## Range Estimation by Optical Differentiation (1997)

Venue: | JOSA A |

Citations: | 32 - 0 self |

### BibTeX

@ARTICLE{Farid97rangeestimation,

author = {Hany Farid and Eero P. Simoncelli},

title = {Range Estimation by Optical Differentiation},

journal = {JOSA A},

year = {1997},

volume = {15},

pages = {1777--1786}

}

### Years of Citing Articles

### OpenURL

### Abstract

We describe a novel formulation of the range recovery problem based on computation of the differential variation in image intensities with respect to changes in camera position. This method uses a single stationary camera and a pair of calibrated optical masks to directly measure this differential quantity. We also describe a variant based on changes in aperture size. The subsequent computation of the range image involves simple arithmetic operations, and is suitable for real-time implementation. We present the theory of this technique and show results from a prototype camera which we have constructed. 1 Introduction Visual images are formed via the projection of light from the three-dimensional world onto a two-dimensional sensor. In an idealized pinhole camera, all points lying on a ray passing through the pinhole will be projected onto the same image position. Thus, information about the distance to objects in the scene (i.e., range) is lost. Range information can be recovered by ...

### Citations

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(Show Context)
Citation Context ...mputed by capturing images from a set of discrete viewpoints, either simultaneously (using two or more cameras), or sequentially (using a single moving camera). In the case of binocular stereo (e.g., =-=[2]-=-), I v (x) is approximated as the difference of two images taken from cameras at different viewpoints. Similarly, differences of consecutive images are often used to compute viewpoint derivatives for ... |

1409 |
Robot Vision
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(Show Context)
Citation Context ...r stereo), or via sequential measurements collected from a moving camera (structure from motion). The recovery of range in these approaches frequently relies on the assumption of brightness constancys=-=[1]-=-: the brightness of the image of a point in the world is constant when seen from different viewpoints. Consider the formulation of this assumption in one dimension (the extension to two dimensions is ... |

191 |
A new sense for depth of field
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(Show Context)
Citation Context ... technique for estimating range that is based on the derivative with respect to aperture size. Discrete versions of this concept have been studied and are generally called "range from defocus&quo=-=t; (e.g., [4, 5, 6, 7, 8, 9]-=-). The generalized intensity function for a mask with aperture size A is written as: f(x; A) = 1 Aff M \Gamma x Aff \Delta : (16) The 1 A factor is included to ensure that the changes in the aperture ... |

179 | Probability distributions of optical flow
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(Show Context)
Citation Context ..., a singularity still exists when I x (x) is zero over the entire image patch. This singularity may be avoided by considering a maximum a posteriori (MAP) estimator with a Gaussian prior on ff (as in =-=[3]-=-). For a prior variance of oe 2 , the resulting estimate is: ff = \Gamma P x2P I v (x)I x (x) P x2P [I x (x)] 2 + oe 2 : (13) 6 This algorithm extends to a two-dimensional image plane: we need only co... |

116 | Single lens stereo with a plenoptic camera
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- 1992
(Show Context)
Citation Context ...ems are not based on differential operations. Furthermore, these systems operate on a single image and must therefore rely on assumptions regarding the spectral content of the scene. Adelson and Wang =-=[12] describe -=-a single-lens, single-image range camera, termed the "plenoptic camera". This approach is based on the same underlying principles as our own, but is quite different in implementation. The au... |

92 | Real-time focus range sensor
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(Show Context)
Citation Context ... technique for estimating range that is based on the derivative with respect to aperture size. Discrete versions of this concept have been studied and are generally called "range from defocus&quo=-=t; (e.g., [4, 5, 6, 7, 8, 9]-=-). The generalized intensity function for a mask with aperture size A is written as: f(x; A) = 1 Aff M \Gamma x Aff \Delta : (16) The 1 A factor is included to ensure that the changes in the aperture ... |

79 |
An adaptive algorithm for spatial grey scale
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(Show Context)
Citation Context ...nly 4 transmittance levels). In order to minimize the quantization effects due to this low resolution, a standard stochastic error diffusion dithering algorithm based on the Floyd/Steinberg algorithm =-=[17]-=- was employed. The value of a pixel is first quantized to one of the four available levels. The difference between the quantized pixel value and the desired value is computed and distributed in a weig... |

