Gaze Estimation from Low Resolution Images Insensitive to Segmentation Error

Σχετικά έγγραφα
[2], [3], [8], [20] [4] [6], [18] [1], [11], [19] [13] [10] N SVD PCA N SVD Vasilescu Vasilescu N SVD [14] [17] Y Li [7] Y Li N SVD [12] 2,,,,, 596

HOSVD. Higher Order Data Classification Method with Autocorrelation Matrix Correcting on HOSVD. Junichi MORIGAKI and Kaoru KATAYAMA

Detection and Recognition of Traffic Signal Using Machine Learning

ΕΥΡΕΣΗ ΤΟΥ ΔΙΑΝΥΣΜΑΤΟΣ ΘΕΣΗΣ ΚΙΝΟΥΜΕΝΟΥ ΡΟΜΠΟΤ ΜΕ ΜΟΝΟΦΘΑΛΜΟ ΣΥΣΤΗΜΑ ΟΡΑΣΗΣ

n 1 n 3 choice node (shelf) choice node (rough group) choice node (representative candidate)

Bundle Adjustment for 3-D Reconstruction: Implementation and Evaluation

3: A convolution-pooling layer in PS-CNN 1: Partially Shared Deep Neural Network 2.2 Partially Shared Convolutional Neural Network 2: A hidden layer o

Buried Markov Model Pairwise

Schedulability Analysis Algorithm for Timing Constraint Workflow Models

An Automatic Modulation Classifier using a Frequency Discriminator for Intelligent Software Defined Radio

[4] 1.2 [5] Bayesian Approach min-max min-max [6] UCB(Upper Confidence Bound ) UCT [7] [1] ( ) Amazons[8] Lines of Action(LOA)[4] Winands [4] 1

GPU. CUDA GPU GeForce GTX 580 GPU 2.67GHz Intel Core 2 Duo CPU E7300 CUDA. Parallelizing the Number Partitioning Problem for GPUs

Speeding up the Detection of Scale-Space Extrema in SIFT Based on the Complex First Order System

Mapping Textures on 3D Geometric Model Using Reflectance Image

[1] DNA ATM [2] c 2013 Information Processing Society of Japan. Gait motion descriptors. Osaka University 2. Drexel University a)

Ανάκτηση Εικόνας βάσει Υφής με χρήση Eye Tracker

MIDI [8] MIDI. [9] Hsu [1], [2] [10] Salamon [11] [5] Song [6] Sony, Minato, Tokyo , Japan a) b)

Anomaly Detection with Neighborhood Preservation Principle

Identifying Scenes with the Same Person in Video Content on the Basis of Scene Continuity and Face Similarity Measurement

Fourier transform, STFT 5. Continuous wavelet transform, CWT STFT STFT STFT STFT [1] CWT CWT CWT STFT [2 5] CWT STFT STFT CWT CWT. Griffin [8] CWT CWT

Optimization, PSO) DE [1, 2, 3, 4] PSO [5, 6, 7, 8, 9, 10, 11] (P)

Development of a Seismic Data Analysis System for a Short-term Training for Researchers from Developing Countries

Evolution of Novel Studies on Thermofluid Dynamics with Combustion

ΤΕΙ ΘΕΣΣΑΛΙΑΣ. Αναγνώριση προσώπου με επιλογή των κατάλληλων κυρίων συνιστωσών. ΤΜΗΜΑ ΜΗΧΑΝΙΚΩΝ ΠΛΗΡΟΦΟΡΙΚΗΣ Τ.Ε ΚΑΒΒΑΔΙΑ ΑΛΕΞΑΝΔΡΟΥ.

Development of a Tiltmeter with a XY Magnetic Detector (Part +)

Technical Research Report, Earthquake Research Institute, the University of Tokyo, No. +-, pp. 0 +3,,**1. No ,**1

Current Status and Future Prospects of Camera-Based Character Recognition and Document Image Analysis

High order interpolation function for surface contact problem

A research on the influence of dummy activity on float in an AOA network and its amendments

CSJ. Speaker clustering based on non-negative matrix factorization using i-vector-based speaker similarity

IPSJ SIG Technical Report Vol.2014-CE-127 No /12/6 CS Activity 1,a) CS Computer Science Activity Activity Actvity Activity Dining Eight-He

