He used the odd and even textures as examples. He claimed that the odd and even textures have the same third-order statistics. Hence they must have the same second-order statistics. Since they can easily be seen as different( spontaneously discriminated), the Julesz Conjecture must be wrong.
These are special cases for random square coloring
I(m,n)=I(m,0)+I(0,n)+I(0,0) (mod 2)
I(m,n)=I(m,0)+I(0,n)+I(0,0)+m*n (mod 2)
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| Fig 1 (a) Even & Odd Textures |
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| Fig 1 (b) Coin & Odd Textures |
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| Fig 1 (c) Even & Coin Textures |
Although his conjecture was proved to be wrong, Julesz still stated that texture images with the same second-order statistics, iso-second-order textures, are usually indiscriminable. He proposed a Modified Julesz Conjecture
The pre-attentive textural system cannot globally compute third- or higher-order statistics
He and his co-workers adopted a four-disk method to generate isometric dual micropatterns. They claimed that these texture images will have identical second-order statistics if these micropatterns are randomly thrown.
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Julesz and his co-workers generated several pre-attentive indistinguishable texture pairs with identical second-order but different third- and higher-order statistics.
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| Micropatterns and mirrors | Dual micropatterns | Dual micropatterns |
Because iso-second-order statistics means identical autocorrelation functions and identical power spectrum, Julesz concluded that the pre-attentive visual system ignores the phase (position) spectrum that is so conspicuous when the elements are viewed by focal attention. This implies that
The operation of two visual system
The insensitivity of pre-attentive texture perception implies a parallel system.
Julesz observed that many seemingly conspicuous features do not yield texture discrimination in the iso-second-order statistical constraint, so he thought those local features should be very special ones. They should be regarded as the basic elements of pre-attentive perception, and named texton.
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| Just below threshould | Well above the threshold |
Several discriminable local conspicuous features were found: closure, corner, connectivity, granular
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| Closure | Connectivity | Granularity |
Although the local features above make the above textures discriminable, Julesz didn't think they are all qualified to be the basic elements, textons. From his research, he concluded that he found only three kinds of textons
He showed that open/closed and connected/unconnected texture pairs cannot be pre-attentive discriminated by the example below
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In this case, the pre-attentive visual system, cannot determine the location of terminators, but can count their numbers or their first-order statistics.
The corner, closure and connectivity can actually be described by the differences in terminator numbers.
Julesz used another example to conclude that
It is the texton, instead of the second-order statistics, to cause the texture discrimination
| Replications of a random pattern | |
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| Random patterns and random textures | Random patterns filled with random textures |
| Replications of a stripes pattern | |
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| Stripes patterns and random textures | Stripes patterns filled with random textures |