Transforming images

"Without a tagline since 2010"

Image transformer

This page shows some transformed images. The transformation takes a rectangular image and changes it into polar coordinates.

Here are some "before" and "after" images of the transformer at work!

Trees

Sunset

Lightning

Lake

Bruges

Los Angeles

HMS Belfast

Stonehenge

Southwark Bridge

San Diego

London

London

New Jersey

Palm trees

Giraffes

Angel of the North

Botanique, Brussels

Lake Geneva

M&Ms store, London

Palace of Fine Arts

Belgrade church

Trams

Rue Royale

Roof of Saint Marie

Office building

Saints

St Pancras

Gallery

Roof

CERN stairs

Tangles

Antwerp station

Antwerp station

The transformation

The transformation is actually a little more complicated than you might expect. Each pixel in the target image is mapped to a pixel from the source image according to:

\[ X = w \arctan\left(\frac{\sqrt{2}x-h}{\sqrt{2}y-h}\right) \] \[ Y = \frac{h-\sqrt{(\sqrt{2}x-h)^2+(\sqrt{2}y-h)^2}}{h}\arctan\left(\frac{\sqrt{2}x-h}{\sqrt{2}y-h}\right) \]

where \((X,Y)\) is the coordinate in the source image, \((x,y)\) is the coordinate in the target image and \(w\) and \(h\) are the width and height of the source image. Here is what the transformation looks like when applied to rectangular coordinates:

make_gallery_table('Grid', 'grid') ;