Post Correspondence Problem and Small Dimensional Matrices

Ohzawa, Izumi, Gregory C. DeAngelis, and Ralph D. Freeman. Encoding of binocular disparity by complex cells in the cat's visual cortex. J. Neurophysiol. 77: 2879–2909, 1997. To examine the roles that complex cells play in stereopsis, we have recorded extracellularly from isolated single neurons in the striate cortex of anesthetized paralyzed cats. We measured binocular responses of complex cells using a comprehensive stimulus set that encompasses all possible combinations of positions over the receptive fields for the two eyes. For a given position combination, stimulus contrast could be the same for the two eyes (2 bright or 2 dark bars) or opposite (1 bright and 1 dark). These measurements provide a binocular receptive field (RF) profile that completely characterizes complex cell responses in a joint domain of left and right stimulus positions. Complex cells typically exhibit a strong selectivity for binocular disparity, but are only broadly selective for stimulus position. For most cells, selectivity for disparity is more than twice as narrow as that for position. These characteristics are highly desirable if we assume that a disparity sensor should exhibit position invariance while encoding small changes in stimulus depth. Complex cells have nearly identical binocular RFs for bright and dark stimuli as long as the sign of stimulus contrast is the same for the two eyes. When stimulus contrast is opposite, the binocular RF also is inverted such that excitatory subregions become suppressive. We have developed a disparity energy model that accounts for the behavior of disparity-sensitive complex cells. This is a hierarchical model that incorporates specific constraints on the selection of simple cells from which a complex cell receives input. Experimental data are used to examine quantitatively predictions of the model. Responses of complex cells generally agree well with predictions of the disparity energy model. However, various types of deviations from the predictions also are found, including a highly elongated excitatory region beyond that supported by a single energy mechanism. Complex cells in the visual cortex appear to provide a next level of abstraction in encoding information for stereopsis based on the activity of a group of simple-type subunits. In addition to exhibiting narrow disparity tuning and position invariance, these cells seem to provide a partial solution to the stereo correspondence problem that arises in complex natural scenes. Based on their binocular response properties, these cells provide a substantial reduction in the complexity of the correspondence problem.

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REDUCTION TREE OF THE BINARY GENERALIZED POST CORRESPONDENCE PROBLEM

International Journal of Foundations of Computer Science ◽

10.1142/s0129054111008143 ◽

2011 ◽

Vol 22 (02) ◽

pp. 473-490 ◽

Cited By ~ 4

Author(s):

VESA HALAVA ◽

ŠTĚPÁN HOLUB

Keyword(s):

Detailed Analysis ◽

Polynomial Time ◽

Upper Bound ◽

Decision Process ◽

Correspondence Problem ◽

Single Instance ◽

Binary Case

An instance of the (Generalized) Post Correspondence Problem is during the decision process typically reduced to one or more other instances, called its successors. In this paper we study the reduction tree of GPCP in the binary case. This entails in particular a detailed analysis of the structure of end blocks. We give an upper bound for the number of end blocks, and show that even if an instance has more than one successor, it can nevertheless be reduced to a single instance. This, in particular, implies that binary GPCP can be decided in polynomial time.

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Amodal Completion and the Perception of Depth without Binocular Correspondence

Perception ◽

10.1068/p3305 ◽

2002 ◽

Vol 31 (9) ◽

pp. 1037-1045 ◽

Cited By ~ 11

Author(s):

Benoit A Bacon ◽

Pascal Mamassian

Keyword(s):

Amodal Completion ◽

Correspondence Problem ◽

Illusory Contours ◽

Binocular Matching ◽

Partially Occluded ◽

Global Surface

Half-occlusions and illusory contours have recently been used to show that depth can be perceived in the absence of binocular correspondence and that there is more to stereopsis than solving the correspondence problem. In the present study we show a new way for depth to be assigned in the absence of binocular correspondence, namely amodal completion. Although an occluder removed all possibility of direct binocular matching, subjects consistently assigned the correct depth (convexity or concavity) to partially occluded ‘folded cards’ stimuli. Our results highlight the importance of more global, surface-based processes in stereopsis.

