Robotic Arm Motion for Verifying Signatures Moises Diaz 1 Miguel A. - PowerPoint PPT Presentation

Introduction VSA Robotic features Results Conclusions Robotic Arm Motion for Verifying Signatures Moises Diaz 1 Miguel A. Ferrer 2 Jose J. Quintana 2 1 Universidad del Atlantico Medio, Spain 2 Instituto para el Desarrollo Tecnológico y la Innovación en Comunicaciones Universidad de Las Palmas de Gran Canaria, Spain 16th ICFHR, Niagara Fall, August 8th, 2018 Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 1 / 25

Introduction VSA Robotic features Results Conclusions Outline Introduction 1 Virtual Skeletal Arm model 2 Robotic/Anthropomorphic Feature Extraction 3 Results 4 Conclusions 5 Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 2 / 25

Introduction VSA Robotic features Results Conclusions Automatic Signature Verification Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 3 / 25

Introduction VSA Robotic features Results Conclusions On-line: Local features The signature is analyzed locally The signature is represented through timing sequences or functions in diverse domains Basic functions: obtained directly from the digital tablet Position: x n , y n Pressure: p n Pen-tip angles from the writing area: φ n , ψ n Extended functions Tan angle: θ n = tan − 1 ( ˙ y n / ˙ x n ) � ˙ n + ˙ velocity (module): v n = x 2 y 2 n log-radius curvature: ρ n = log ( 1 / k n ) = log ( v n / ˙ θ n ) � ˙ � acceleration (module): a n = t 2 n + c 2 n = v n + v 2 n θ 2 n Time derivatives of the above functions ... Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 4 / 25

Introduction VSA Robotic features Results Conclusions Our proposal A novel feature space for on-line signature verification Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 5 / 25

Introduction VSA Robotic features Results Conclusions Main characteristics Based on the arm posture when signing: joint angles and positions Physical meaning, simple, fast and verifiable solution Designing of a Virtual Skeletal Arm (VSA) model Mathematical fundamentals from forward and direct kinematic in robotics Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 6 / 25

Introduction VSA Robotic features Results Conclusions Outline Introduction 1 Virtual Skeletal Arm model 2 Robotic/Anthropomorphic Feature Extraction 3 Results 4 Conclusions 5 Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 7 / 25

Introduction VSA Robotic features Results Conclusions Virtual Skeletal Arm (VSA) model Similarities with the theoretical model Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 8 / 25

Introduction VSA Robotic features Results Conclusions Virtual Skeletal Arm (VSA) model Proposal Architecture based on an anthropomorphic robot We got two sets of timing functions: joint angle movements and joint position Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 9 / 25

Introduction VSA Robotic features Results Conclusions Outline Introduction 1 Virtual Skeletal Arm model 2 Robotic/Anthropomorphic Feature Extraction 3 Results 4 Conclusions 5 Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 10 / 25

Introduction VSA Robotic features Results Conclusions Coordinate Frames in the VSA Relationship among them by homogeneous transformation matrices. E.g.: n i o i a i p i   x x x x n i o i a i p i 0 T i  y y y y  6 =  n i o i a i p i   z z z z  0 0 0 1 Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 11 / 25

Introduction VSA Robotic features Results Conclusions Forward Kinematics Goal: To calculate the pose of the coordinate frames (CFs) relating to the VSA model, as a function of its joints angles Q ( q i k ) . Strategy: Denavit-Hartenberg (DH) algorithm is widely used. Table: DH parameters, DH i k δ i Joint k d k a k α k k q i 1 L 1 0 − π 1 2 q i 2 0 L 2 0 2 − π 2 q i 3 0 L 3 − π 3 2 q i 4 L 4 0 π 4 2 q i 5 0 0 − π 5 2 q i 6 L 5 0 0 6 Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 12 / 25

