## Learning to Perceive Transparency from the Statistics of Natural Scenes (2002)

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Venue: | In NIPS-15; The 2002 Conference on Advances in Neural Information Processing Systems |

Citations: | 34 - 6 self |

### BibTeX

@INPROCEEDINGS{Levin02learningto,

author = {Anat Levin and Assaf Zomet and Yair Weiss},

title = {Learning to Perceive Transparency from the Statistics of Natural Scenes},

booktitle = {In NIPS-15; The 2002 Conference on Advances in Neural Information Processing Systems},

year = {2002},

publisher = {MIT Press}

}

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### Abstract

Certain simple images are known to trigger a percept of transparency: the input image I is perceived as the sum of two images I(x,y) = Ii(x,y) + I2(x,y). This percept is puzzling. First, why do we choose the "more complicated" description with two images rather than the "simpler" explanation I(x, y) = I1(x, y) + 0 ? Sec- ond, given the infinite number of ways to express I as a sum of two images, how do we compute the "best" decomposition ? Here we suggest that transparency is the rational percept of a system that is adapted to the statistics of natural scenes. We present a probabilistic model of images based on the qualitative statistics of derivative filters and "corner detectors" in natural scenes and use this model to find the most probable decomposition of a novel image. The optimization is performed using loopy belief propagation. We show that our model computes perceptually "correct" decompositions on synthetic images and discuss its application to real images.

### Citations

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Citation Context ...rs and for the gradient magnitude: There are many ways to describe the non Gaussian nature of this distribution (e.g. high kurtosis, heavy tails). Figure 2b illustrates the observation made by Mallat =-=[4]-=- and Simoncelli [8]: that the distribution is similar to an exponential density with exponent less than 1. We show the log probability for densities of the form p(x) x e-x. We assume x C [0,100] and p... |

928 |
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Citation Context ...ges A remarkably robust property of natural images that has received much attention lately is the fact that when derivative filters are applied to natural images, the filter outputs tend to be sparse =-=[5, 7]-=-. Figure 2 illustrates this fact: the histogram of the horizontal derivative filter is peaked at zero and fall off much faster than a Gaussian. Similar histograms are observed for vertical derivative ... |

289 | A parametric texture model based on joint statistics of complex wavelet coefficients
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Citation Context ...nsparency in this image. There are two ways to go beyond marginal histograms of derivative filters. We can either look at joint statistics of derivative filters at different locations or orientations =-=[6] or look at marginal-=- statistics of more complicated feature detectors (e.g. [11]). We looked at the marginal statistics of a "corner detector". The output of the "corner detector" at a given location ... |

192 | Minimax entropy principle and its application to texture modeling
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- 1997
(Show Context)
Citation Context ... derivative filters. We can either look at joint statistics of derivative filters at different locations or orientations [6] or look at marginal statistics of more complicated feature detectors (e.g. =-=[11]). We looked at the -=-marginal statistics of a "corner detector". The output of the "corner detector" at a given location x0, Y0 is defined as: ( I2(x,y) Ix(x,y)Iy(x,y) ) c(xo, Yo) = da(y. w(x, y) x(, y... |

191 | Deriving intrinsic images from image sequences
- Weiss
- 2001
(Show Context)
Citation Context ...0 150 , b d f Figure 2: a. A natural image.sHistogram of filter outputs. e Histogram of corner detector outputs. d,e log histograms. filters has the qualitative nature of a distribution e-x with csIn =-=[9]-=- the sparsity of derivative filters was used to decompose an image sequence as a sum of two image sequences. Will this prior be sufficient for a single frame ? Note that decomposing the image in figur... |

185 | On the optimality of solutions of the max-product belief-propagation algorithm in arbitrary graphs
- Weiss, Freeman
(Show Context)
Citation Context ...y searches over an exponentially large number of possible decompositions and chooses decompositions that agree with the percept. is a local maximum of equation 4 with respect to a large neighbourhood =-=[10]-=-. This gradient field also defines the complementary gradient field {fi} and finally we integrate the two gradient fields to find the two layers. Since equation 4 is completely symmetric in {f} and {g... |

89 | Bayesian denoising of visual images in the wavelet domain
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- 1999
(Show Context)
Citation Context ...ient magnitude: There are many ways to describe the non Gaussian nature of this distribution (e.g. high kurtosis, heavy tails). Figure 2b illustrates the observation made by Mallat [4] and Simoncelli =-=[8]-=-: that the distribution is similar to an exponential density with exponent less than 1. We show the log probability for densities of the form p(x) x e-x. We assume x C [0,100] and plot the log probabi... |

61 | Lightness perception and lightness Illusions
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- 2000
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Citation Context ...solutions to equation i but our visual system prefers the single layer solution. Studies of the conditions for the percept of transparency go back to the very first research on visual perception (see =-=[1]-=- and references within). Research of this type has made great progress in understanding the types of junctions and their effects (e.g. X junctions of a certain type trigger transparency, T junctions d... |

37 | Learning to estimate scenes from images
- Freeman, Pasztor
- 1999
(Show Context)
Citation Context ...et to zero when gi, gj, gu, gI violate the integrability constraint (cf. [3]). The graphical model defined by equation 4 has many loops. Nevertheless motivated by the recent results on similar graphs =-=[2, 3]-=- we ran the max-product belief propagation algorithm on it. The max-product algorithm finds a gradient field {gi} that Input I Output I1 Output 12 Figure 4: Output of the algorithm on synthetic images... |

27 | Very loopy belief propagation for unwrapping phase images
- Frey, Koetter, et al.
- 2001
(Show Context)
Citation Context ...istogram of the corner operator: '.,(g, g., g,, g) = To enforce integrability of the gradient fields the fourway potential is set to zero when gi, gj, gu, gI violate the integrability constraint (cf. =-=[3]-=-). The graphical model defined by equation 4 has many loops. Nevertheless motivated by the recent results on similar graphs [2, 3] we ran the max-product belief propagation algorithm on it. The max-pr... |

10 |
Statistical models for images:compression restoration and synthesis
- Simoncelli
- 1997
(Show Context)
Citation Context ...ges A remarkably robust property of natural images that has received much attention lately is the fact that when derivative filters are applied to natural images, the filter outputs tend to be sparse =-=[5, 7]-=-. Figure 2 illustrates this fact: the histogram of the horizontal derivative filter is peaked at zero and fall off much faster than a Gaussian. Similar histograms are observed for vertical derivative ... |