Adaptive grouping difference variation wolf pack algorithm

No. 7 Modular Machine Tool & Automatic Manufacturing Technique. Jul TH166 TG659 A

Yoshifumi Moriyama 1,a) Ichiro Iimura 2,b) Tomotsugu Ohno 1,c) Shigeru Nakayama 3,d)

A Study on Segmentation of Artificial Grayscale Image for Vector Conversion

(Υπογραϕή) (Υπογραϕή) (Υπογραϕή)

Control Theory & Applications PID (, )

Robust Feature Extraction Method Based on Run-Length Compensation for Degraded Character Recognition

ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΣΧΟΛΗ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΜΗΧΑΝΙΚΩΝ ΥΠΟΛΟΓΙΣΤΩΝ

Resurvey of Possible Seismic Fissures in the Old-Edo River in Tokyo

Simplex Crossover for Real-coded Genetic Algolithms

Stabilization of stock price prediction by cross entropy optimization

Retrieval of Seismic Data Recorded on Open-reel-type Magnetic Tapes (MT) by Using Existing Devices

: Monte Carlo EM 313, Louis (1982) EM, EM Newton-Raphson, /. EM, 2 Monte Carlo EM Newton-Raphson, Monte Carlo EM, Monte Carlo EM, /. 3, Monte Carlo EM

ER-Tree (Extended R*-Tree)

ES440/ES911: CFD. Chapter 5. Solution of Linear Equation Systems

Free-viewpoint Video Rendering in Large Outdoor Space such as Soccer Stadium based on Object Extraction and Tracking Technology

Quantitative chemical analyses of rocks with X-ray fluorescence analyzer: major and trace elements in ultrabasic rocks

Ι ΑΚΤΟΡΙΚΗ ΙΑΤΡΙΒΗ. Χρήστος Αθ. Χριστοδούλου. Επιβλέπων: Καθηγητής Ιωάννης Αθ. Σταθόπουλος

ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ ΕΠΑΝΑΣΧΕΔΙΑΣΜΟΣ ΓΡΑΜΜΗΣ ΣΥΝΑΡΜΟΛΟΓΗΣΗΣ ΜΕ ΧΡΗΣΗ ΕΡΓΑΛΕΙΩΝ ΛΙΤΗΣ ΠΑΡΑΓΩΓΗΣ REDESIGNING AN ASSEMBLY LINE WITH LEAN PRODUCTION TOOLS

Supplementary Materials for Evolutionary Multiobjective Optimization Based Multimodal Optimization: Fitness Landscape Approximation and Peak Detection

Study on Re-adhesion control by monitoring excessive angular momentum in electric railway traction

Nov Journal of Zhengzhou University Engineering Science Vol. 36 No FCM. A doi /j. issn

Πτυχιακή Εργασι α «Εκτι μήσή τής ποιο τήτας εικο νων με τήν χρή σή τεχνήτων νευρωνικων δικτυ ων»


ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. «Προστασία ηλεκτροδίων γείωσης από τη διάβρωση»

VSC STEADY2STATE MOD EL AND ITS NONL INEAR CONTROL OF VSC2HVDC SYSTEM VSC (1. , ; 2. , )

Bayesian Discriminant Feature Selection

1 (forward modeling) 2 (data-driven modeling) e- Quest EnergyPlus DeST 1.1. {X t } ARMA. S.Sp. Pappas [4]

Echo path identification for stereophonic acoustic echo cancellation without pre-processing

Quick algorithm f or computing core attribute

Estimation of stability region for a class of switched linear systems with multiple equilibrium points

Approximation of distance between locations on earth given by latitude and longitude

A Method for Creating Shortcut Links by Considering Popularity of Contents in Structured P2P Networks

Probabilistic Approach to Robust Optimization

Newman Modularity Newman [4], [5] Newman Q Q Q greedy algorithm[6] Newman Newman Q 1 Tabu Search[7] Newman Newman Newman Q Newman 1 2 Newman 3


Development of the Nursing Program for Rehabilitation of Woman Diagnosed with Breast Cancer

GPGPU. Grover. On Large Scale Simulation of Grover s Algorithm by Using GPGPU

Area Location and Recognition of Video Text Based on Depth Learning Method

Presentation Structure

A Determination Method of Diffusion-Parameter Values in the Ion-Exchange Optical Waveguides in Soda-Lime glass Made by Diluted AgNO 3 with NaNO 3

