8.1 Stereoscopic vision

Stereoscopic vision is a key concept in computer vision, mimicking how our eyes perceive depth. It uses two cameras to capture slightly different views of a scene, allowing for 3D reconstruction and depth estimation.

This topic covers the fundamentals of stereoscopic vision, including binocular disparity, camera calibration, and correspondence matching. It also explores advanced techniques like multi-view stereo and machine learning approaches for improving depth estimation accuracy and efficiency.

Fundamentals of stereoscopic vision

• Stereoscopic vision forms a crucial component in Computer Vision and Image Processing by enabling depth perception and 3D scene understanding
• Utilizes the slight differences between images captured by two eyes or cameras to infer depth information
• Plays a vital role in various applications ranging from robotics to virtual reality systems

Binocular disparity concept

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• Refers to the difference in image location of an object seen by the left and right eyes
• Calculated as the difference in horizontal position of a feature in the left and right images
• Inversely proportional to the distance of the object from the viewer
• Brain uses binocular disparity to estimate relative depths of objects in a scene
• Measured in units of visual angle (degrees or arc minutes)

Depth perception mechanisms

• Stereopsis extracts depth information from binocular disparity
• Monocular cues contribute to depth perception (motion parallax, occlusion, perspective)
• Accommodation and convergence provide additional depth cues
• Integration of multiple depth cues occurs in the visual cortex
• Depth perception accuracy varies with distance and viewing conditions

Parallax and stereopsis

• Parallax describes the apparent displacement of an object when viewed from different positions
• Motion parallax occurs when objects at different distances appear to move at different speeds
• Stereopsis specifically refers to depth perception arising from binocular disparity
• Requires fusion of left and right eye images in the brain
• Enables fine depth discrimination, especially for nearby objects

Stereo camera systems

• Mimic human binocular vision by using two cameras separated by a known distance
• Essential for capturing 3D information in computer vision applications
• Enable reconstruction of 3D scenes from 2D image pairs

Camera calibration techniques

• Intrinsic calibration determines internal camera parameters (focal length, principal point)
• Extrinsic calibration finds the relative pose between cameras
• Zhang's method uses a planar checkerboard pattern for calibration
• Bundle adjustment refines calibration parameters globally
• Stereo calibration establishes the geometric relationship between two cameras

Epipolar geometry basics

• Describes the geometric relationship between two views of a 3D scene
• Epipolar line constrains the search for corresponding points
• Fundamental matrix $F$ encapsulates the epipolar geometry
• Essential matrix $E$ relates normalized image coordinates
• Epipoles represent the projection of one camera center onto the other camera's image plane

Rectification process

• Transforms stereo image pairs to align epipolar lines horizontally
• Simplifies the correspondence search to a 1D problem along scanlines
• Involves rotating and reprojecting images onto a common plane
• Reduces the disparity search range
• Can introduce image distortions, especially at image borders

Correspondence problem

• Involves finding matching points between left and right stereo images
• Critical for accurate depth estimation in stereoscopic vision
• Challenges include occlusions, repetitive patterns, and textureless regions

Feature matching algorithms

• SIFT (Scale-Invariant Feature Transform) detects and describes local features
• SURF (Speeded Up Robust Features) offers faster computation than SIFT
• ORB (Oriented FAST and Rotated BRIEF) provides efficient binary descriptors
• Template matching uses correlation to find similar image patches
• Deep learning-based methods learn feature representations for matching

Dense vs sparse correspondence

• Sparse correspondence finds matches for a subset of image points (corners, edges)
• Dense correspondence attempts to match every pixel in the image
• Sparse methods are faster but provide less complete depth information
• Dense methods produce full depth maps but are computationally intensive
• Hybrid approaches combine sparse and dense techniques for efficiency

Occlusion handling

• Occlusions occur when parts of a scene are visible in only one image
• Left-right consistency check identifies potential occlusions
• Ordering constraint assumes consistent depth ordering along epipolar lines
• Uniqueness constraint ensures one-to-one matching between images
• Occlusion-aware cost functions in global optimization methods

Disparity computation

• Calculates the pixel offset between corresponding points in stereo images
• Directly related to depth: larger disparity indicates closer objects
• Forms the basis for generating depth maps from stereo image pairs

Block matching methods

• Compare small image windows between left and right images
• Sum of Absolute Differences (SAD) measures pixel-wise intensity differences
• Normalized Cross-Correlation (NCC) robust to illumination changes
• Census transform encodes local intensity patterns for matching
• Adaptive window sizes can improve performance near depth discontinuities

Dynamic programming approaches

• Formulates disparity computation as an optimization problem along epipolar lines
• Enforces ordering and smoothness constraints
• Scanline optimization solves for optimal disparities one row at a time
• Can handle occlusions by allowing "jumps" in the disparity function
• Efficient for real-time applications but may produce streaking artifacts

Global optimization techniques

• Minimize a global energy function over the entire disparity map
• Graph cuts algorithm finds a global minimum for certain energy functions
• Belief propagation uses message passing to approximate optimal solutions
• Variational methods formulate disparity estimation as a continuous optimization problem
• Semi-global matching combines global and local methods for efficiency

Depth map generation

• Converts disparity information into a 3D representation of the scene
• Crucial for applications in 3D reconstruction and scene understanding
• Provides a foundation for higher-level computer vision tasks

Disparity to depth conversion

• Uses triangulation principle to convert disparity to metric depth
• Depth $Z = (f * B) / d$, where $f$ is focal length, $B$ is baseline, and $d$ is disparity
• Requires accurate camera calibration for precise depth estimates
• Depth resolution decreases quadratically with distance from the cameras
• Sub-pixel disparity estimation improves depth accuracy

