Computer Vision Course Outline

Зміст курсу

Computer Vision Course Outline

1. Introduction to Computer Vision

What is Computer Vision?Fundamentals of Image Processing Linear algebra for image manipulation

2. Image Processing with OpenCV

Basic Transformations Fourier Transform Low-pass and High-pass Filters Noise Reduction and Smoothing Histogram Equalization Super-Resolution Techniques Edge Detection Corner and Blob Detection

3. Convolutional Neural Networks

Introduction to Convolutional Neural Networks Convolution Layers Pooling Layers Flattening Activation Functions Overview of Popular CNN Models

Activation Functions

Why Activation Functions Are Crucial in CNNs

Activation functions introduce non-linearity into CNNs, allowing them to learn complex patterns beyond what a simple linear model can achieve. Without activation functions, CNNs would struggle to detect intricate relationships in data, limiting their effectiveness in image recognition and classification. The right activation function influences training speed, stability, and overall performance.

Common Activation Functions

ReLU (Rectified Linear Unit): the most widely used activation function in CNNs. It passes only positive values while setting all negative inputs to zero, making it computationally efficient and preventing vanishing gradients. However, some neurons may become inactive due to the "dying ReLU" problem.

f (x) = max (0, x)

Leaky ReLU: a variation of ReLU that allows small negative values instead of setting them to zero, preventing inactive neurons and improving gradient flow.

f (x) = {\begin{cases} x & , x > 0 \\ α x & , x \leq 0 \end{cases}

Sigmoid: compresses input values into a range between 0 and 1, making it useful for binary classification. However, it suffers from vanishing gradients in deep networks.

f (x) = \frac{1}{1 + e^{- x}}

Tanh: similar to Sigmoid but outputs values between -1 and 1, centering activations around zero.

f (x) = \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}}

Softmax: typically used in the final layer for multi-class classification, Softmax converts raw network outputs into probabilities, ensuring they sum to one for better interpretability.

f (x_{i}) = \frac{e^{x_{i}}}{\sum_{j}^{} e^{x_{j}}}

Choosing the Right Activation Function

ReLU is the default choice for hidden layers due to its efficiency and strong performance, while Leaky ReLU is a better option when neuron inactivity becomes an issue. Sigmoid and Tanh are generally avoided in deep CNNs but can still be useful in specific applications. Softmax remains essential for multi-class classification tasks, ensuring clear probability-based predictions.

Selecting the right activation function is key to optimizing CNN performance, balancing efficiency, and preventing issues like vanishing or exploding gradients. Each function contributes uniquely to how a network processes and learns from visual data.