Bernal S D_2010.pdf - University of Plymouth

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3..1. DEHSmOS AND MATHEM/mCAL FORMULATION the inference problem defined by the network (Kschischang el al. 21)01). In this thesis however, I have used Pearl's original belief propagation algorithm applied to Bayesian networks (Pearl 1988). The rationale behind this choice is that, although factor graphs can capture the same phenomena, Hayesian networks provide a more intuitive and explicit ac count of the causal relations between the variables, T believe this is crucial when modelling hierarchical object recognition in Ihe visual system from the the generative model perspective. 3.3.3.2 Combination of evidence and belief calculation The aim of behef propagation is to calculate the marginal probability of u variable X given some evidence e. The inllucnce of evidence can propagate to ntxie X either Ihrough its parent or ihrough its child nodes, thus evidence can be divided into two subsets such that. c-eÛCx (3.13) e^nex-0 (3.14) where C;t represents the evidence oftovf node X, and 6;^ represents ihc evidence below node X. This is shown in Figure 3.4. Similarly, in this section we will use the symbol e,;;^ to designate the evidence above the link (I, -> X: while e[^r^ refers to the evidence below the link Uj —> X. The probability of a node X given some evidence e, i.e. P(xle), is usually referred to as the posterior probability, P'iX), or the belief. Bel{X). Taking into account all the above, as well a-s Bayes rule (Equation (3.8)), we can write, 85
.1.3. DERNrnON AmMAnWMATtCAL FORMULATION Figure 3.4: Message passing in belief propagation in a Bayesian network. Node X receives all hotioni-up messages A^, (.V),...,ACM(.V) from its ciiildrcn. and all lup-dnwn messages jrx(i/;),.••,%("«} from ils parents. The belief can ihen be calculated by combining all boitom-up evidence ej( and lop-down evidence ej. Node X generates outgoing messages Ax(ui),..,^;f(wjv) for ils parent nodes, and messages 'tj(-v),-.,?iCM{
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A cortical model of object percepti
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A cortical model of object percepti
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Contents Ab.stract V AcknowlcdRcnie
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4.7 Original contrihutions in this
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3.9 Example of belief propagation i
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5.19 SI and CI model responses to a
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XVI
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2009 Durabernal S. Wennekers T, Den
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J.I. OVERVIEW retinal stimulation (
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J.2. MAIN CONTRfBUTlONS • A revie
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2,1. OBJECT RECOGNITION ihe princip
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2.1. OBJECT REC(JGNmON The dorsal s
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2.1. OBJECT RECOGNJTION properties
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2.1. OBJECT RECOGNITION of input em
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2.1. OBJEOTRBCXiGNrnON ta) u I/I ^.
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2.1. OBJECT RECOGNITION 2.1.2.1 HMA
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2.1. OBJECT RECnCNmON unit will be
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2.1. OBJECT REC(X}NIT!ON tivity, st
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2.1. OBJECT RECOGNITION response fr
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2.2. HSGH-LEVEL FEEDBACK feature an
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2.2. HIGH-LEVEL FEEDBACK Thirdly, p
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2.2. mCH-LBVEL FEEDBACK Kandom 2 LO
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1.2. HIGH-LEVEL FEEDBACK « 70 U M
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2.2. HIGH-LEVEL FEEDBACK D Receptiv
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Page 55 and 56: 2.2. HIGH-LEVEL FEEDBACK activity g
Page 57 and 58: 2.2. HIGH-LEVEL FEEDBACK task, such
Page 59 and 60: 2.2. HIGH'lMîm,_WEDBACK 2004), and
Page 61 and 62: 2.2. HIGH-LEVEL FEEDBACK However, t
Page 63 and 64: 2.2. HIGH-LEVEL FEEDBACK sizes that
Page 65 and 66: 2.3. ILLUSORY AND OCCLUDED CONTOURS
Page 79 and 80: 2.3. a.LVSORY AND OCCLUDED CONTnURS
Page 81 and 82: 2.4. ORIGINAL CONTRIBUTIONS IN THIS
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Page 87 and 88: 3.1. THE BAYESJAN BRAIN HYPOmESIS T
Page 89 and 90: 3.2. EVIDENCE FROM THE BRAIN ity in
Page 91 and 92: 3.3. DEFINITION AND MATHEMATlCACPOR
Page 93 and 94: 3.3. DEFINITION AND MATHEMATICAL FO
Page 95 and 96: XX DEFINITION AND MATHEMATICAL FORM
Page 97 and 98: .1,3. DEHNITION AND MATHEMATICAL FO
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Page 115 and 116: 3.3. OmNmON AND MATHEMATSOALFORMVLA
Page 117 and 118: 3.3. DEFlNmON AND MATHEMATICAL FORM
Page 119 and 120: 3 J. DEFINITION AND MATHEMATICAL f-
Page 123 and 124: 3.3. D^JmnON AND MATHEMATICAL F0RMU
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Page 127 and 128: 3.3. DEFINITION AND MATHEMATICAl. F
Page 129 and 130: 3J. DEFINITION AND MATHEMATICAL FOR
Page 131 and 132: 3.4. EXISTING MODELS is on models t
Page 133 and 134: .1.4. EXISTING MODELS Figure J. 10:
Page 135 and 136: 3.4. EXISTING MODELS the node encod
Page 137 and 138: 3.4. EXISTING MOOm^ Type of f>raph
Page 139 and 140: 3.4. EXISTING MODELS The model comp
Page 141 and 142: X4. EXISTING MODELS ;v 1,1 gi (8>^8
Page 143 and 144: 3A. EXISTING MODELS proposes a triv
Page 145 and 146: 3.4. EXISTING MODELS by the higher
Page 147 and 148: 3.4. EXISTING MODELS aleni lo findi
Page 149 and 150: 3.4. EXISTING MODELS Model Epshtein
Page 151 and 152: 3.4. EXISTING MODELS Fristonelal. 2
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3.4. EXISTING MODELS Oulgoing teedl
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3.5. ORIGINAL CONTRIBUTIONS IN THIS
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4.1 HMAX AS A BAYESIAN NETWORK 4.1
