Biologically Motivated Computer Vision Digital Image Processing Sumitha

Biologically Motivated Computer Vision Digital Image Processing Sumitha Balasuriya Department of Computing Science, University of Glasgow

General Vision Problem • Machine vision has been very successful in finding solutions to specific, well constrained problems such as optical character recognition or fingerprint recognition. In fact machine vision has surpassed human vision in many such closed domain tasks. • However it is only in biology where we find systems that can handle unconstrained, diverse vision problems. • How can a biological or machine system which just captures two dimensional visual information from a view of a cluttered field even attempt to reason with and function in the environment? An accurate detailed spatial model of the environment is difficult to compute and the whole problem of scene analysis is ill-posed. A problem is well posed if (1) a solution exists, (2) the solution is unique, (3) the solution depends continuously on the initial data (stability property).

Ill-posed problem ? Several possible solutions exist

The general vision problem isn’t really solved in biology … • For example I can't build an accurate spatial world model of the scene I look at. . . • Biological systems have evolved to process visual data to extract just enough information to perform the reasoning for everyday tasks that are part of survival. • Visual information is combined with higher level knowledge and other sensory modalities that constrain the reasoning in the solution space and finally makes vision possible.

Visual cortex and a bit more … Direct feedback projections to V 1 originate from: V 2 (complex features) V 3 (orientation, motion, depth) V 4 (colour, attention) MT (motion) MST (motion) FEF (saccades, spatial memory) LIP (saccade planning) IT (recognition) Lower visual cortex Feedback from higher cortical areas Frontal cortex V 2, V 4, FEF, IT V 1 Face features V 1

Held and Hein, 1963 • Newborn kittens • Placed in a carousel • One active, other passively towed along • Both receive same stimulation • The actively moving kitten receives visual stimulation which results from its own movements • Only the active kitten develops sensory-motor coordination.

Conventional Computer Vision Architecture Input Feature Extraction Action Classification, Recognition, Disparity Output

The Future - Biologically Motivated Computer Vision Architecture Feedback processing Is there a square, triangle or circle? Hierarchical processing Square triangle s t Other modalities More abstract features / symbols Optical illusions Feedforward processing Lateral processing Input

Biologically Motivated Computer Vision Architectures in action Simple colour cues. Foveated sensors. Also: Learnt arm control, Learn how to act on objects http: //www. lira. dist. unige. it/babybotvideos. htm

Biologically Inspired features • Machine vision and biological vision systems process similar information (visual scenes) and perform similar tasks (recognition, targeting) • Not surprisingly the optimal features that are extracted by many machine vision system look surprising like those found in biology • But first ….

Why bother with feature extraction? • Why not use the actual image/video itself for reasoning/analysis? INVARIANCE! • The information we extract (i. e. the features) from the ‘entity’ must be insensitive to changes. • The extracted features might be invariant to rotation and scaling of objects in images, lighting conditions, partial occlusions 11

What features should we extract? • Depends…. • Modality (video/image/audio …) • Task (eg: topic categorisation/face recognition/ audio compression) • Dimensionality reduction / sparsification • Invariance vs descriptiveness If they generalise to much – everything looks just about the same If the features are too descriptive they can’t generalise to new examples As the feature we extract becomes more complex/descriptive it will also become less invariant to even minor changes in the entity that we are measuring.

Human visual pathway • Inspiration for feature extraction methodology Receptive field: area in the FOV in which stimulation leads to a response in the neuron Circularly symmetric retinal ganglion receptive fields Orientated simple cell cortical receptive fields (similar to Gabor filter)

Gabor filter • A function f(t) can be decomposed into cosine (even) and sine (odd) functions. Good for defining periodic structures. Not localised. • There is an uncertainty relation between a signals specificity in time and frequency. • Dennis Gabor defined a family of signals that optimised this trade-off • Enables us to extract local features • Daugman(1995) defined a 2 D filter based on the above which was called a Gabor filter • These filters resemble cortical simple cells

Gabor filter • Localise the sine and cosine functions using a Gabor envelope. σ Assuming symmetric Gaussian envelope Modulating cosine Modulating sine U, V v In the Fourier domain the Gabor is a Gaussian centred about the central frequency (U, V). The orientation of the Gabor in the spatial domain is u Even symmetric cosine Gabor wavelet Odd symmetric sine Gabor wavelet

Spatial Frequency Bandwidth Spatial Spectral (Fourier) • Bandwidth at half power point frequency • Bandwidth depends on symmetric Gaussian envelope’s sigma. Large sigma results in narrow bandwidth at the Gabor filter exactly filters at its central frequency. Also due to the uncertainty relation a narrow frequency bandwidth will result in reduced spatial localisation by the filter. Spatial filter profile Wide bandwidth Narrow bandwidth Even symmetric cosine Gabor wavelet Odd symmetric sine Gabor wavelet

Gabor filter with asymmetric Gaussian • • However the Gabor’s Gaussian envelope need not be circular symmetric! An elliptical spatial Gaussian envelope lets us control orientation bandwidth. Better formulation for asymmetric Gaussian envelope Spatial domain along direction of wave propagation Spectral domain fo= central frequency θ = angle γ = sigma in direction of propagation η = sigma perpendicular to direction of propagation along direction of wave propagation Fourier domain

Bandwidth of Gabor with asymmetric Gaussian Half power points Along direction of wave propagation, Perpendicular to direction of wave propagation, Spatial bandwidth in direction of wave propagation Spatial bandwidth perpendicular to wave propagation

Orientation Bandwidth • Orientation bandwidth is related to the number of orientations we want to extract. The half power points of the filters should coincide in the spectral domain. If the filter bank consists of k orientated filters, and redundancy in orientation sampling l=rθ small θ v Half power Spatial frequency bandwidth Orientation bandwidth Δθ ωo u

Orientation Bandwidth Spatial domain v Half power Spatial frequenc bandwidth Orientation bandwidth Δθ ωo Frequency domain Filter bank u

Hypercolumn • Experiments by Hubel and Weisel (1962, 1968) • A set of orientation selective units over a common patch of the FOV. • Organised as a vertical column in the visual cortex • In computational system use information in hypercolumn for higher level reasoning Only using the even symmetric component in the filter bank Feature vector

Properties of the hypercolumn feature vector • Invariance to rotation in image plane stimulation Hypercolumn responses Even symmetric detector

Cycle to canonical orientation • Invariance to rotation in image plane stimulation Cycle responses in feature vector

Properties of the hypercolumn feature vector • Invariance to scaling (i. e. spatial frequency) stimulation central frequency

Scale Invariance Feature Transform • Pandemonium model (Selfridge, 1959!) • Build ever more complex / abstract features along the hierarchy • Aggregate hypercolumn feature vectors to complex feature

SIFT features Rotate hypercolumn features to canonical of large support region Rotate descriptor canonical of large support region Complex feature vector Hypercolumn features

Recognition • Extract SIFT features at corner locations (Harris corner detector), and scale space peaks Training Recognition

Recap • Biologically motivated computer vision architecture • Feedforward, feedback, lateral processing in architecture • Hierarchical processing • Feature extraction provides information about entities which are (somewhat!) invariant to changes • Gabor filter • Hypercolumn feature vector. • SIFT features

The End