Luận án tiến sĩ: Learning-based Approach for Vision Problems

Luận án tiến sĩ về phương pháp học máy cho xử lý ảnh. Nghiên cứu stereo vision, video super-resolution và phát hiện con người sử dụng CNN, MRF, CRF.

Trường ĐH

University of California Santa Cruz

Chuyên ngành

Computer Engineering

Tác giả

Luan An

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Luận án tiến sĩ

Năm xuất bản

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190

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29 phút

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I. Learning Based Stereo Vision Fundamentals

Learning-based approaches revolutionize traditional stereo vision problems through adaptive methods. The dissertation explores how machine learning techniques address fundamental challenges in depth estimation and image matching. Stereo vision requires matching corresponding points between two images to reconstruct three-dimensional scenes. Traditional methods struggle with texture variations, depth discontinuities, and illumination changes. Learning-based stereo introduces adaptive matching behaviors that respond to local image characteristics. The approach represents a paradigm shift from fixed-parameter algorithms to data-driven solutions. Neural networks and probabilistic models form the foundation of this methodology. Feature extraction techniques identify relevant patterns in image pairs. Computer vision applications benefit from improved accuracy in challenging scenarios. The dissertation establishes theoretical frameworks combining deep learning with classical stereo constraints.

1.1. Stereo Matching Problem Definition

Stereo matching establishes pixel correspondence between left and right images. The epipolar constraint reduces search space to one-dimensional scanlines. Rectification aligns image pairs to simplify the matching process. Disparity values indicate depth through geometric relationships. Window-based methods compare local neighborhoods around candidate pixels. Correlation measures quantify similarity between matching windows. The fundamental challenge involves balancing accuracy with computational efficiency. Texture-less regions create ambiguity in correspondence estimation. Depth discontinuities introduce systematic errors near object boundaries. Learning-based approaches adapt matching strategies to local image properties.

1.2. Probabilistic Framework for Depth Estimation

Maximum A Posteriori (MAP) formulation combines data terms with smoothness priors. Markov Random Fields (MRF) encode spatial relationships between neighboring pixels. The energy function balances matching costs against depth continuity assumptions. Belief propagation algorithms solve the optimization problem iteratively. Conditional probability distributions model uncertainty in depth estimates. Learning algorithms discover optimal parameter settings from training data. The probabilistic model accommodates noise and ambiguity inherent in real images. Prior distributions encode expectations about scene structure and geometry. Image segmentation informs adaptive smoothness constraints across boundaries.

1.3. Adaptive Matching Behavior Learning

Multiple experts represent different matching window configurations and positions. Each expert specializes in specific image conditions like texture or boundaries. Statistical learning determines expert reliability for local image characteristics. Texture strength, proximity to discontinuities, and gradient information guide expert selection. The system learns probability distributions over expert performance from ground truth data. Adaptive bin selection optimizes the representation of continuous features. The approach outperforms fixed-window methods in challenging regions. Feature extraction identifies texture patterns and structural elements. Convolutional neural networks could enhance feature representation in modern implementations.

II. Video Super Resolution Through Primal Sketches

Video super-resolution reconstructs high-resolution frames from low-resolution input sequences. The dissertation introduces primal sketch priors as powerful constraints for image reconstruction. Primal sketches represent images through geometric primitives like edges, ridges, and corners. Learning-based methods discover statistical relationships between low and high-resolution image patches. Example-based approaches retrieve similar patterns from training databases. The combination of reconstruction constraints with learned priors produces superior results. Temporal information from video sequences provides additional constraints beyond single images. Motion estimation aligns frames to exploit redundancy across time. Deep learning architectures could extend these principles through end-to-end training. The methodology bridges classical image processing with modern machine learning techniques.

2.1. Primal Sketch Representation Theory

Primal sketches decompose images into fundamental geometric elements. Edge primitives capture intensity discontinuities and object boundaries. Ridge and valley structures represent elongated features in images. Corner points indicate junctions and high-curvature locations. The representation provides compact encoding of essential image structure. Learning algorithms discover co-occurrence patterns among primitives. Statistical models capture relationships between primitive configurations and local image content. The approach reduces dimensionality compared to raw pixel representations. Primal sketches enable efficient matching and retrieval operations. Feature extraction focuses on perceptually significant image components.

