Post on 11-Jan-2016
transcript
A Bayesian Approach A Bayesian Approach For 3D For 3D
Reconstruction From Reconstruction From a Single Imagea Single Image
Presented By: Erick DelagePresented By: Erick Delage
Supervisor: Prof. Andrew Y. NgSupervisor: Prof. Andrew Y. NgAI Laboratory, Stanford UniversityAI Laboratory, Stanford University
Erick Delage, Stanford University, 2Erick Delage, Stanford University, 2005005
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Can a robot reconstruct 3D from a single image?
Autonomous Monocular Vision Autonomous Monocular Vision Depth Reconstruction for Indoor Depth Reconstruction for Indoor
ImageImage
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Review of PublicationsReview of PublicationsPopular 3d reconstruction
Stereo Vision (Trucco et Verri, 1998) Structure from Motion
Single View 3d reconstruction
Shape from Shading (Zhang et al., 1999) 3d Metrology (Criminisi et al., 2000)
Our Goal
To develop an autonomous algorithm that recovers 3D information from a single image in a complex environment
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Simplification of the ProblemSimplification of the Problem
Assumptions
1. Image contains flat floor and walls2. Camera is parallel to the ground plane3. The camera is at a known height above the ground4. The image is obtained by perspective projection
Our Theory:
Given the floor boundary position, the 3D coordinates in an image of all points can be recovered
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General ApproachGeneral Approach
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General Approach (2)General Approach (2)
Prior Knowledge about Indoor + Machine Learning
Image Analysis Floor Boundary detection (Machine Learning) 3D reconstruction
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Input Image
Difference from the floor color
Floor Boundary DetectionFloor Boundary DetectionMagnitude of Image gradient
Difference in chromatic space
How can we combine these image features for floor boundary detection ?
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Input Image
Training Mask
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Using Logistic Regression :
(Martin, D. R., et al., 2002)
The model was trained using 25 labeled images of a diverse range of indoor environments on Stanford’s campus
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Floor Boundary DetectionFloor Boundary Detection
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Floor Boundary Detection : Floor Boundary Detection : ResultsResults
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Floor Boundary Detection : Floor Boundary Detection : ResultsResults
Precision = “true positives” / “all positives”
Recall = “true positives” / “all true’s”
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Bayesian Inference on FloorBayesian Inference on Floor BoundaryBoundary
Can we use prior knowledge about the structure of floors and their boundaries?
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Yi : Position of floor boundary in column i
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C : Color of the floor
Bayesian InferenceBayesian Inference
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Bayesian InferenceBayesian Inference
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Bayesian InferenceBayesian Inference
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Training / Bayesian InferenceTraining / Bayesian Inference
60 images of indoor environment in 8 different buildings of Stanford’s campus
Leave-one-out cross-validation: train on 7 buildings, test on 1
Parameters for density models estimated from training data using Maximum Likelihood
Exact inference on graph done using Viterbi-like algorithm
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Results – Floor Boundary Results – Floor Boundary DetectionDetection
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Results – Floor Boundary Results – Floor Boundary DetectionDetection
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3D Reconstruction3D Reconstruction
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3D Reconstruction3D Reconstruction
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3D Reconstruction3D Reconstruction
Extra Material:
Exemples #1, #2, #3
Or at:
http://www.stanford.edu/~edelage/indoor3drecon
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PerformancePerformance
Precision of floor boundary in segmentation
Precision of floor boundary in 3d localization
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ConclusionConclusion
Monocular 3d reconstruction is a good example of an Monocular 3d reconstruction is a good example of an ambiguous problem that can be resolved using prior ambiguous problem that can be resolved using prior knowledge about the domainknowledge about the domain
The presented Bayesian network proves high efficiency The presented Bayesian network proves high efficiency in learning prior knowledge necessary for this in learning prior knowledge necessary for this applicationapplication
This is the first autonomous algorithm for depth recovery This is the first autonomous algorithm for depth recovery in a rich, textured indoor scene.in a rich, textured indoor scene.
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Future WorkFuture Work
Apply graphical modeling for more complex geometry.Apply graphical modeling for more complex geometry. Formulate the problem in a form that scales precision Formulate the problem in a form that scales precision
performance with depth of objects.performance with depth of objects. Embed this approach in real robot navigation problem Embed this approach in real robot navigation problem
(ex. RC car, night indoor navigation)(ex. RC car, night indoor navigation)
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Questions ?Questions ?
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ReferencesReferencesCriminisi, A., Reid, I., & Zisserman, A. (2000). Single View Metrology. IJCV, 40, 123-148.
Martin, D. R., Fowlkes, C. C., & Malik, J. (2002). Learning to Detect Natural Image Boundaries using Brightness and Texture. NIPS.
Trucco, E., & Verri, A. (1998). Introductory techniques for 3d computer vision. Prentice Hall.
Zhang, R., Tsai, P.-S., Cryer, J. E., & M. Shah (1999). Shape from shading: a survey. IEEE Trans. On PAMI, 21, 690-706.