Complex Cells and the Representation of Local Image-Structure

Miles Hansard 1, * Radu Horaud 1
* Corresponding author
1 PERCEPTION - Interpretation and Modelling of Images and Videos
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : The receptive fields of simple cells in the visual cortex can be understood as linear filters. These filters can be modelled by Gabor functions, or by Gaussian derivatives. Gabor functions can also be combined in an 'energy model' of the complex cell response. This paper proposes an alternative model of the complex cell, based on Gaussian derivatives. It is most important to account for the insensitivity of the complex response to small shifts of the image. The new model uses a linear combination of the first few derivative filters, at a single position, to approximate the first derivative filter, at a series of adjacent positions. The maximum response, over all positions, gives a signal that is insensitive to small shifts of the image. This model, unlike previous approaches, is based on the scale space theory of visual processing. In particular, the complex cell is built from filters that respond to the 2D differential structure of the image. The computational aspects of the new model are studied in one and two dimensions, using the steerability of the Gaussian derivatives. The response of the model to basic images, such as edges and gratings, is derived formally. The response to natural images is also evaluated, using statistical measures of shift insensitivity. The relevance of the new model to the cortical image representation is discussed.
Complete list of metadatas

Cited literature [63 references]  Display  Hide  Download


https://hal.inria.fr/inria-00546779
Contributor : Miles Hansard <>
Submitted on : Tuesday, December 14, 2010 - 5:08:43 PM
Last modification on : Wednesday, April 11, 2018 - 1:58:01 AM
Long-term archiving on : Monday, November 5, 2012 - 1:41:10 PM

Files

RR-7485.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : inria-00546779, version 1

Collections

Citation

Miles Hansard, Radu Horaud. Complex Cells and the Representation of Local Image-Structure. [Research Report] RR-7485, INRIA. 2010. ⟨inria-00546779⟩

Share

Metrics

Record views

410

Files downloads

159