2.2. Scene Specific Prior Learning

Scene-specific priors adapt to characteristics of particular video sequences. Training data comes from high-resolution regions within the same scene. The system learns correlations between low and high-frequency components. Conditional Random Fields (CRF) model spatial dependencies in reconstruction. Pairwise potentials enforce smoothness while preserving edges. Unary potentials connect observations to reconstruction variables. The learning process discovers optimal potential functions from examples. Scene-specific adaptation improves results over generic training databases. Object detection and image recognition benefit from similar adaptive strategies. The methodology demonstrates transfer learning principles in computer vision.

2.3. Temporal Coherence in Video Processing

Motion estimation registers frames across temporal sequences. Optical flow algorithms compute pixel trajectories between frames. Temporal consistency constraints reduce flickering artifacts in reconstructed video. Multiple frames provide redundant information about scene structure. The system aggregates evidence across time to improve spatial resolution. Occlusions and disocclusions require special handling in temporal integration. Robust estimation techniques handle outliers from motion errors. Neural networks could learn temporal relationships directly from data. The approach combines classical motion models with learning-based reconstruction. Visual perception benefits from temporally coherent high-resolution output.

III. Deep Learning for Human Detection Systems

Human detection represents a critical computer vision application with broad practical impact. The dissertation explores both regression-based and detection-based approaches to human counting. Convolutional neural networks provide powerful feature extraction for person detection. Multi-scale processing handles variations in person size and distance. Learning-based methods outperform hand-crafted features for this challenging task. Crowded scenes introduce occlusions and overlapping person instances. Detection-based approaches localize individual persons before counting. Regression methods directly estimate person counts from image features. Object detection frameworks apply to pedestrian detection in surveillance applications. The methodology demonstrates deep learning effectiveness for visual perception tasks.

3.1. Regression Based Counting Framework

Direct regression maps image features to person count estimates. The approach avoids explicit detection and localization steps. Feature extraction captures crowd density and distribution patterns. Machine learning algorithms discover relationships between features and counts. Training data consists of images with ground truth person counts. The method handles severe occlusions where individual detection fails. Computational efficiency improves over detection-based alternatives. Global image features complement local detection cues. Neural networks learn non-linear mappings from features to counts. Image segmentation could improve feature localization for counting.

3.2. Convolutional Neural Networks Architecture

Convolutional layers extract hierarchical features from input images. Pooling operations provide translation invariance and reduce dimensionality. Multiple scales capture persons at different distances from camera. The network learns discriminative features automatically from training data. Deep architectures model complex patterns in human appearance. Backpropagation optimizes network weights for detection accuracy. The approach eliminates manual feature engineering requirements. Convolutional neural networks excel at image recognition tasks. Transfer learning from large datasets improves performance. Object detection benefits from shared feature representations.

3.3. Multi Scale Detection Strategy

Image pyramids represent scenes at multiple resolutions. Detectors trained at different scales handle size variations. Non-maximum suppression eliminates duplicate detections. The system combines responses across scales for final detection. Feature extraction operates consistently across resolution levels. Deep learning architectures incorporate multi-scale processing inherently. Spatial pooling aggregates information across receptive fields. The approach improves robustness to scale variations. Computer vision systems require scale-invariant representations. Visual perception operates across multiple spatial frequencies naturally.

IV. Machine Learning Integration in Vision Problems

The dissertation demonstrates systematic integration of machine learning across diverse vision problems. Learning-based approaches adapt to problem-specific characteristics through training data. Statistical models capture complex relationships that resist analytical formulation. Feature extraction transforms raw pixels into meaningful representations. Neural networks provide flexible function approximation for vision tasks. The methodology emphasizes data-driven solutions over hand-crafted algorithms. Computer vision benefits from advances in deep learning and optimization. Training procedures discover optimal parameters from labeled examples. The approach generalizes across stereo matching, super-resolution, and human detection. Probabilistic frameworks handle uncertainty inherent in visual perception tasks.

4.1. Statistical Learning for Visual Features

Statistical models capture distributions of visual features in natural images. Training data provides examples of input-output relationships. Maximum likelihood estimation discovers model parameters. The learning process generalizes from finite samples to new instances. Feature extraction identifies relevant image characteristics for each task. Texture, edges, and gradients form fundamental visual primitives. Learning algorithms weight features according to predictive power. Cross-validation prevents overfitting to training data. Machine learning techniques handle high-dimensional feature spaces. Image recognition depends on robust statistical feature models.

