1. ter Haar Romeny, EMBS Berder 2004 How can we find a dense optic flow field from a motion sequence in 2D and 3D? Many approaches are taken: - gradient based (or differential); - phase-based (or frequency domain); - correlation-based (or area); - feature-point (or sparse data) tracking. Multi-scale optic flow

2. ter Haar Romeny, EMBS Berder 2004 Reichardt detector In the visual front-end retinal receptive fields are organized in pairs, tuned to a specific velocity and direction. The pairs are coupled by a delay cell, possibly the amacrine cell. Neurons act as temporal coincidence detectors This leads to a redundant representation, all velocities and directions are measured at all scales.

3. ter Haar Romeny, EMBS Berder 2004 Amacrine cells are found next to ganglion cell bodies Similar RF pairs are present in both eyes for disparity detection

4. ter Haar Romeny, EMBS Berder 2004 Calibration We generate a test sequence with a warping vector field, so we know the absolute displacement of each pixel

5. ter Haar Romeny, EMBS Berder 2004 The isophote landscape of an image changes drastically when we change our aperture size. This happens when we move away or towards the scene with the same camera. Left: observation of an image with  = 1 pix, isophotes L=50 are indicated. Right: same observation at a distance twice as far away. The isophotes L=50 have now changed.

6. ter Haar Romeny, EMBS Berder 2004 Scalar images: intensity is kept constant with the divergence Density images: intensity ‘dilutes’ with the divergence Two types of images need to be considered:

7. ter Haar Romeny, EMBS Berder 2004

8. Multi-scale optic flow constraint equation: For scalar images: For density images: The velocity field is unknown, and this is what we want to recover from the data. We like to retrieve the velocity and its derivatives with respect to x, y, z and t. We insert this unknown velocity field as a truncated Taylor series, truncated at first order.

9. ter Haar Romeny, EMBS Berder 2004 Multi-scale density flow: in each pixel 8 equations of third order and 8 unknowns:

10. ter Haar Romeny, EMBS Berder 2004 Scale selection: The condition number of the coefficient matrix exhibits an optimum over scale in many pixels, given the local density of texture.

11. ter Haar Romeny, EMBS Berder 2004 Artificially created test image sequence for validation purposes Scale selection map

12. ter Haar Romeny, EMBS Berder 2004 A. Suinesiaputra, UMCL / TUE, MICCAI 2002