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4.1. HMAX AS A BAYBSIAN NETWORK ini
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4.1. HMAX AS A BAYESIAN NETWORK fea
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4.1. HMAX AS A BAYESIAN NETWORK S3
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4.1. HMAX AS A BAYESIAN NETWORK Nod
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4.2. ARCHITECTURES 4.2 Architecture
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4,2. ARCHITECTURES S3 C2 1 node Kj,
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4.2. ARCmm^TVRES S3 I C2 s f S2 o o
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4.2. ARCHITECTURES S4 f C3 S3 I C2
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4.3. LEARNING 4.3.2 S1-C1 CRTs The
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4.3. LEARNING Weight matrix applied
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4.3. LEARNING CI group -1 •B •
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4.3. LEARNING 2. The list of select
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4.3. LEARNING node=«. Therefore, t
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4.3. LEARNING 4.3.4 S2-C2CPTS The w
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4.3. WARNING 60 S3 tealures (object
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4.4. FEEDFORWARD PROCESSING (he sim
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4.4. FEEDFORWARD PROCFSSING Figure
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4.5. FEEDBACK PROCESSING is proport
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4.5. F^mSACK PRCKESSING n^ (U,) i^(
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4.5. FEEDBACK PfiOCESSWG t.(VJ,) ji
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4.5. {REDBACK PROCESSING true vs. r
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4.5. FEEDBACK PROCES.SING 4.5.3.2 D
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4.5. FEEDBACK PROCESSING evidence i
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4.6. SUMMARY OF MODEL APPROXIMATION
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5,1. FEEDFORWARD PROCESSING using t
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5.L FEEDFORWARD PROCESSING Slate =
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5.1. FEEDFORWARD PROCESSING 1^ Onem
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5.1. FEEDFORWARD PROCESSING j • H
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5.1. FEEDFORWARD PROCESSING 5.1.2 O
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5.1. FEEDFORWARD PROCESSING Normal
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5.1. FEEDFORWARD PROCESSING c g ra
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5-1. FEEDFORWARD PROCESSING 4 5 Non
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5.1. FEEDFORWARD PROCESSING 100 8 9
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S.i. FEEDFORWARD PnOCESSING 5.1.2.4
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5.2. FEEDBACK-MEDIATED ILLUSORY CON
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5.2. FEEDBACK MEDIATED ILLUSORY CON
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5.2. FEiiDBACK-MEDWTHD ILLUSORY CON
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5.2. FEEDBACK MEDIATED ILLUSORY CON
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5.2. FEEDBACK-MHDIATED ILLUSORY CON
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5.2. FEEDBACK'MEDIATED ILLUSORY CON
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5.2. FEEDBACK-MEDIATED ILLVSORY CON
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.5.2. FEEDBACK-MEDIATED ELUSORY CON
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5.2. FEEDBACK-MEDIATED SILUSORY CON
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5.2. FEEDBACK-MEDIATED ILLUSORY CON
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6.1. ANALYSIS OF RESULTS dence and
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6.1. ANALYSIS OF RESULTS The graph
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6.t. ANALYSIS OF RESULTS used 10 co
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6.1. ANALYSIS OF RF.SULTS the image
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6.1. ANALYSIS OF RESULTS feedback w
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6.1. ANALYSIS OF RESULTS over lime.
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6.1. ANALYSIS OF RESULTS 6.1.2.5 Fe
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6.1. ANALYSIS Ot RESULTS step. Alth
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6.1. ANALYSIS OF RESULTS operations
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6.J. ANALYSIS OFRBSULTS model could
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6.1. ANALYSIS OF RESULTS Alternativ
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6.2. COMPARISON WITH EXPERIMENTAL B
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6.3. COMPARISON WITH PRKVIOUS MODBL
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6.4. FUTURE WORK to temporal contex
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6.5. CONCLUSIONS AND SUMMARY OF CON
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6.5. CONCLUSIONS AND SUMMARY OF CON
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• The HTM paliems correspond lo t
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268
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270
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Bolz, J.& Gilbert, CD. (1986), CJcn
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Friston, K. & Kiebel, S. (2009). 'C
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Hoffman. K. L. & Lngothetis, N K. (
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Lanyon. L. & Denham. S. (2(X)9), 'M
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Murray, M. M.. Wylie. G, R., Higgin
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Reynolds, J. H. &, Chelazzi, L. (20
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Stanley. D. A. & Rubin, N. (2003),
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