4.2. Probabilistic Models for Vision Tasks

Bayesian frameworks combine prior knowledge with observed data. Conditional probability models relate observations to hidden variables. Markov Random Fields encode spatial dependencies in images. Inference algorithms compute posterior distributions over unknowns. Learning procedures estimate model parameters from training examples. Probabilistic models quantify uncertainty in vision estimates. The approach handles noise and ambiguity systematically. Energy minimization connects probabilistic inference to optimization. Graph-based representations enable efficient computation. Computer vision tasks benefit from principled probabilistic reasoning.

4.3. Optimization Methods for Learning

Gradient descent optimizes objective functions iteratively. Belief propagation solves inference problems on graphical models. Graph cuts provide efficient solutions for certain energy functions. Convolutional neural networks use backpropagation for training. The optimization landscape contains local minima requiring careful initialization. Regularization prevents overfitting and improves generalization. Stochastic methods handle large-scale training datasets. Convergence analysis ensures algorithms reach satisfactory solutions. Deep learning requires specialized optimization techniques. Object detection and image segmentation depend on effective optimization.

V. Feature Extraction and Representation Learning

Feature extraction transforms raw image data into meaningful representations. The dissertation explores both hand-crafted and learned features. Texture descriptors quantify local image patterns and statistics. Gradient-based features capture edge orientation and magnitude. Primal sketch primitives provide geometric image descriptions. Learning-based methods discover optimal features automatically from data. Convolutional neural networks learn hierarchical feature representations. Deep architectures extract increasingly abstract features in successive layers. Feature quality determines performance across vision tasks. Visual perception relies on appropriate feature representations for recognition and understanding.

5.1. Traditional Feature Engineering

Hand-crafted features encode domain knowledge about images. Texture measures include variance, gradient magnitude, and frequency content. Edge detection identifies intensity discontinuities using derivative operators. Corner detectors locate high-curvature points through eigenvalue analysis. The approach requires expertise to design effective features. Feature selection identifies most discriminative measurements for tasks. Dimensionality reduction techniques compress feature vectors. Traditional methods provide interpretable and efficient representations. Computer vision research established extensive feature engineering literature. Image recognition historically depended on carefully designed features.

5.2. Deep Learning Feature Discovery

Convolutional neural networks learn features through supervised training. Early layers detect edges and simple patterns automatically. Deeper layers combine low-level features into complex representations. The learning process optimizes features for specific tasks. Backpropagation adjusts feature detectors to minimize prediction error. Transfer learning reuses features across related problems. Deep architectures discover hierarchical feature organizations. The approach eliminates manual feature engineering effort. Machine learning automatically adapts features to data characteristics. Object detection benefits from learned feature representations.

5.3. Multi Scale Feature Representations

Image pyramids provide features at multiple spatial resolutions. Coarse scales capture global structure and context. Fine scales preserve detail and precise localization. Multi-scale processing handles size variations in objects. Feature extraction operates consistently across scales. Spatial pooling aggregates information across receptive fields. The approach improves robustness and invariance properties. Neural networks incorporate multi-scale processing through architecture design. Computer vision systems combine information across scales. Visual perception operates naturally at multiple spatial frequencies.

VI. Applications and Future Directions in Vision

The dissertation establishes foundations applicable to diverse computer vision problems. Stereo vision enables depth perception for robotics and autonomous systems. Video super-resolution enhances surveillance and multimedia applications. Human detection supports crowd analysis and security systems. Learning-based approaches continue evolving with deep learning advances. Convolutional neural networks now dominate many vision benchmarks. Object detection frameworks build on principles established in this work. Image segmentation benefits from learned features and probabilistic models. Future research directions include end-to-end learning and weakly supervised methods. The methodology demonstrates enduring value of combining learning with domain knowledge.

6.1. Practical Applications in Computer Vision

Autonomous vehicles require robust stereo depth estimation. Surveillance systems benefit from super-resolution and human counting. Robotics applications depend on accurate visual perception. Medical imaging uses learning-based reconstruction techniques. Augmented reality requires precise depth and object detection. The methods enable real-time processing for interactive applications. Computer vision powers commercial products across industries. Image recognition supports search and organization systems. Object detection enables automated inspection and quality control. Visual perception capabilities continue expanding application domains.