Correction of chromatic aberration for human eyes with diffractive-refractive hybrid elements

Design and Fabrication of Water Heater with Electromagnetic Induction Heating

Gemini, FastMap, Applications. Εαρινό Εξάμηνο Τμήμα Μηχανικών Η/Υ και Πληροϕορικής Πολυτεχνική Σχολή, Πανεπιστήμιο Πατρών

Δυσκολίες που συναντούν οι μαθητές της Στ Δημοτικού στην κατανόηση της λειτουργίας του Συγκεντρωτικού Φακού

Gait Identification Using a View Transformation Model in the Frequency Domain

Διπλωματική Εργασία. Του φοιτητή του Τμήματος Ηλεκτρολόγων Μηχανικών και Τεχνολογίας Υπολογιστών της Πολυτεχνικής Σχολής του Πανεπιστημίου Πατρών

Reaction of a Platinum Electrode for the Measurement of Redox Potential of Paddy Soil

Automatic extraction of bibliography with machine learning

Development of a basic motion analysis system using a sensor KINECT

An Advanced Manipulation for Space Redundant Macro-Micro Manipulator System

ΔΗΜΟΚΡΙΤΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΡΑΚΗΣ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΑΓΩΓΗΣ

IMES DISCUSSION PAPER SERIES

«ΑΝΑΠΣΤΞΖ ΓΠ ΚΑΗ ΥΩΡΗΚΖ ΑΝΑΛΤΖ ΜΔΣΔΩΡΟΛΟΓΗΚΩΝ ΓΔΓΟΜΔΝΩΝ ΣΟΝ ΔΛΛΑΓΗΚΟ ΥΩΡΟ»

Indexing Methods for Encrypted Vector Databases

Efficient Top-k Search for Random Walk with Restart

Arbitrage Analysis of Futures Market with Frictions

Research on real-time inverse kinematics algorithms for 6R robots

A Method for Detection of Occlusal Position Using a Robust Estimator

MOTROL. COMMISSION OF MOTORIZATION AND ENERGETICS IN AGRICULTURE 2014, Vol. 16, No. 5,

CLIMATE CHANGE IMPACTS ON THE WATER BALANCE OF SMALL SCALE WATER BASINS

ΕΛΕΓΧΟΣ ΤΩΝ ΠΑΡΑΜΟΡΦΩΣΕΩΝ ΧΑΛΥΒ ΙΝΩΝ ΦΟΡΕΩΝ ΜΕΓΑΛΟΥ ΑΝΟΙΓΜΑΤΟΣ ΤΥΠΟΥ MBSN ΜΕ ΤΗ ΧΡΗΣΗ ΚΑΛΩ ΙΩΝ: ΠΡΟΤΑΣΗ ΕΦΑΡΜΟΓΗΣ ΣΕ ΑΝΟΙΚΤΟ ΣΤΕΓΑΣΤΡΟ

Vol. 31,No JOURNAL OF CHINA UNIVERSITY OF SCIENCE AND TECHNOLOGY Feb

Kernel Methods and their Application for Image Understanding

2D23D. Seamless 2D23D Texture Mapping , : (1) ; (2) 1 ( LI Xiaolan 2),3) ZHA Hongbin 3)

Conductivity Logging for Thermal Spring Well

Improvement of wave height forecast in deep and intermediate waters with the use of stochastic methods


ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΓΗΑΣΜΖΜΑΣΗΚΟ ΠΡΟΓΡΑΜΜΑ ΜΔΣΑΠΣΤΥΗΑΚΩΝ ΠΟΤΓΩΝ «ΤΣΖΜΑΣΑ ΔΠΔΞΔΡΓΑΗΑ ΖΜΑΣΩΝ ΚΑΗ ΔΠΗΚΟΗΝΩΝΗΩΝ» ΣΜΖΜΑ ΜΖΥΑΝΗΚΩΝ Ζ/Τ ΚΑΗ ΠΛΖΡΟΦΟΡΗΚΖ

Transcript:

(MIRU2005) 2005 7 153 8505 4 6 1 E-mail: {onoy,takahiro,ysato}@iis.u-tokyo.ac.jp appearance-based methods SVDSingular Value Decomposition N-mode SVD N-mode SVD, PCAPrincipal Component Analysis appearance-based method, N-modeSVD Gaze Estimation from Low Resolution Images Insensitive to Segmentation Error Yasuhiro ONO, Takahiro OKABE, and Yoichi SATO Institute of Indusctiral Science, The University of Tokyo 4 6 1, Meguro-ku, Tokyo, 153 8503 Japan E-mail: {onoy,takahiro,ysato}@iis.u-tokyo.ac.jp Abstract We propose an appearance-based method for estimating gaze directions from low resolution images. In estimation of gaze directions from low resolution images, there exist inevitable errors in segmentation of eye regions. To improve the accuracy of gaze estimation, two key ideas are introduced in our method: using a set of training images of eye regions with artificially added segmentation error, and using N-mode singular value decomposition in order to treat image variation due to different gaze directions and segmentation errors separately. In this paper, we describe the details of our proposed method and report experimental results demonstrating the advantage of our method over the conventional PCA-based method. Key words gaze estimationlow resolutionappearance-based methodsegmentation, N-mode SVD 1.,, model-based methods appearance-based methods model-based methods [2], [3], [7], [17] [4], [5], [15] 96

model-based methods 3 model-based methods appearance-based methods [1], [9], [16] [10] 3 appearance-based methods Appearance-based methods [6], N-mode SVD [11][14] SVDSingular Value Decomposition N-mode SVD Vasilescu N-mode SVD [12] N-mode SVD PCAPrincipal Component Analysis 2 N-mode SVD 3 4 2.,,, N-mode SVD [11],,,,,,, N-mode SVD, 2. 1 N-mode SVD N-mode SVD [11] N-mode SVD N,,,,, 3-mode SVD 1 2 3 4 5,,, 3 2. 1. 1 3 3 3 D ijk i(1< = i< = I),j(1< = j< = J),k(1< = k< = K), 97

, 2. 1. 2 3,, SVD SVD, 2, i(1< = i< = I) j(1< = j< = J) 2 D ij, D ij D ij = U gazeσv pixel SVD, U gaze V pixel 3-mode SVD 3 D ijk SVD,, SVD, D ijk,,, i D i(kj) (gaze) R I KJ D i(kj) (gaze) =[D ij1, D ij2, D ij3,..., D ijk] (1) D ij1, D ij2, D ij3,..., D ijk D ijk () (A 1) (A 2) 2. 1. 3 D ijk SVD D i(kj) (gaze) SVD D i(kj) (gaze) =U gazeσ gazev gaze (2) [ def U gaze = u (1) gaze, u (2) gaze, u (3) gaze u (I) gaze u (i) gaze R I (1< = i< = I),u (i) gaze,u gaze u (j) cut R J (1< = j< = J) u (k) pixel RK (1< = k< = K) () (A 4) (A 6) 2. 1. 4 ] (3) u (i) gaze, u (j) cut, u (k) pixel D ijk D ijk = I J K i=1 j=1 k=1 Z ijk u (i) gazeu (j) cutu (k) pixel (4) Z ijk R I J K D = Z U gaze U cut U pixel (5) Z = D Ugaze Ucut Upixel 2. 1. 5 N-mode SVD, gaze(i)(1< = i< = I) c gaze(i) U gaze ( 2. ) U gaze def =[c gaze(1), c gaze(2), c gaze(3),..., c gaze(i) ] (6) gaze(i) cut(1< = cut< = J) d gaze(i),cut, c gaze(i) ( 2. ) c gaze(i) = ( B cut (gaze) ) 1 dgaze(i),cut (7), d gaze(i),cut ( B cut (gaze) ) 1, c gaze(i) 2. 2 1 2 3 1 PC 2, 2. 1. 1 D ijk, (1), D i(kj) (gaze) (2) (6) c gaze(i). 3 (A 14) ( Bcut (gaze) ) 1 (0 < = cut< = J) ( B cut (gaze) ) 1 ( ) = D 1 cut (gaze) U gaze (8),. 2. 3 98

