What the spider s eyes don t tell the spider s brain

Depth Perception from Image Defocus in a Jumping Spider (*) Depth Perception from Image Defocus in a Jumping Spider Nagata, Koyanagi, Tsukamoto, Saeki, Isono, Shichida, Tolunaga, Kinoshita, Arikawa, and Terakita.

How to judge distance to prey? World is 3-D images are 2-D Can t determine distance monocularly Scale factor ambiguity

How to judge distance to prey? World is 3-D images are 2-D Can t determine distance monocularly Scale factor ambiguity Many depth cues Ratio image size to object size Ratio image motion to object motion...

Accomodation? (1/f = 1/a + 1/b)

Binocular stereo? (*) Jumping Spider Vision, David Hill, Wikipedia

Defocus blurring?

Defocus blurring? R PSF

Defocus blurring? 2J 1 (Rρ)/(Rρ) R PSF 3.8317 / R MTF

Multi-layer retina (*) Depth Perception from Image Defocus in a Jumping Spider Nagata, Koyanagi, Tsukamoto, Saeki, Isono, Shichida, Tolunaga, Kinoshita, Arikawa, and Terakita.

Depth from two image planes (*) Depth Perception from Image Defocus in a Jumping Spider Nagata, Koyanagi, Tsukamoto, Saeki, Isono, Shichida, Tolunaga, Kinoshita, Arikawa, and Terakita.

What s wrong with that model?

What is wrong with that model? Assumes image on back layer (L1) is always in focus But this would require accomodation; then there is no need for anything else!

What is wrong with that model? Assumes image on back layer (L1) is always in focus But this would require accomodation; then there is no need for anything else! Assumes blur on front layer (L2) depends on distance If back is in focus then the blur in front is fixed; blur in front merely reflects inter image layer spacing! Assumes amount of blur can be ascertained from image Problem is ill posed; for example: Blurry image of sharp texture same as sharp image of blurry texture!

Some possible approaches Transport of Intensity Equation (TIE) ( xy I(x,y,z) ) xyφ(x,y,z) = I(x,y,z) k z

Some possible approaches Transport of Intensity Equation (TIE) ( xy I(x,y,z) ) xyφ(x,y,z) = I(x,y,z) k z Light-field propagation

Some possible approaches Transport of Intensity Equation (TIE) ( xy I(x,y,z) ) xyφ(x,y,z) = I(x,y,z) k z Light-field propagation Deconvolution...

System model b1(x,y) E1(x,y) E(x,y) b2(x,y) E2(x,y)

Solution based on this b1(x,y) E1(x,y) b2(x,y) E(x,y) b2(x,y) E2(x,y) b1(x,y)

Solution based on this b1(x,y) E1(x,y) b2(x,y) E(x,y) b1 b2 = b2 b1 b2(x,y) E2(x,y) b1(x,y)

Doing it in parallel E(x,y) b(z) E1(x,y) b(z+d) E2(x,y) b(1+d) b(1) mag b(2+d) b(2) mag b(3+d) b(3) arg min mag b(4+d) b(4) mag

0.00 mm

0.15 mm

0.30 mm

0.45 mm

0.60 mm

0.75 mm

0.90 mm

1.05 mm

1.20 mm

Recovery of in-focus distance 4 3 2 1 0 0 1 2 3 4 5 6

Recovering the in focus image Ill-posed problem from single defocused image: P 1 (u) = P(u)M 1 (u) can t recover frequency components where M 1 (u) = 0.

Recovering the in focus image Ill-posed problem from single defocused image: P 1 (u) = P(u)M 1 (u) can t recover frequency components where M 1 (u) = 0. But with two images defocused to different degrees: P 2 (u) = P(u)M 2 (u) P 1 (u)m1 (u) + P 2(u)M2 (u) = P(u)( M 1 (u) 2 + M 2 (u) 2) works as long as, for any u, either M 1 (u) 0 or M 2 (u) 0. (actually, use Wiener filtering)

What the spider s eyes don t tell the spider s brain

Pillbox convolved with pillbox is not a pillbox 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

Calibration of lens motion f (mm) 63 62 61 60 steps 0 10 20

Lens motion from estimates of zeros in DFT mm 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1208 1209 1210 1211 1212 1213 1214 1215 1216 frame