6.2. Deep Learning Evolution and Impact

Modern convolutional neural networks extend dissertation principles. Deep architectures achieve state-of-the-art performance across benchmarks. Transfer learning leverages large-scale datasets like ImageNet. End-to-end training optimizes entire systems jointly. Attention mechanisms focus processing on relevant image regions. Generative models create realistic synthetic images. Self-supervised learning reduces dependence on labeled data. Neural architecture search automates network design. Machine learning advances accelerate through computational improvements. Computer vision benefits from continuous deep learning innovation.

6.3. Research Challenges and Opportunities

Weakly supervised learning reduces annotation requirements. Domain adaptation transfers knowledge across different datasets. Explainable AI makes learned models more interpretable. Efficient architectures enable mobile and embedded deployment. Few-shot learning handles limited training data scenarios. Multimodal fusion combines vision with other sensor modalities. Temporal modeling improves video understanding capabilities. Adversarial robustness addresses security concerns. Neural networks require better theoretical understanding. Object detection and image segmentation continue advancing rapidly.

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UNIVERSITY OF CALIFORNIA SANTA CRUZ LEARNING-BASED APPROACH FOR VISION PROBLEMS A dissertation submitted in partial satisfaction of the requirements for the degree of DOCTOR OF PHILOSOPHY in COMPUTER ENGINEERING by Dan Kong December 2006 The Dissertation of Dan Kong is approved: Professor Hai Tao, Chair ho rofessor R O Manduchi (pms. Prdfessor James Davis LO. Sloan Vice Provost and Dean of Graduate Studies UMI Number: 3241208 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction.

In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. ® UMI UMI Microform 3241208 Copyright 2007 by ProQuest Information and Learning Company. All rights reserved.

This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P. Box 1346 Ann Arbor, MI 48106-1346 Copyright @ by Dan Kong 2006 Table of Contents List of Figures vii List of Tables xi Abstract xii Dedication xV Acknowledgments xvi I Learning-based Stereo 1 Introduction 11 The Problem .00 00004 12 Foundations of Stereo. cv co ee ees 1.

ee eee es 12. ns 2 Related Work and Motivation 2.2 Window-based Matching.165 MRF-based Methods.6 Segmentation-based Methods Cr — 2. ee et ee. ee ee es 2.

eee ee ee ee 2. es The Approach 3.1 Representing and Learning Matching Behaviors .11 Representing matching behaviors.2 Learning the distribution .3 Adaptive bin selection .00 e ee eee eens 3.2 A Probabilistic Stereo Model .1 Stereo as an MAP-MRF problem. HQ Q kg kg kia Results and Discussion 4. HQ eee eee kg và 4.

ng nà g kg kg va IT Video Super-resolution Introduction and Related Work 5. kg và kg kg cv VN Và kia 5.2 Reconstruction-based Methods.3 Learning-based Methods.050 eee eae Primal Sketch Priors 6.2 Example-based Priors .2 Primal Sketch Priors. ee ee k kấ 6.2 Learning primal sketch priors. Why primal sketch.

HQ HQ HQ na Video Super-resolution 7.1 Overview of the Approach. ch và kg va 7. g k k NT gà Nà KV va 1V 73 Scene-specific pIiOTS. LH Q Q HQ nu Hà Q kg Tà kg 73.

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000 ee ee eens 74.gaä< Implementation and Results 101 8. 0 ee ee và 101 8. ee et ee 105 83 Quantitative Results. eee eee eee 110 Discussion 113 9.

kg và ga àna 114 92 >1 -. ai es 114 93 Primitive co-occurrence. 00 0c eee eee eee en 115 9.eee 115 III Human Detection and Counting 10 Introduction and Related Work 10. 00 ee tk ke và 11 Human Counting: A Regression Approach 11.

eee eee ee es 11. Q cv ng vn cv vn gà kg kg cv va 11.3 Results and Diacussion. ee 12 Human Counting: A Detection-based Approach 12.1 Convolutional Neural Network(CNN). HQ ng và va 12.

ee ee ee 12.3 Multi-scale Detection. QC ne va 13 Conclusions and Future work Bibliography vi List of Figures 1.1 The geometry of nonverged stereo.2 Rectification can make parallel scanlines and enforce reduce the epipo- lar constraint to1D.0 ee ee ees 2.1 (a) Tsukuba left image. (b) Synthetically alteration of the Tsukuba right image by increasing the intensity. (c) Depth map computed us- ing multi-scale Belief Propagation.

