#KostasVisualizations
The collection
See it. Move it. Understand it.
Interactive visual explanations for the geometry and mathematics behind modern computer vision. Each experience turns an abstract construction into something you can inspect, manipulate, and understand.
Projective Geometry
Sphere to Cubemap
Six views. One environment.
Projective Geometry
Sphere to Equirectangular Projection
Same world. Different coordinates.
Optimization
Stuck in a Bad Local Minimum?
Why local minima are rarely the problem.
Optimization
The Goldilocks Principle of Learning Rates
One number. Three very different outcomes.
Optimization
Gradient Descent
Tighten up your learning rate. We’re going down.
Calculus
Partial Derivatives
Hold one variable constant. Follow the curve. Read the slope.
Linear Algebra
Linear Systems as Geometry
Where constraints meet, solutions appear.
Projective Geometry
Stereo Rectification
From arbitrary cameras to parallel views.
Projective Geometry
Parallel Stereo
Two views. One point. One matching scanline.
Projective Geometry
Epipolar Geometry
The geometry behind stereo vision.
Computational Photography
Video as a Spacetime Volume
Where space meets time.
Projective Geometry
Planar Homography
Plane-to-plane projective mapping.
Projective Geometry
Perspective Projection
One point. One ray. One image.
Signal Processing
Steerable Filters
A Few Filters. Infinite Orientations.
Signal Processing
Correlation (aka "Convolution")
Slide. Pointwise multiply. Sum. Repeat.
Linear Algebra
2D Transformations
Geometry in motion.
Signal Processing
2D Discrete Fourier Transform
One image. Two representations.
Signal Processing
Fourier Series
Complicated Shapes. Simple Ingredients.
Calculus
Taylor Series Approximation
Local Insight. Global Impact.
Signal Processing
Signal Aliasing
High frequencies in disguise.
Computational Photography
Global vs. Rolling Shutter
One Frame. Many Moments.
Computational Photography
Dolly Zoom
Zoom In. Pull Back.
Linear Algebra
Eigenfaces
Face It: It’s Just Linear Algebra