blur assigned to each pixel, then creates the final image.
Fig. 11. Input and output of the semiautomated blurring algorithm. The algorithm can estimate the blur pattern required to simulate a desired focal length. | can either derive scene information from parallel lines in a scene or use manual feedback from the user on the overall orientation of the scene. (a) Two pairs o parallel lines were selected from a carpentered scene for use with the first approach. (b) The resulting image once blur was applied. Intended focal distance se to 0.06m. (c) A grid was manually aligned to lie parallel to the overall scene. (d) The blurred output designed to simulate a focal distance of 0.50m.
Fig. 11. Input and output of the semiautomated blurring algorithm. The algorithm can estimate the blur pattern required to simulate a desired focal length. | can either derive scene information from parallel lines in a scene or use manual feedback from the user on the overall orientation of the scene. (a) Two pairs o parallel lines were selected from a carpentered scene for use with the first approach. (b) The resulting image once blur was applied. Intended focal distance se to 0.06m. (c) A grid was manually aligned to lie parallel to the overall scene. (d) The blurred output designed to simulate a focal distance of 0.50m.
Fig. 12. Results of the psychophysical experiment averaged across the seven subjects. Panels (a) and (b) respectively show the data when the images had low and high depth variation. The type of blur manipulation is indicated by the colors and shapes of the data points. Blue squares for consistent blur, green circles for vertical blur gradient, and red triangles for horizontal blur gradient. Error bars represent standard errors. Individual subject data are included in the supplemental material.
Fig. 12. Results of the psychophysical experiment averaged across the seven subjects. Panels (a) and (b) respectively show the data when the images had low and high depth variation. The type of blur manipulation is indicated by the colors and shapes of the data points. Blue squares for consistent blur, green circles for vertical blur gradient, and red triangles for horizontal blur gradient. Error bars represent standard errors. Individual subject data are included in the supplemental material.
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