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Solving the Correspondence Problem in Haptic/Multisensory Interface Design

Advances in Haptics ◽

10.5772/8694 ◽

2010 ◽

Cited By ~ 3

Author(s):

Charles Spence ◽

Mary K. ◽

Ju-Hwan Lee ◽

Hong T

Keyword(s):

Interface Design ◽

Correspondence Problem

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Solving the correspondence problem between two views using a priori constraints

Journal of Vision ◽

10.1167/11.11.343 ◽

2011 ◽

Vol 11 (11) ◽

pp. 343-343

Author(s):

T. Sawada ◽

Y. Li ◽

Z. Pizlo

Keyword(s):

A Priori ◽

Correspondence Problem

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A Novel Dbmd Implementation for Big Data Mining and Clustering Via Cloud Computing

Journal of University of Shanghai for Science and Technology ◽

10.51201/jusst/21/05205 ◽

2021 ◽

Vol 23 (06) ◽

pp. 29-35

Author(s):

A. Vaitheeswari ◽

◽

Dr. N. Krishnaveni ◽

Keyword(s):

Data Mining ◽

Cloud Computing ◽

Big Data ◽

Virtual Machines ◽

Big Data Analysis ◽

Correspondence Problem ◽

Weighted Norm ◽

Matrix Structure ◽

Method Of Multipliers ◽

Big Data Mining

Matrix structure was one of the most important devices for finding data from big data. Here you’ll find data produced by current applications using cloud computing. However, moving big data using such a system in a performance computer or through virtual machines is still inefficient or impossible. Furthermore, big data is often gathered data from a variety of data sources and stored on a variety of machines using scheduling algorithms. As a result, such data usually bear solid shifted commotion. Growing circulated matrix deterioration is necessary and beneficial for big data analysis. Such a plan should have a good chance of succeeding. Represent the diverse clamor and deal with the correspondence problem in a disseminated manner. In order to do this, we used a Bayesian matrix decay model (DBMD) for big data mining and grouping. Only three approaches to disseminated computation are considered: 1) accelerate slope drop, 2) alternating path method of multipliers (ADMM), and 3) observable derivation. We look at how these approaches could be mixed together in the future. To deal with the commotion’s heterogeneity, we suggest an ideal module weighted norm that reduces the assessment’s differentiation. Finally, a comparison was made between these approaches in order to understand the differences in their outcomes.

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Solving the binocular correspondence problem with ghost matches

Journal of Vision ◽

10.1167/13.9.933 ◽

2013 ◽

Vol 13 (9) ◽

pp. 933-933 ◽

Cited By ~ 1

Author(s):

B. Farell

Keyword(s):

Correspondence Problem

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Local-Level and Global-Level Form Characteristics in Apparent-Motion Correspondence

Perception ◽

10.1068/p241233 ◽

1995 ◽

Vol 24 (11) ◽

pp. 1233-1245 ◽

Cited By ~ 4

Author(s):

Terry Palmer ◽

Ovid J L Tzeng ◽

Sheng He

Keyword(s):

Apparent Motion ◽

Motion Detection ◽

Local Level ◽

The Other ◽

Correspondence Problem ◽

Global Level ◽

Global Precedence ◽

Detection Mechanism ◽

Motion Display ◽

Motion Correspondence

This study addressed the ‘correspondence’ problem of apparent-motion (AM) perception in which parts of a scene must be matched with counterparts separated in time and space. Given evidence that AM correspondence can be mediated by two distinct processes—one based on a low-level motion-detection mechanism (the Reichardt process), the other involving the tracking of objects by visual attention (the attention-based process)—the present study explored how these processes interact in the perception of apparent motion between hierarchically structured figures. In three experiments, hierarchical figures were presented in a competition motion display so that, across frames, figures were identical at either the local or the global level. In experiment 1 it was shown that AM occurred between locally identical figures. Furthermore, with the Reichardt AM component eliminated in experiments 3 and 4, no preference was obtained for either level. While evidence from previous studies suggests that form extraction for hierarchically structured figures proceeds from the global to the local level, the present results indicate the irrelevance of such a global precedence in AM correspondence. In addition, it is suggested that Reichardt AM correspondence between local elements constrains attention-based AM correspondence between global figures so that both components move in the same direction. It is argued that this constraining process represents an elegant means of achieving AM correspondence between objects undergoing complex transformations.

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