Computer Vision

Image formation and sampling

A digital image samples a scene after optics, sensor response, and image processing have transformed incoming light. Pixel coordinates are measurements in an image frame, not direct three-dimensional world positions. Sampling can lose detail or create aliasing; blur before downsampling suppresses frequencies the coarser grid cannot represent. A convolution combines neighboring pixels with a kernel. Border handling, channel order, numeric range, and integer rounding can change results even when the high-level algorithm is correct.

References: OpenCV — Camera Calibration and 3D Reconstruction

Features and matching

A feature detector chooses distinctive locations; a descriptor summarizes the appearance around a location. Matching compares descriptors, but the closest candidate can still be incorrect, particularly in repeated textures. Geometric verification adds a model-based consistency check. Separate invariance to translation, rotation, and scale from robustness to noise or illumination. A transformation that helps one task can remove useful information for another. Evaluate correspondences with representative images rather than assuming an attractive visualization means they are correct.

References: OpenCV — Camera Calibration and 3D Reconstruction

Camera models and projective geometry

The pinhole model relates a three-dimensional point to an image point using camera intrinsics and extrinsics. Intrinsics describe quantities such as focal scale and principal point; extrinsics describe the camera's pose relative to a world frame. Homogeneous coordinates express projective mappings up to nonzero scale. A homography describes a planar projective mapping under suitable scene or camera-motion assumptions. It cannot generally explain arbitrary parallax from a nonplanar scene viewed after translation.

References: OpenCV — Camera Calibration and 3D Reconstruction

RANSAC and a worked iteration estimate

RANSAC repeatedly fits a model to a minimal nondegenerate random sample, then counts data consistent with that model under a residual threshold. It is useful when correspondences contain outliers. If a model needs four points and each sampled point is independently an inlier with probability 0.5, a sample is all-inlier with probability 0.5^4 = 0.0625. Requiring 99% chance of at least one clean sample gives N >= log(0.01)/log(0.9375), or 72 iterations after rounding up. Independence and inlier-fraction assumptions matter.

References: OpenCV — Camera Calibration and 3D Reconstruction

Stereo, epipolar geometry, and motion

Two camera views constrain corresponding points through epipolar geometry. Rectification can align corresponding epipolar lines and simplify disparity search. In a simplified rectified stereo setup, depth is proportional to focal length times baseline divided by disparity, so small disparity errors can produce large depth errors for distant objects. Optical flow estimates image motion, which mixes camera movement, object movement, depth, and appearance effects. Brightness constancy is an approximation, especially under lighting changes or occlusion.

References: OpenCV — Camera Calibration and 3D Reconstruction

Segmentation, learning, and evaluation

Segmentation assigns labels to regions or pixels; recognition may assign a category to an image or object. Neural networks learn representations but still depend on training distribution, annotation quality, and a suitable objective. Separate training, validation, and test imagery by relevant groups to avoid near-duplicate leakage. Report the metric appropriate to the task: pixel accuracy may conceal failure on a small foreground object, while intersection-over-union measures overlap. Inspect failure cases involving occlusion, scale, lighting, and unfamiliar scenes.

References: OpenCV — Camera Calibration and 3D Reconstruction

Practice & worked answers

Original exercises for this guide.

Public notes & references

Course sources establish the scope above. Reference materials support the explanations; linked lecture notes and books remain with their authors.

• Carleton COMP 4102 — Fall 2026 outline ↗Course scope · Fall 2026
• OpenCV — Camera Calibration and 3D Reconstruction ↗Official library documentation
• Carleton COMP 4102 — Fall 2026 vision topic map ↗Topic map