Introduction to Computer Vision

Part 1: Classical 2D Image Processing (1960–1990)

Images and Basic Operations

• Lesson 1: Images as ArraysBuild and display images as NumPy arrays, grayscale and color
• Lesson 2: Image ArithmeticEdit images with arithmetic: brightening, blending, and a common overflow pitfall

Binary Images and Blob Analysis

• Lesson 3: Thresholding, Erosion, and DilationBinarize images with thresholding, then clean up noise with erosion and dilation
• Lesson 4: Flood Fill and Connected ComponentsFind and label connected blobs in a binary image with flood fill
• Lesson 5: Image MomentsSummarize a blob's shape with moments: area, centroid, and orientation
• Lesson 6: Eigenvectors and Eigenvalues of the Covariance MatrixDerive a blob's orientation and axes from its covariance matrix's eigenvectors
• Lesson 7: Distance MeasuresCompare Euclidean, Manhattan, and Mahalanobis distance on a pixel grid

Geometric Transformations

• Lesson 8: Geometric TransformationsMove, resize, and reshape images with Euclidean, similarity, and affine transforms
• Lesson 9: Image Warping, Inverse Mapping, and Bilinear InterpolationResample a warped image correctly using inverse mapping and bilinear interpolation

Convolution and Filtering

• Lesson 10: ConvolutionBuild convolution from scratch, the operation behind blurring, sharpening, and edges
• Lesson 11: Smoothing and Gaussian PyramidsBlur before downsampling to avoid aliasing, building a Gaussian pyramid
• Lesson 12: Differentiation and Edge DetectionDetect edges from image derivatives using Sobel, Prewitt, and Scharr kernels
• Lesson 13: Second Derivatives and the LaplacianFind edges as zero crossings of the second derivative with the Laplacian
• Lesson 14: Nonlinear FiltersGo beyond convolution with nonlinear filters like the median filter

Frequency-Domain Methods

• Lesson 15: The Fourier Transform and Frequency-Domain FilteringDecompose an image into sinusoids with the Fourier transform for frequency filtering
• Lesson 16: Wavelets and Gabor FiltersLocalize frequency content in space with wavelets and Gabor filters
• Lesson 17: Image Compression – Lossless and LossyCompress images losslessly and lossily by exploiting redundancy

Color and Clustering

• Lesson 18: Color SpacesCompare RGB, HSV, YCbCr, and L*a*b* color spaces and what each is good for
• Lesson 19: Clustering – k-Means, GMMs, and DBSCANGroup pixels or points into clusters with k-means, GMMs, and DBSCAN

Part 2: Classical 3D Computer Vision (1980–2010)

Correspondence and Matching

• Lesson 20: Feature Detection and MatchingDetect and match distinctive keypoints across images
• Lesson 21: Optical Flow and Motion EstimationEstimate per-pixel motion between video frames with Lucas-Kanade optical flow
• Lesson 22: Stereo MatchingRecover depth from two images by matching pixels along epipolar lines
• Lesson 23: Model Fitting, Robust Estimation, and RANSACFit models to noisy data robustly with RANSAC

Planar Geometry

• Lesson 24: Projective GeometryModel homographies, the general 2D transform a camera induces on a plane
• Lesson 25: Image Stitching and MosaickingStitch two overlapping photos into a seamless panorama

Camera Geometry and 3D Reconstruction

• Lesson 26: Image FormationDerive how a pinhole camera projects a 3D scene onto a 2D image
• Lesson 27: Camera CalibrationRecover a camera's intrinsic parameters from checkerboard images
• Lesson 28: Epipolar GeometryRelate two camera views through the epipolar constraint and fundamental matrix
• Lesson 29: Structure from MotionRecover 3D structure and camera poses from multiple 2D images

Part 3: Deep Learning for Computer Vision (2012–2022)

Neural Network Fundamentals

• Lesson 30: Projection – The Central IdeaSee classification, regression, and neurons as the same underlying linear projection
• Lesson 31: Gradient Descent and BackpropagationReplace hand-picked projections with gradient descent and backpropagation
• Lesson 32: Multi-Layer PerceptronsStack linear layers with nonlinearities to separate non-linearly-separable data
• Lesson 33: OptimizationSpeed up gradient descent with momentum, RMSProp, and Adam