(d) Depth computed using 9 x 9 correlation window. 000 eee eee eee eee ees 2. (c) Depth computed using graph cut (d) Depth computed using 9 x9 correlation window. eee ee ee 2.3 All the experts used in the algorithm.

Black dot means the center of the matching window.0 eee eee eee eee 2.4 For depth discontinuity regions, the accuracy of depth estimates de- pends on the matching position of the correlation window. In this example, window A is betterthanB.5 Tsukuba color image (a) and the depth map computed using 7 x 7 NCC (b) Typical errors in NCC-based stereo matching.6 (a) probability of depth error as a function of distance to the near- est foreground object. (b) probability of depth error as a function of texture strength. (c) Probability of estimating true depth for 36 ex- perts on the textured and textureless foreground.

(d) Probability of estimating true depth for 36 experts at depth discontinuity regions.1 Disparity map using 9 x 9 correlation window and pixels A, B, C from three typical regions. 6 ee ee vii 3.2 The depth map for a scene of two objects: foreground (white rect- angle) and background (gray rectangle). The shade rectangle A is a background region close to the foreground. (a) Depth map with fat- tening effect where A has the foreground depth.

(b) True map for the left view where A has the background depth.3 The texture and structure attributes around a pixel.4 (a) The marginal likelihood density of the 3 x 3 scale texture strength evaluated on Middlebury stereo data. The vertical axis labels the probaiblity density and the horizontal axis labels the texture strength. The vertical dashed lines indicate the position of the bin boundaries which are adaptively choosen (b) The posterior probability distribution based on the adaptively chosen bỉns.5 The expectation of the posterior entropy rapidly reaches an asymptotic value as a function of the number of bins.6 Graphical model for stereo (a): Traditional MRF model. (b): MRF model in this paper.7 Illustration of how to compute the proposal probability ration for one 3.8 (a):Color segmentation using mean-shift.

(b): Depth segmentation based on median filtered SSD depth map. (c): Joint color and depth segmentation.9 Computation of likelihood and smoothness change for one super-pixel in segmentation-based approach.0 00 ee eee nes 4.1 The learned matching behavior for 7 x 7 correlation window. ee ee ees 4.2 Dense disparity map for the ” Tsukuba” ,” Sawtooth” ,” Venus” and ” Map” images.3 Intermediate results on Tsukuba data at different iterations.4 Comparisons of the disparity maps for the ” Tsukuba”, ”Sawtooth”, ”Venus” and ”"Map” images using 7 x 7 NCC matching cost as the likelihood.5 Dense disparity maps for the ” Teddy” and ”Cones” images.6 Comparisons of the disparity maps for the ”face” stereo pair. (a) Left image (b) Right Image (c) Initial depth from 7 x 7 correlation window.

(d) Belief propagation result. (e) Graph cut result.7 Energy of estimated depth map and ground truth.1 The filter bank used for primitives extraction (a) and typical primitives extracted (b) CS Sy 7.1 Overview of our video super-resolution approach.2 The ROC curves of primitive training data (a) and component training data (b) at different sizes. X-axis is match error and Y-axis is hit-rate.3 The prediction ROC curves of primitive training data (a) and com- ponent training data (b) at different sizes. X-axis is match error and Y-axis is hit-rate.4 The ROC curves for scene-specific dictionary D, and general dictionary D, that measures sufficiency (a) and predictability (b).

The scene- specific dictionary outperforms the general dictionary.5 Graphical model for super-resolution. (b) Video super-resolution.6 Comparison of video super-resolution results. Top: the original ad- jacent low resolution frames. (a)(b) Independent super-resolution of each frame.

