Introduction to Regression

Regression is a fundamental supervised learning technique in machine learning that predicts continuous numerical values based on input data. Unlike classification, which assigns inputs to discrete categories (e.g., "cat" or "dog"), regression estimates quantities along a continuous scale (e.g., temperature, price, or coordinate position). This makes regression essential for applications requiring precise numerical predictions rather than categorical decisions.

In the context of computer vision and robotics, regression enables systems to predict positions, trajectories, distances, and other continuous measurements. For example, an autonomous vehicle uses regression to predict the continuous steering angle needed to follow a road, while a robotic arm uses regression to estimate the precise coordinates where it should move to grasp an object.

Classification vs Regression

The fundamental distinction between classification and regression lies in their output types:

Classification predicts discrete labels or categories. The model assigns each input to one of a predefined set of classes. For example, determining whether an image contains a cat, dog, or bird is a classification problem. The output is categorical, and performance is typically measured using accuracy, precision, recall, or F1-score.

Regression predicts continuous numerical values. The model estimates a quantity that can take any value within a range. For example, predicting the exact (x, y) pixel coordinates of a hand in an image is a regression problem. The output is numerical, and performance is measured using metrics like Mean Squared Error (MSE), Mean Absolute Error (MAE), or R-squared.

In this laboratory, we apply regression to predict the precise pixel coordinates of body parts in camera images—a problem that requires continuous predictions rather than discrete classifications.

Neural Networks for Regression

While neural networks are often associated with classification tasks, they are equally powerful for regression. The key differences when using neural networks for regression include:

Output Layer Architecture: Regression networks typically use linear activation (no activation function) in the output layer, allowing the network to produce any real-valued number. For predicting XY coordinates, the output layer has two neurons—one for the x-coordinate and one for the y-coordinate.

Loss Functions: Instead of cross-entropy loss used in classification, regression employs loss functions that measure the distance between predicted and actual continuous values. Mean Squared Error (MSE) is the most common, calculated as the average of squared differences between predictions and targets. MSE penalizes larger errors more heavily, encouraging the model to minimize significant deviations.

Evaluation Metrics: Regression performance is assessed using metrics like MSE, Root Mean Squared Error (RMSE), or Mean Absolute Error (MAE), which quantify how close predictions are to actual values in the original units of measurement.

Transfer Learning for Regression

Transfer learning—using pre-trained models as starting points—is not limited to classification. We can adapt classification models like ResNet-18 for regression tasks by modifying the final layer. A pre-trained ResNet-18 has learned to extract rich visual features from images (edges, textures, shapes, objects) through training on millions of images. These learned features are equally valuable for regression tasks.

To convert a classification model to regression, we replace the final fully connected layer. Instead of outputting class probabilities, the modified layer outputs continuous values. For XY coordinate prediction, we replace the original (512, 1000) classification layer with a (512, 2) regression layer—where the two outputs represent x and y coordinates. The rest of the network remains unchanged, allowing us to leverage the pre-trained feature extraction capabilities while adapting only the final prediction layer for our specific regression task.

Real-Time Object Tracking with Regression

Object tracking involves following the position of objects across video frames. Traditional computer vision approaches used techniques like optical flow or template matching. Modern deep learning approaches use regression to directly predict object coordinates, offering robustness to appearance changes, occlusions, and varying backgrounds.

In this laboratory, we track body parts (hands, nose, etc.) by training a regression model to predict their (x, y) pixel coordinates. The process involves three stages:

1. Data Collection: We capture camera images and manually click on the target body part (e.g., hand) in each image. The system records both the image and the clicked coordinates as a labeled training example. Collecting diverse examples with the body part in different positions, angles, and backgrounds helps the model generalize.

2. Model Training: Using the collected data, we train a regression neural network to predict coordinates from images. The model learns to identify visual patterns associated with the target body part and map them to spatial locations. Transfer learning accelerates this process by starting with pre-trained feature extractors.

3. Live Inference: Once trained, the model processes live camera frames, predicting the coordinates of the target body part in real-time. These predictions can drive robotic actions, gesture controls, or visual feedback—making the system interactive and responsive.

Coordinate Normalization

When predicting pixel coordinates, we often normalize values to improve training stability and model performance. Instead of predicting raw pixel values (e.g., x from 0 to 640), we normalize coordinates to a standard range like [-1, 1] or [0, 1]. This normalization helps the neural network learn more effectively by keeping values in a consistent range across different image resolutions.

During inference, we convert the normalized predictions back to pixel coordinates for visualization and use. For example, if the model predicts normalized coordinates (0.5, -0.2), we can convert these to actual pixel locations using the image dimensions: x_pixel = (x_norm + 1) * image_width / 2.