Texture and Image Pyramids

Texture and Image Pyramids

Prof. Dr. Elli AngelopoulouChair of Pattern Recognition (Computer Science 5)

Friedrich-Alexander-University Erlangen-Nuremberg

Elli Angelopoulou Texture and Image Pyramids

Texture

Texture : a repeatable pattern of small elements Stripes Brick wall

Appearance related Single leaf vs. foliage Single stripe vs. the stripes on a zebra

Texture can be formed by: The presence of a large number of small objects

Pebbles Coffee beans

Orderly patterns that look like large numbers of small elements Spots on cats Grains on wooden surfaces


Examples of Texture


Texture Filters

Sample texture filters 2 dot filters 6 bar filters

Original image

Squared response of each texture filter.


Texture Filters

Same sample texture filters 2 dot filters 6 bar filters

Original image at half size

Squared response of each texture filter.

Filtering was performed at coarser scale, since the filter size remained fixed but the image was half the size of the original.


Texture Filtering at Different Scales

Finer Scale

Enlarged coarser scale


The Gaussian Pyramid

Low-pass Pyramid First smooth an image

Downsample smoothed image, typically by a factor of two.

Repeat

Each successive layer is a low-pass filtered image of the higher resolution image.


Gaussian Pyramid Example


The Laplacian Pyramid

Band-pass Pyramid Given a Gaussian (or other lowpass) pyramid

Store the difference between adjacent levels. Lowest resolution image must be first upsampled via some form of interpolation to allow for pixel-wise difference computation.

Each successive layer stores the information lost (the error) between an expanded coarser level and its preceding finer level.

Caution: The Laplacian pyramid, does not compute the Laplacian of Gaussian (LoG) of an image.


Laplacian Pyramid Example


Shape from Texture

When the texture pattern is known, we can use its distortion to infer shape.

We can only compute the surface normals.

The sphere on the left is projected on the image plane using perspective projection. The one on the right using orthographic projection.

Texture images courtesy of J.T. Todd, L. Thaler, T.M.H. Dijkstra, J.J. Koenderink, and A.M.L. Kappers.


Sample Results of Shape from Texture

Images courtesy of A.M. Loh


Most of the material in this presentation is based on the slides by D. A. Forsyth for his book “Computer Vision - A Modern Approach”

Texture and Image Pyramids

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