(c)(d) Super-resolution with temporal smoothing.1 Training phase of the algorithm.2 Select the training frame using relative blurriness measure.3 Super-resolution results for frame 8 and 87 from the plant video se- quence. The input videos has resolution 240x160. Top: Bi-cubic inter- polation results (720x480). Bottom: results using customized dictio- nary plus temporal constraint (720x480).4 Super-resolution results for frame 12 and 78 from the face video se- quence.

The input videos has resolution 240x160. Top: Bi-cubic interpolation results (720x480). Bottom: results using scene-specific dictionary plus temporal constraint (720x480) .5 Super-resolution results for frame 9, and 121 from the keyboard video sequence. The input videos has resolution 160x120.

Top: Bi-cubic interpolation results (640x480). Bottom: results using customized dic- tionary plus temporal constraint (640x480) .6 Super-resolution results for frame 56, and 73 from the MPEG-4 en- coded video sequence. The input videos has resolution 352x288. (a)(b): Low resolution frame 117 x 96.

(c)(d): Bicubic interpolation to 352 x 288 (e)(f): Super-resolution using our approach.7 RMS errors for first 20 frames of testing video sequences (a) plant” (b) "face (c)"keyboard”.1 Features for crowd counting: (a) one frame from the videos, (b) fore- ground mask image, (c) edge map, (d) the edge map after the AND’ operation between (b) and (c). ee ee ix 11.2 The same person has different projected height in the image when translates on the ground plane.3 (a)Density estimation using homography. (b) ROI in the image.4 Three layer neural network architecture. The input is the normalized blob and edge orientation histograms.

The output is the crowdedness MEASUTE 6 HQ HH HH ng k va k kg kg kia 130 11.5 Model selection: the cross validation errors for different number of hidden layers.6 Crowd counting results from site A. nu ng vu gà sa 134 11.7 Crowd counting results for sequence from site B 12.1 Architecture of our Convolutional Neural Networks for human detection 140 12.2 Multi-scale detector.3 Some example images from MIT database.4 Some example images from INRIA database.5 CNN performance on MIT database with different scale. (b) False alarm rate.6 CNN performance on INRIA database with different scale. (a) Detec- tion rate.

(b) False alarm rate.7 Crowd counting results for video sequence from Beijing, China. (a)(b): Initial detection results for two frames. (c)(d): Results after bootstrap- ping the CNN using 'hard examples.8 Crowd counting results for Bookstore, UCSC. (a): Initial detection results for one frame.

(b): Results after bootstrapping the CNN using hard examples’,. Q0 Q HQ Vu v va va 153 List of Tables 4.1 Performance comparisons using NCC matching cost - 4.2 Performence of the proposed method for the new testbed images ` 12.1 Confusion matrix for MIT testing data of size 16 x 32 12.2 Confusion matrix for INRIA testing data of size 16 x 32 xi Abstract Learning-based Approach for Vision Problems by Dan Kong Learning-based techniques have seen more and more successful application in com- puter vision. ”Learning for vision” is viewed as the next challenging frontier for computer vision. Technical challenges in applying learning-based methods in vision include picking the appropriate representation, model generalization and complexity.

This dissertation investigated different vision problems together with the proposed learning algorithms for them. In particular, three vision problems are studied from low-level to high level: stereo, super-resolution and human detection. In the first part, we present a learning-based approach [73, 74]to address the visual correspondence problems when the stereo images have different intensity level. The algorithm first learns the matching behaviors of multiple local-window methods (called experts) using a simple histogram-based method.

The learned behaviors are then integrated into a MAP-MRF depth estimation framework and the Metropolis- Hastings algorithm is used to find the MAP solution. Segmentation is also used to accelerate the computation and improve the performance. Qualitative and quanti- tative experimental results are presented, which demonstrate that, for stereo image pair having different intensity level, the proposed algorithm significantly outperforms the state-of-the-art methods. Using prior knowledge can significantly improve the performance of low-level image processing and vision problems.

In the second part, we propose a learning- based approach [72, 71] for video super-resolution. The approach extends previous primal sketch image hallucination method via learning a scene-specific priors using examples. This is achieved by constructing training examples using the high resolution images captured by still camera and use that to increase the low resolution videos. As a result, information from cameras with different spatio-temporal resolutions is combined in our framework.

In addition, we use conditional random field (CRF) to enforce smoothness constraint between adjacent super-resolved frames and the video super-resolution is posed as finding the high resolution video that maximize the conditional probability.

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