Krubitzer & Kaas S1 S2

Transcription

1 Krubitzer & Kaas S1 S2 V1 V2 A1 MT

2 30 μm pia white matter Somato- Mean of Motor sensory Frontal Temporal Parietal Visual means Mouse ± ± ± ± ± ± ±6.8 Rat ± ± ± ± ± ± ±7.4 Cat ± ± ± ± ± ± ±7.7 Monkey ± ± ± ± ± ± Man ± ± ± ± ± ± mean ± s.d. Rockel AJ, Hiorns RW & Powell TP (1980) The basic uniformity in structure of the neocortex, Brain 103:

3 receptive fields mm Hubel & Wiesel 1974 cortex visual field 45º 22º. 0º 7º 10º Hubel º

4 Hubel & Wiesel 2 mm

5 Hypercolumn ~2 mm after Hubel & Wiesel 1962 ~2 mm

6 Re-routing experiments (ferret) visual auditory Sur et al.

7 5 mm 1 mm Roe et al. 1990

8 Sur et al. 1988

9 10,000 porpoise 1,000 modern human elephant blue whale Brain weight (grams) hummingbird goldfish crow eel Primates Mammals Birds ,000 10, ,000 Body weight (Kilograms) alligator Bony Fish Reptiles Crile & Quiring

10 Van Essen et al cm 2º Tootell et al Half of area V1 represents the central 10º (2% of the visual field)

11 ? Krubitzer & Kaas S1 S2 V1 V2 A1 MT

12 Lateral view of monkey brain Medial view of monkey brain Cortex unfolded Felleman and Van Essen 1991

13 Barlow 1994 "Thus the hypothesis is that the cerebral cortex confers skill in deriving useful knowledge about the material and social world from the uncertain evidence of our senses, it stores this knowledge, and gives access to it when required."

14 Finding New Associations in Sensory Data 1. Remove evidence of associations you already know about to facilitate detecting new ones. (1/f 2 and center-surround) 2. Make available the probabilities of the features currently present to determine chance expectations. (-logp, adaptation) 3. Choose features that occur independently of each other in the normal environment Choose suspicious coincidences as features to determine chance expectations or combinations of them. (lateral inhibition)... to reduce redundancy and ensure appropriate generalization. (orientation selectivity) Barlow 1994

15 Context: Previous sense data Task priorities Unsatisfied appetites Stored knowledge about environment Model of current scene New associative knowledge Sensory messages Compare and remove matches What we actually see New information about environment This cycle can be repeated Barlow 1994, fig. 1.3

16 Schematic of a Kalman Filter Time Update ( Predict ) (1) Project the state ahead ) ) x = Ax + Bu k k 1 k 1 (2) Project the error covariance ahead P = k AP k A 1 T + Q Measurement Update ( Correct ) (1) Compute the Kalman gain 1 T T K = P H HP H + R k k k (2) Update estimate with measurement z k ) ) x = x + K ) z Hx k k k k k (3) Update the error covariance P = 1 K H P k k k Initial estimates for x ) and P k 1 k 1 Welch & Bishop, fig. 1.2

17 Neighboring pixels tend to have similar values Simoncelli & Olshausen 2001

18 Neighboring pixels tend to have similar values natural image 1/f 2 Simoncelli & Olshausen 2001

19 Sophie in the Arctic Whitened : 2 G or what ctr-sur does barlow_filt3.m

20 Finding New Associations in Sensory Data (The yellow Volkswagen problem) Yes Yellow Volkswagen? No Reward? Yes No Harris 1980

21 Finding New Associations in Sensory Data (The yellow Volkswagen problem) sparse dense yellow Volkswagen cell YV red Ferrari cell combinatorial explosion Harris 1980

22 Finding New Associations in Sensory Data (The yellow Volkswagen problem) sparse dense yellow cell Y V Volkswagen cell Harris 1980

23 Finding New Associations in Sensory Data (The yellow Volkswagen problem) Reward? Yes No Reward? Yes No Yes Yellow? No Volkswagen? Yes No Harris 1980

24 Finding New Associations in Sensory Data (The yellow Volkswagen problem) sparse dense g n e k s y cell y v v cell o l a w Harris 1980

25 Y V The curve shows how statistical efficiency for detecting associations with a feature X varies with the value of a parameter defined as follows: Gardner-Medwin & Barlow 2001 Γ x =α x p x Z/ α sparseness where α x, α are the activity ratio for feature X and the average activity ratio, p x is the probability of X, and Z is the number of neurons in the subset under consideration. For instance, one could identify an association with any one of the 45 possible pairs of active neurons in a subset of 10 with an efficiency of 50% provided that the neurons were active independently, the pair caused two neurons to be active, the probability of the pair occurring was 0.1, and the average fraction active was 0.2. (From Gardner-Medwin and Barlow 1994)

26 What are the desirable properties of directly represented features?... primitive conjunctions of active elements that actually occur often, but would be expected to occur only infrequently by chance, that is, curious coincidences Gardner-Medwin & Barlow 2001

27 Sophie in the Arctic Whitened : 2 G or what ctr-sur does log 10 (#) Random Suspicious Coincidences log 10 (#) p < Line sum of 9 pixels barlow_filt3.m

28 The perfect map?

29 K L M A more useful map T T Streets Aberdeen Rd..C7 Academy St....D9 Acorn Pk....F9 Acton St..C7 Adamian Pk... C9 Adams St....D9 Addison St.. D9 Aerial St....C8 Albermarle St. D8 Alfred Rd...E9 Allen St...D9 Alpine St.....C Longwood Ave.L12

30 MBTA map

31 Linking Features: Orientation Guzmann 1968

32 Striate cortex contains a map of orientation. after Hubel & Wiesel 1962 Hypercolumn

33 Space Feature Tootell et al. 1982

34 Bosking et al. 1997

35 Tootell et al. 1982

36 Guzmann 1968 Linking Features: Orientation

37 hierarchy gain adjustment (1024 * 768)pixels * 24 bits/pixel = 18,874,368 bits edge detection invariance a) position b) sign of contrast curvature 38 points * 2 words/point * 16 bits/word = 1,216 bits compression ratio = 15,522

38 Horace Barlow 1986 Hough Transform

39

40 Horace Barlow 1986

41 V1 post. bank of STS * * MT fundus of STS 5 mm 1 mm Visual Field fovea VM * HM Tootell & Born

42 MT Up direction Down map inferior VF d m periphery fovea 1 mm superior VF Tootell & Born, unpub d