Depth map refinement

• Bilateral filtering preserves edges while smoothing depth estimates
• Guided filtering uses color image to improve depth map quality
• Hole filling interpolates missing depth values
• Temporal consistency enforces smooth depth changes across video frames
• Super-resolution techniques enhance depth map resolution

Handling of ambiguities

• Multiple hypotheses tracking for regions with uncertain disparities
• Confidence measures assess reliability of depth estimates
• Fusion of stereo with other sensors (lidar, time-of-flight) resolves ambiguities
• Semantic segmentation guides depth estimation in challenging regions
• Iterative refinement updates depth estimates using initial approximations

Applications of stereoscopic vision

• Stereoscopic vision enables a wide range of applications in computer vision and robotics
• Provides crucial depth information for scene understanding and interaction
• Continues to evolve with advancements in algorithms and hardware

3D reconstruction

• Creates detailed 3D models from multiple stereo image pairs
• Structure from Motion (SfM) reconstructs scenes from unordered image collections
• Multi-view stereo generates dense 3D point clouds
• Photogrammetry uses stereo vision for accurate measurements in surveying and mapping
• 3D scanning applications for cultural heritage preservation and reverse engineering

Autonomous navigation

• Enables depth perception for obstacle avoidance in self-driving cars
• Used in drone navigation for collision-free path planning
• Assists in simultaneous localization and mapping (SLAM) for mobile robots
• Provides visual odometry for estimating camera motion
• Enhances situational awareness in advanced driver assistance systems (ADAS)

Virtual and augmented reality

• Generates realistic depth cues for immersive VR experiences
• Enables occlusion handling in AR applications
• Used in 3D displays to create stereoscopic images without glasses
• Facilitates gesture recognition and hand tracking in interactive systems
• Enhances depth perception in telerobotic applications

Challenges in stereoscopic vision

• Stereoscopic vision faces several challenges that impact its accuracy and reliability
• Addressing these challenges is crucial for robust performance in real-world applications
• Ongoing research aims to develop more resilient stereo vision algorithms

Illumination variations

• Differences in lighting between left and right images affect matching accuracy
• Global illumination changes can be addressed by normalized correlation measures
• Local illumination variations require more sophisticated matching techniques
• Shadow detection and removal improve robustness to lighting changes
• Exposure bracketing captures multiple images at different exposures for HDR stereo

Textureless regions

• Lack of distinct features makes correspondence matching difficult
• Propagation of disparities from textured to textureless regions
• Use of larger matching windows in homogeneous areas
• Edge-preserving smoothness constraints in global optimization methods
• Integration of semantic information to guide disparity estimation

Real-time processing constraints

• High computational demands of stereo algorithms challenge real-time performance
• GPU acceleration enables faster processing of stereo algorithms
• Hierarchical approaches process images at multiple resolutions for efficiency
• Trade-off between accuracy and speed in algorithm design
• Hardware implementations (FPGA, ASIC) for low-latency stereo vision systems

Advanced techniques

• Cutting-edge approaches in stereoscopic vision push the boundaries of accuracy and efficiency
• Incorporate insights from other fields of computer vision and machine learning
• Address limitations of traditional stereo methods

Multi-view stereo

• Extends stereo vision to multiple camera viewpoints
• Patch-based multi-view stereo (PMVS) for dense 3D reconstruction
• Volumetric approaches fuse depth information from multiple views
• Photometric stereo uses varying illumination for surface normal estimation
• Light field cameras capture multiple views in a single exposure

Active stereo systems

• Project patterns onto the scene to simplify correspondence problem
• Structured light systems use coded light patterns for 3D reconstruction
• Time-of-flight cameras measure depth using modulated light pulses
• Laser scanners combine stereo vision with laser rangefinding
• Kinect-style depth sensors for gaming and human-computer interaction

Machine learning in stereo vision

• Deep learning models learn to predict disparity from stereo pairs
• End-to-end stereo networks (DispNet, PSMNet) outperform traditional methods
• Unsupervised learning approaches train on unlabeled stereo data
• Transfer learning adapts models to new domains with limited data
• Generative adversarial networks (GANs) for realistic depth map refinement

Evaluation metrics

• Quantitative assessment of stereo vision algorithms is crucial for benchmarking and improvement
• Various metrics capture different aspects of algorithm performance
• Standardized datasets enable fair comparison between methods

Accuracy vs computational efficiency

• Trade-off between depth estimation accuracy and processing speed
• Mean absolute error (MAE) measures average disparity error
• Root mean square error (RMSE) penalizes large errors more heavily
• Bad pixel percentage counts disparity errors exceeding a threshold
• Runtime and throughput metrics assess computational efficiency

Quantitative assessment methods

• Disparity error metrics compare estimated disparities to ground truth
• 3D error metrics evaluate reconstructed point clouds against reference models
• Perceptual metrics assess the visual quality of depth maps
• Robustness measures evaluate performance under varying conditions
• Consistency checks assess left-right disparity agreement

Benchmarking datasets

• Middlebury Stereo Dataset provides high-resolution indoor scenes with ground truth
• KITTI dataset offers real-world driving scenarios with LiDAR ground truth
• ETH3D dataset includes both indoor and outdoor scenes with varying difficulty
• Scene Flow datasets provide large-scale synthetic data for training and evaluation
• Tanks and Temples benchmark focuses on multi-view reconstruction evaluation