, 1 2 3 1, 2 m n d mn ( B cut (gaze) ) 1 cut(0< = j< = J) c m(cut) c m(cut) = ( B cut (gaze) ) 1 dmn (9) c m(cut) m m c m(cut) cut cut ( B cut (gaze) ) 1 3, gaze cut (gaze,cut) =arg min gaze,cut c m(cut) c gaze 2 (10) (gaze,cut) =(gaze(1),cut(1)) c gaze(1) gaze(1) c m(cut(1)), cut(1) cut(1) 2 3 2 3 gaze(2),gaze(3) 2 3 c gaze(1), c gaze(2), c gaze(3) 3 3, 2 3 ɛ = c m(cut(1)) w ic gaze(i) 2 (11) i=1 3 wi< i=1 = 1 0 < = w i < = 1(i =1, 2, 3) g(test) 3 g(test) = w ig(i) (12) i=1 g(i)(0< = i< = I) 3 c gaze(i) 3.. 3. 1,, [8], 3. 2. 2 3 IEEE1394 (Point Grey Research Flea) 3 1,, PC(OS: Windows XPCPU: Intel Pentium4 3.0GHz), 1280 1024 18 50cm, 3. 2 1 2 3. 3. 2. 1 1 1 1, 30, 1 50, 144 144 2 1 99

3 4 1 () () 5 2 3. 2. 2, (144 144 ), (144 144 ) 72 72 36 36,, [8] 1 ( 3 ) 1 36 36 72 72 144 144 1 2 4 2,, 2 81, 1 2 4 3 3 4144 144 72 72 36 36 48 16 24 812 4,,,, 30 30 81 6 30 81 = 2430 50 50 81 = 4050, 5., 12 4=48. 5 x, y, 5,,., 6. 6 3. 2. 3,. 2. 2 c ( gaze(i) Bcut (gaze) ) 1., 2. 3 c m(cut). 3. 3,3-mode SVD,3-mode SVD PCA 3-mode SVD, 7. 3 3 7 1,2,3,... 100

7 9 8 10 7 1,2,3,...., 7 x, y, z 3 3 7,3. 3. 3. 1 3-mode SVD PCA 8. 12 4=48,24 8 = 192,48 16 = 768 3, 8, 3-mode SVD PCA.,.,, PCA 3. 3. 3. 2 3-mode SVD PCA 9., 12 4 9,3 6., 3-mode SVD PCA. 3. 3. 3 3-mode SVD PCA 10. 10, 3. 2. 2., 12 4 10 3-mode SVD PCA. 3-mode SVD PCA 10. 10 3-mode SVD PCA. 4. appearance-based methods,,,n-mode SVD N-mode SVD PCA, 101

