Deep Learning for Computer Vision

Deep Learning for Computer Vision is a specialized field that applies deep neural networks, most notably Convolutional Neural Networks (CNNs), to enable computers to interpret and understand visual information from images and videos. Unlike traditional computer vision techniques that relied on manually engineered feature extractors, deep learning models automatically learn a hierarchy of features directly from raw pixel data, leading to breakthrough performance in tasks such as image classification, object detection, semantic segmentation, and image generation. This powerful approach has become the cornerstone of modern computer vision, driving innovations in autonomous vehicles, medical image analysis, facial recognition, and augmented reality.

1. Foundations of Computer Vision and Deep Learning
   1. Overview of Computer Vision
      1. Definition and Scope
      2. Historical Development
      3. Key Applications
         1. Medical Imaging
         2. Autonomous Vehicles
         3. Surveillance and Security
         4. Industrial Automation
         5. Entertainment and Media
   2. Mathematical Prerequisites
      1. Linear Algebra
         1. Vectors and Vector Operations
         2. Matrices and Matrix Operations
         3. Eigenvalues and Eigenvectors
         4. Matrix Decomposition
      2. Calculus
         1. Partial Derivatives
         2. Chain Rule
         3. Gradients and Jacobians
      3. Probability and Statistics
         1. Probability Distributions
         2. Bayes' Theorem
         3. Maximum Likelihood Estimation
         4. Statistical Inference
      4. Information Theory
         1. Entropy
         2. Cross-Entropy
         3. Kullback-Leibler Divergence
   3. Traditional Computer Vision
      1. Digital Image Fundamentals
         1. Image Representation
            1. Pixels and Digital Images
            2. Bit Depth and Dynamic Range
            3. Image Coordinates and Indexing
         2. Color Spaces
            1. RGB Color Model
            2. Grayscale Conversion
            3. HSV Color Space
            4. LAB Color Space
         3. Image File Formats
            1. Lossless vs Lossy Compression
            2. Common Formats
      2. Image Processing Operations
         1. Point Operations
            1. Brightness and Contrast Adjustment
            2. Histogram Equalization
            3. Gamma Correction
         2. Spatial Filtering
            1. Convolution Operation
            2. Linear Filters
            3. Gaussian Smoothing
            4. Sharpening Filters
         3. Morphological Operations
            1. Erosion and Dilation
            2. Opening and Closing
            3. Structuring Elements
      3. Feature Detection and Description
         1. Edge Detection
            1. Gradient-based Methods
            2. Canny Edge Detector
            3. Sobel Operator
            4. Laplacian of Gaussian
         2. Corner Detection
            1. Harris Corner Detector
            2. FAST Corner Detector
            3. Shi-Tomasi Corner Detector
         3. Blob Detection
            1. Difference of Gaussians
            2. Laplacian of Gaussian
         4. Local Feature Descriptors
            1. SIFT
               1. Keypoint Detection
               2. Orientation Assignment
               3. Descriptor Computation
            2. SURF
               1. Hessian Matrix-based Detection
               2. Descriptor Generation
            3. ORB
               1. FAST Keypoint Detection
               2. BRIEF Descriptors
            4. HOG
               1. Gradient Computation
               2. Cell and Block Structure
               3. Normalization
      4. Classical Machine Learning for Vision
         1. Feature Engineering Pipeline
            1. Feature Extraction
            2. Feature Selection
            3. Dimensionality Reduction
         2. Classification Algorithms
            1. Support Vector Machines
               1. Linear SVM
               2. Kernel SVM
               3. Multi-class Classification
            2. Decision Trees
               1. Splitting Criteria
               2. Pruning Techniques
            3. Random Forests
               1. Bootstrap Aggregating
               2. Feature Randomness
            4. K-Nearest Neighbors
               1. Distance Metrics
               2. Curse of Dimensionality
            5. Naive Bayes
            6. Logistic Regression
         3. Clustering Algorithms
            1. K-Means Clustering
            2. Hierarchical Clustering
            3. DBSCAN
         4. Limitations of Traditional Approaches
            1. Manual Feature Engineering
            2. Scalability Issues
            3. Limited Invariance
            4. Shallow Representations
   4. Introduction to Neural Networks
      1. Biological Inspiration
         1. Neurons and Synapses
         2. Neural Processing
      2. Mathematical Foundation
         1. The Perceptron Model
            1. Linear Combination
            2. Activation Function
            3. Bias Term
            4. Decision Boundary
         2. Perceptron Learning Algorithm
            1. Weight Update Rule
            2. Convergence Properties
      3. Activation Functions
         1. Linear Activation
         2. Sigmoid Function
            1. Mathematical Definition
            2. Properties and Limitations
         3. Hyperbolic Tangent
            1. Mathematical Definition
            2. Comparison with Sigmoid
         4. Rectified Linear Unit
            1. Mathematical Definition
            2. Advantages and Disadvantages
         5. Leaky ReLU
            1. Addressing Dead Neurons
         6. Parametric ReLU
         7. Exponential Linear Unit
         8. Swish Activation
         9. Softmax Function
            1. Multi-class Classification
            2. Temperature Parameter
      4. Multi-Layer Perceptrons
         1. Network Architecture
            1. Input Layer
            2. Hidden Layers
            3. Output Layer
         2. Universal Approximation Theorem
            1. Theoretical Foundation
            2. Practical Implications
         3. Capacity and Expressiveness
      5. Training Neural Networks
         1. Forward Propagation
            1. Layer-wise Computation
            2. Matrix Operations
         2. Loss Functions
            1. Mean Squared Error
            2. Cross-Entropy Loss
            3. Custom Loss Functions
         3. Backpropagation Algorithm
            1. Chain Rule Application
            2. Gradient Computation
            3. Weight Update Process
         4. Gradient Descent Optimization
            1. Batch Gradient Descent
            2. Stochastic Gradient Descent
            3. Mini-batch Gradient Descent
         5. Advanced Optimizers
            1. Momentum
               1. Exponential Moving Average
               2. Nesterov Momentum
            2. AdaGrad
               1. Adaptive Learning Rates
            3. RMSProp
               1. Exponential Moving Average of Gradients
            4. Adam Optimizer
               1. Bias Correction
               2. Hyperparameter Selection
            5. AdamW
            6. Learning Rate Scheduling
               1. Step Decay
               2. Exponential Decay
               3. Cosine Annealing
         6. Training Challenges
            1. Vanishing Gradients
            2. Exploding Gradients
            3. Overfitting and Underfitting
            4. Local Minima and Saddle Points