Convolutional Neural Networks

• Lesson 34: Convolutional Neural Networks (CNNs)Build convolutional layers that exploit the spatial structure of images
• Lesson 35: Training a CNNTrain a CNN while diagnosing and fixing overfitting
• Lesson 36: Evaluating a ClassifierEvaluate a classifier properly with precision, recall, and confusion matrices
• Lesson 37: Classic ArchitecturesTrace CNN architecture history to the residual connection and vanishing gradients
• Lesson 38: Transfer LearningReuse a pretrained backbone to train on small, data-starved tasks
• Lesson 39: Visualizing and Understanding CNNsVisualize what a CNN "sees" with saliency maps and Grad-CAM

Detection and Segmentation

• Lesson 40: Object Detection from Sliding WindowsDetect objects by sliding a classifier window across the image
• Lesson 41: Object Detection as RegressionDetect objects by directly regressing boxes instead of sliding windows
• Lesson 42: Semantic SegmentationLabel every pixel with a class using fully convolutional networks
• Lesson 43: Instance SegmentationSeparate touching objects of the same class into distinct instances

Training at Scale

• Lesson 44: Precision and Parallel TrainingTrain faster with mixed precision and multiple GPUs

Part 4: Transformers and Foundation Models (2020–present)

Architectural Foundations

• Lesson 45: The Attention MechanismMix information across a sequence with the attention mechanism
• Lesson 46: The Transformer ArchitectureAssemble attention into the full Transformer architecture
• Lesson 47: Vision Transformers (ViT)Apply the Transformer to images by treating patches as tokens

Self-Supervised Pretraining

• Lesson 48: AutoencodersLearn compressed image representations without any labels
• Lesson 49: Masked AutoencodersPretrain by reconstructing images from mostly-masked patches
• Lesson 50: Self-Supervised and Contrastive LearningPretrain on unlabeled images with self-supervised, contrastive learning
• Lesson 51: DINO and Self-DistillationLearn visual representations through self-distillation, the idea behind DINO
• Lesson 52: Video Transformers and PretrainingExtend self-supervised pretraining from still images to video

Promptable Segmentation

• Lesson 53: Segment AnythingSegment any object on demand from a point or box prompt
• Lesson 54: Promptable Video SegmentationPropagate a promptable mask across video frames, as in SAM 2

Vision-Language and Open-Vocabulary Recognition

• Lesson 55: Vision-Language Models (VLMs)Connect images and text in a shared embedding space with CLIP
• Lesson 56: Open-Vocabulary DetectionDetect objects from arbitrary text categories, not a fixed label set
• Lesson 57: Open-Vocabulary SegmentationSegment arbitrary text concepts with pixel-accurate masks, as in SAM 3
• Lesson 58: Decoder-Only Language ModelsBuild a GPT-style decoder-only model and pin down self- vs. cross-attention
• Lesson 59: Visual Question Answering (VQA)Answer natural-language questions about an image's content

Geometric Foundation Models

• Lesson 60: Monocular Depth EstimationEstimate per-pixel depth from a single image with no stereo pair
• Lesson 61: Depth AnythingGeneralize monocular depth estimation to any image with Depth Anything
• Lesson 62: Stereo Depth with Foundation ModelsCombine classical stereo matching with a learned foundation model like FoundationStereo
• Lesson 63: Feed-Forward Camera Pose EstimationPredict camera pose directly in one pass instead of an iterative pipeline

Generative Models and Rendering

• Lesson 64: Generative and Diffusion ModelsGenerate realistic images by learning to reverse a noising process
• Lesson 65: Video Diffusion and GenerationExtend diffusion from single images to temporally consistent video
• Lesson 66: Neural Rendering and Gaussian SplattingRender novel views of a 3D scene learned from multiple images, from NeRF to Gaussian Splatting

References

Citation

If you find this material useful, please cite it as:

@misc{birchfield2026cvintro,
  author        = {Birchfield, Stan},
  title         = {Introduction to Computer Vision: Lecture Notes with Working {P}ython Code},
  year          = {2026},
  eprint        = {2609.39627},
  archivePrefix = {arXiv},
  url           = {https://arxiv.org/abs/2609.39627},
}