C2 13224051 [1] S. Baluja and D. Pomerleau, Non-intrusive gaze tracking using artificial neural networks, CMU CS Technical Report, CMU-CS-94-102, 1994. [2] D. Beymer and M. Flickner, Eye Gaze Tracking Using an Active Stereo Head, In Proc. IEEE CVPR 2003, pp. II- 451-458, 2003. [3] T. Hutchinson, K. White, JR., W. Martin, K. Reichert, and L. Frey, Human-Computer Interaction Using Eye-Gaze Input, IEEE Trans. SMAC, Vol. 19, No. 6, pp. 1527-1534, 1989. [4] T. Ishikawa, S. Baker, I. Matthews, and T. Kanade, Passive Driver Gaze Tracking with Active Appearance Models, In Proc. WCITS 2004, 2004. [5] Y. Matsumoto and A. Zelinsky, An algorithm for real-time stereo vision implementation of head pose and gaze direction measurement, In Proc. IEEE FG 2000, pp. 499-504, 2000. [6],,,,,, Vol. J64-D, No.3, pp. 276-283, 1981. [7] T. Ohno and N. Mukawa, A Free-head, Simple Calibration, Gaze Tracking System That Enables Gaze-Based Interaction, In Proc. ACM ETRA 2004, pp. 115-122, 2004. [8] Kenji Oka, Yoichi Sato, Yasuto Nakanishi, and Hideki Koike, Head pose estimation system based on particle filtering with adaptive diffusion control, In Proc. IAPR MVA 2005, pp.586-589, 2005. [9] R. Stiefelhagen, J. Yang, and A. Waibel, Tracking Eyes and Monitoring Eye Gaze, In Proc. WPUI, 1997. [10] K. Tan, D. Kriegman, and N. Ahuja, Appearance-based EyeGazeEstimation, InProc. IEEE WACV, pp. 191-195, 2002. [11] M. A. O. Vasilescu and D. Terzopoulos, Multilinear Analysis of Image Ensembles: TensorFaces, In Proc. ECCV 2002, pp. 447-460, 2002. [12] M. A. O. Vasilescu and D. Terzopoulos, Multilinear Image Analysis for Facial Recognition, In Proc. IAPR ICPR 2002, pp. II-20511-20514, 2002. [13] M. A. O. Vasilescu, Human Motion Signatures: Analysis, Synthesis, Recognition, In Proc. IAPR ICPR 2002, pp. III-30456-30460, 2002. [14] M. A. O. Vasilescu and D. Terzopoulos, TensorTextures: Multilinear Image-Based Rendering, In Proc. ACM SIG- GRAGH 2004, Vol. 23, No. 3, pp. 336-342, 2004. [15] J. Wang, E. Sung, and R. Venkteswarlu, Eye gaze Estimation from a Single Image of One Eye, In Proc. IEEE ICCV 2003, pp. I-136-143, 2003. [16] L. Xu, D. Machin, and P. Sheppard, A Novel Approach to Real-time Non-intrusive Gaze Finding, In British Machine Vision Conference, 1998. [17] D. Yoo and M. Chung, Non-intrusive Eye Gaze Estimation without Knowledge of Eye Pose, In Proc. IEEE FG 2004, pp. 785-790, 2004. 1. 3 D ijk D j(ik) (cut) =[D 1jk, D 2jk,..., D Ijk ] (A 1) D j(ik) (cut) R J IK 3 D ijk D k(ji) (pixel) =[D k1i, D k2i,..., D kji ] (A 2) D k(ji) (pixel) R K JI D j(ik) (cut) SVD D j(ik) (cut) =U cutσ cutv cut U cut = [ ] u (1) cut, u (2) cut, u (3) cut,..., u (J) cut (A 3) (A 4) u (j) cut R J U cut R J J D k(ji) (pixel) SVD D k(ji) (pixel) =U pixel Σ pixel V pixel U pixel = [ ] u (1) pixel, u(2) pixel, u(3) pixel,..., u(k) pixel (A 5) (A 6) u (k) pixel RK U pixel R K K 2. B B def = Z U cut U pixel (A 7) 3 D D = B U gaze D N N N N [11] D = Z U 1 U 2 U N (A 8) D n D(n) [11] D(n) =U nz(n)(u n+1 U n+2 U N U 1 U n 1), 3 D N =3,n=1 D(gaze) =U gazez(gaze)(u cut U pixel ) (A 10) = U gazeb(gaze) (A 11) D(gaze) (A 9) 102

D i(kj) (gaze) =[D ij1, D ij2,..., D ijk] (A 12) j = cut D ijk D i(k,cut) (gaze) =[D i,cut,1, D i,cut,2,..., D i,cut,k] (A 13) i ( J ) c i = j=1 cij /J 2. 3 D cut(gaze),b cut(gaze) j = cut B, (A 11), D cut(gaze) =U gazeb cut(gaze) (A 14), c gaze(i) R I (1< = i< = I) U gaze def =[c gaze(1), c gaze(2),..., c gaze(i) ] (A 15), d gaze(i),cut R K (1< = i< = I) D cut(gaze) def =[d gaze(1),cut, d gaze(2),cut,..., d gaze(i),cut ] (A 16), d gaze(i),cut, gaze(i), cut (A 15) (A 16), (A 14) c gaze(i) = ( B cut (gaze) ) 1 dgaze(i),cut (A 17), (B cut (gaze)) 1 gaze(i), cut d gaze(i),cut c gaze(i), c gaze(i), 2 1 c gaze(i) 2 (A 17) c gaze(i) 3. PCA PCA, i, j d ij D 1< = i< = I,1< = j< = J D =[d 1,1, d 2,1,..., d I,1, d 1,2, d 2,2,..., d I,2,..., d 1,J, d 2,J,..., d IJ] (A 18) D = UΣV U d ij c ij c ij = U d ij 103

2025 © DocPlayer.gr Πολιτική Απορρήτου | Όροι Χρήσης | Σχόλια