Introduction VSA Robotic features Results Conclusions Forward Kinematics k − 1 T i k = δ i δ i δ i δ i  � � � � � � � �  c − c ( α k ) s s ( α k ) s a k c k k k k (1) � δ i � � δ i � � δ i � � δ i � c ( α k ) c − s ( α k ) c s a k s   k k k k   0 − s ( α k ) c ( α k ) d k   0 0 0 1 0 T i 6 = 0 T i 1 · 1 T i 2 · 2 T i 3 · 3 T i 4 · 4 T i 5 · 5 T i (2) 6 Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 13 / 25

Introduction VSA Robotic features Results Conclusions Inverse Kinematics Goal: To deduce the joint angle-based features, Q ( q i k ) , based on the pose of the pen attached to the end of the model. Strategy: kinematic decoupling. Firstly q i 1 , q i 2 , q i 3 , secondly, q i 4 , q i 5 , q i 6 Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 14 / 25

Introduction VSA Robotic features Results Conclusions Kinematics Validation Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 15 / 25

Introduction VSA Robotic features Results Conclusions The function will be availble soon For researching purposes, we share our anthropomorphic feature extractor Developed in Matlab language angles = pos2ang(x,y,z) Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 16 / 25

Introduction VSA Robotic features Results Conclusions Outline Introduction 1 Virtual Skeletal Arm model 2 Robotic/Anthropomorphic Feature Extraction 3 Results 4 Conclusions 5 Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 17 / 25

Introduction VSA Robotic features Results Conclusions Experimental protocol Database: MCYT-100: 25 genuine, 25 forgeries, 100 users Train: first T enrolled signature Test: FAR: remaining genuine signatures: ( 25 − T ) × 100 scores FRR: Random Forgery (RF): 1st testing genuine signature from the other users: 99 × 100 = 9900 scores FRR: Skilled Forgery (SF): all available: 25 × 100 = 2500 scores Features: Q ( q i k ) , ∀ k ∈ 1 , . . . 6 և O UR CONTRIBUTION ASV: Dynamic Time Warping Performance: EER and DET curve Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 18 / 25

Introduction VSA Robotic features Results Conclusions Pen-tip angles for orientating the CF { S 6 } Raw angles ( θ i r , φ i Estimated angles ( θ i e , φ i r ) , and the e ) , and the corresponding joint angles corresponding joint angles Smoothed angles ( θ i s , φ i Fixed angles ( θ i f , φ i s ) , and the f ) , and the corresponding joint angles corresponding joint angles Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 19 / 25

Introduction VSA Robotic features Results Conclusions Performance results for different number of signatures to train MCYT-100, only angle-based features and a DTW verifier Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 20 / 25

Introduction VSA Robotic features Results Conclusions Comparison with on-line ASV, using five signatures to train and the MCYT-100. Performance in ERR (%). Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 21 / 25

Introduction VSA Robotic features Results Conclusions Outline Introduction 1 Virtual Skeletal Arm model 2 Robotic/Anthropomorphic Feature Extraction 3 Results 4 Conclusions 5 Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 22 / 25

Introduction VSA Robotic features Results Conclusions Conclusions Framework to transform the on-line signature samples into a new feature space Mathematical basis for the designing Virtual Skeletal Arm (VSA) models Using robotic concepts to deduce the 3D movement from the pen-tip Features with physical meaning, simple, fast and with a verifiable solution Good results with angle-based features for on-line ASV Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 23 / 25

Introduction VSA Robotic features Results Conclusions Future works Combination of position-based and angle-based robotic/anthropomorphic features Use more signature database and verifiers Modeling the anatomy of the hand: the finger movement supported by the wrist can be also relevant Adapting robotic features for off-line ASV Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 24 / 25

Introduction VSA Robotic features Results Conclusions Robotic Arm Motion for Verifying Signatures Moises Diaz 1 Miguel A. Ferrer 2 Jose J. Quintana 2 1 Universidad del Atlantico Medio, Spain 2 Instituto para el Desarrollo Tecnológico y la Innovación en Comunicaciones Universidad de Las Palmas de Gran Canaria, Spain 16th ICFHR, Niagara Fall, August 8th, 2018 Diaz, Ferrer, Quintana (UNIDAM, ULPGC) 25 / 25