78 | Depth from defocus: a spatial domain approach
- Subbarao, Surya
- 1994
(Show Context)
Citation Context ... technique for estimating range that is based on the derivative with respect to aperture size. Discrete versions of this concept have been studied and are generally called "range from defocus&quo=-=t; (e.g., [4, 5, 6, 7, 8, 9]-=-). The generalized intensity function for a mask with aperture size A is written as: f(x; A) = 1 Aff M \Gamma x Aff \Delta : (16) The 1 A factor is included to ensure that the changes in the aperture ... |

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(Show Context)
Citation Context |

61 | Depth from Focusing and Defocusing
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36 |
Design of a Single-Lens Stereo Camera System
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(Show Context)
Citation Context ...ficulties with this approach, most notably, aliasing and the difficulty of precisely aligning the lenticular array with the CCD sensor. A series of single-lens stereo systems have also been developed =-=[13, 14, 15]-=-. In the first of these 10 systems, a stereo pair of images is generated by two fixed mirrors, at a 45 ffi angle with the camera's optical axis and a rotating mirror made parallel to each of the fixed... |

31 | Optimally rotation-equivariant directional derivative kernels
- Farid, Simoncelli
- 1997
(Show Context)
Citation Context ... back-illuminated with an incandescent lamp to help counter the low light transmittance of the LC SLM optical mask. Spatial derivatives were computed using a pair of 5-tap filter kernels described in =-=[18]. For 15 F-=-igure 6: Illustrated in the first two panels are 1-D slices of the image of a "point light source" taken through a pair of non-negative Gaussian-based masks, I 1 and I 2 . Shown in the third... |

18 |
Minimal operator set for passive depth from defocus
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- 1996
(Show Context)
Citation Context |

10 |
A feature-based stereo model using small disparities
- Nishimoto, Shirai
- 1987
(Show Context)
Citation Context ...ficulties with this approach, most notably, aliasing and the difficulty of precisely aligning the lenticular array with the CCD sensor. A series of single-lens stereo systems have also been developed =-=[13, 14, 15]-=-. In the first of these 10 systems, a stereo pair of images is generated by two fixed mirrors, at a 45 ffi angle with the camera's optical axis and a rotating mirror made parallel to each of the fixed... |

9 |
W.: Single-lens single-image incoherent passive-ranging systems
- Dowski, Cathey
- 1994
(Show Context)
Citation Context ... single-lens range imaging is not. Below are brief descriptions of several such systems. The use of optical attenuation masks for range estimation has been considered in the work of Dowski and Cathey =-=[10]-=- and Jones and Lamb [11]. The former employs a sinusoidal aperture mask and computes range by searching for zero-crossings in the local frequency spectra. The latter system employs an aperture mask co... |

7 |
An inexpensive stereoscopic vision system for robots
- Teoh, Zhang
- 1984
(Show Context)
Citation Context ...ficulties with this approach, most notably, aliasing and the difficulty of precisely aligning the lenticular array with the CCD sensor. A series of single-lens stereo systems have also been developed =-=[13, 14, 15]-=-. In the first of these 10 systems, a stereo pair of images is generated by two fixed mirrors, at a 45 ffi angle with the camera's optical axis and a rotating mirror made parallel to each of the fixed... |

5 |
Analyzing the visual echo: passive 3-D imaging with a multiple aperture camera
- JONES, LAMB
- 1993
(Show Context)
Citation Context ...ng is not. Below are brief descriptions of several such systems. The use of optical attenuation masks for range estimation has been considered in the work of Dowski and Cathey [10] and Jones and Lamb =-=[11]-=-. The former employs a sinusoidal aperture mask and computes range by searching for zero-crossings in the local frequency spectra. The latter system employs an aperture mask consisting of a pair of sp... |

3 | Direct differential range estimation from aperture derivatives - Simoncelli, Farid - 1996 |

3 | A differential optical range camera - FARID, SIMONCELLI - 1996 |

1 | Single-lens range imaging using optical derivative masks - Simoncelli, Farid - 1995 |