Image Transformation

Image Transformations

Image transformations change the domain (pixel coordinates) rather than the range (pixel intensities). Transformations include translation, rotation, scaling, affine warps, and projective warps. See the detailed notes in the companion section for mathematical foundations, homogeneous coordinates, and code demos.

Image Morphing

Image morphing combines warping (geometric transformation) with cross-dissolving (intensity blending) to create smooth transitions between two images. Key steps:

  • Define corresponding feature points/lines in source and target images

  • Compute intermediate warps for each frame

  • Cross-dissolve pixel intensities at each intermediate step

Panorama

Panorama stitching aligns and blends multiple overlapping images into a single wide field-of-view composite:

  • Detect and match features across image pairs

  • Estimate homography (projective transformation) between images

  • Warp images into a common coordinate frame

  • Blend seams to produce the final panorama

High Dynamic Range (HDR)

HDR imaging captures and merges multiple exposures of the same scene to recover the full range of irradiance values:

  • Capture bracketed exposures (short → long)

  • Estimate camera response curve

  • Reconstruct radiance map

  • Apply tone mapping to display on standard monitors

Stereo

Stereo vision uses two images from slightly different viewpoints to estimate depth:

  • Find corresponding points between left and right images

  • Compute disparity (pixel offset) — inversely proportional to depth

  • Generate a depth map from disparity values

Photosynth

Photosynth (Microsoft) reconstructs 3D scenes from large collections of unstructured photographs using structure-from-motion techniques.

Extrinsic Camera Parameters

Extrinsic parameters describe the camera’s position and orientation in world coordinates:

  • Rotation matrix R (3×3): camera orientation

  • Translation vector t (3×1): camera position

  • Combined as a 3×4 matrix [R | t]

Intrinsic Camera Parameters

Intrinsic parameters describe the camera’s internal geometry:

  • Focal length (fx, fy)

  • Principal point (cx, cy) — where optical axis meets image plane

  • Skew coefficient

  • Encoded in the 3×3 camera matrix K

Camera Calibration

Camera calibration recovers intrinsic and extrinsic parameters from images of known calibration targets (e.g., checkerboard patterns) using techniques like Zhang’s method.