TECNOLOGIE PER LA RIABILITAZIONE. lezione # 5 la cattura del movimento. Both movement and morphology are represented. t k. t 3. t 2.

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1 TENOLOGIE PER L RIILITZIONE Università dei Studi di Napoi "Federico II Facotà di Ineneria orso di Laurea in Ineneria iomedica oth movement and morphooy are represented the movement requires time variant information about the pose the morphooy may be time-invariant t 3 t t t 2 1 ezione # 5 a cattura de movimento... Prof. ureio appozzo Dipartimento di Scienze de Movimento Umano e deo Sport Laboratorio di ioineneria Istituto Universitario di Scienze Motorie - Roma dismus a cattura de movimento 1 Let s separate the two probems!! dismus a cattura de movimento 2 Data coection movement data acquisition/estimation (variabes) anatomica data acquisition/estimation (parameters) Data coection movement data acquisition/estimation (variabes) t 1 t 2 t 3 t t 1 t 2 t 3 t dismus a cattura de movimento 3 dismus a cattura de movimento 4 1

2 The description of the pose The term pose audes to the ocation in space of a body The description of the pose In order to describe the pose of the bone, we substitute a compex morphooy with a simpe and time invariant morphooy (riid body hypothesis) dismus a cattura de movimento 5 dismus a cattura de movimento 6 The description of the pose Motion capture In order to describe the pose of the bone, we substitute a compex morphooy with a simpe and time invariant morphooy (riid body hypothesis) Goba system of reference (Goba frame) z For each bone invoved in the anaysis, and in each samped instant of time, motion capture provides two vectors, i.e., six scaar quantities t O t j [ t t t ]; j 1,..., xj position vector yj zj z Loca system of reference (Loca frame) dismus a cattura de movimento 7 orientation vector [ θ θ ]; j 1,..., dismus a cattura de movimento 8 j θ This is, normay, done in an indirect fashion xj yj zj 2

3 Estimate of the instantaneous bone pose usin Stereophotorammetry the reconstructed instantaneous position of marers Given a point in motion in the 3-D aboratory space (marer), stereophotorammetry provides its position vector (three artesian coordinates - X, Y, Z) in each samped instant of time. Minima set up: three non-ained marers [ Y position vectors pij pxij pyij ] pzij ; i 1,...,c ; j 1,..., position vector [ t j t xj j [ t yj ] t zj ; j 1,..., θ xj θ yj X Z orientation vector θzj ]; j 1,..., dismus a cattura de movimento 9 dismus a cattura de movimento 10 amera Stereophotorammetry Given a point in motion in the 3-D aboratory space (marer), stereophotorammetry provides its position vector Principa pane (three artesian coordinates - X, Y, Z) in each samped instant of time. Noda point (N) Optica axis dismus a cattura de movimento 11 dismus a cattura de movimento 12 3

4 amera and object point amera and object point Principa pane Principa pane Noda point (N) Noda point (N) Optica axis Optica axis Object point Object point dismus a cattura de movimento 13 dismus a cattura de movimento 14 amera, object and imae points Imae point Imae point Principa pane Noda point (N) Optica axis Object point chip D Imae pane dismus a cattura de movimento 15 dismus a cattura de movimento 16 4

5 Stereophotorammetry Stereophotorammetry recordin phase N 1 P N 1 P N 2 N 2 dismus a cattura de movimento 17 dismus a cattura de movimento 18 Stereophotorammetry recordin phase Stereophotorammetry recordin phase N 1 P N 1 P N 2 N 2 dismus a cattura de movimento 19 dismus a cattura de movimento 20 5

6 Stereophotorammetry reconstruction phase Stereophotorammetry reconstruction phase N 1 P N 1 P N 2 N 2 dismus a cattura de movimento 21 dismus a cattura de movimento 22 Stereophotorammetry reconstruction phase (with errors) Stereophotorammetry reconstruction phase N 1 P N 1 P N 2 N 2 Object point position reconstruction has been achieved by usin the foowin information: Goba camera position and orientation Loca position of the noda points caibration parameters (time invariant) Loca position of the imae points measured variabe (time variant) dismus a cattura de movimento 23 dismus a cattura de movimento 24 6

7 naytica stereophotorammetry Position and orientation of a camera y aibration parameters x N z Measured variabes Mathematica mode Object point oba coordinates dismus a cattura de movimento 25 dismus a cattura de movimento 26 Position and orientation of a camera Position and orientation of a camera y θ p parameters y θ p parameters x p p (3 numbers) x p p (3 numbers) N θ p (3 numbers) N θ p (3 numbers) z d z d (1 number) p p p p dismus a cattura de movimento 27 dismus a cattura de movimento 28 7

8 Imae coordinates naytica stereophotorammetry y data x x p x p y p N y p p p1, θ p1, d 1, p p2, q p2, d 2 z x p1, y p1, x p2, y p2 Mathematica mode X, Y, Z dismus a cattura de movimento 29 dismus a cattura de movimento 30 System caibration aibration object The contro points (marers) are ocated in nown positions. The system of reference with respect to which their ocation is iven becomes the stereophotorammetric oba frame. p p1, θ p1, d 1, p p2, q p2, d 2 Y x p1, y p1, x p2, y p2 Mathematica mode X, Y, Z X dismus a cattura de movimento 31 Z dismus a cattura de movimento 32 8

9 aibration object So named dynamic caibration fter a first approximation caibration usin a simpe and stationary caibration object, the marers mounted on a riid wand are traced whie movin within the measurement voume. aibration parameters are iterativey modified whie optimizin an objective function. Y ourtesy of NIH Z X dismus a cattura de movimento 33 dismus a cattura de movimento 34 So named dynamic caibration System caibration p p1, θ p1, d 1, p p2, q p2, d 2 x p1, y p1, x p2, y p2 Mathematica mode X, Y, Z ourtesy of NIH dismus a cattura de movimento 35 dismus a cattura de movimento 36 9

10 The experiment ctive marers In each samped instant of time p p1, θ p1, d 1, p p2, q p2, d 2 x p1, y p1, x p2, y p2 Mathematica mode X, Y, Z dismus a cattura de movimento 37 dismus a cattura de movimento 38 The movement anaysis aboratory Marer trajectory reconstruction Determination of the instantaneous bone pose usin the reconstructed instantaneous position of marers? p dismus a cattura de movimento 39 p ij [ p p p ]; i 1,..., c; j 1,..., xij position vectors yij zij orientation vector [ θ θ ]; j 1,..., dismus a cattura de movimento 40 j t j position vector [ t t t ]; j 1,..., xj θ xj yj yj zj zj 10

11 simpe exampe Determination of the pose of a oca set of axes the position vectors or three non-ained marers are iven dismus a cattura de movimento 41 dismus a cattura de movimento 42 Determination of the pose of a oca set of axes Determination of the pose of a oca set of axes z 1. Definition of a pane 2. Definition of two orthoona axes on that pane 3. The third axis is orthoona to the former two axes dismus a cattura de movimento Definition of a pane 2. Definition of two orthoona axes in that pane 3. The third axis is orthoona to the former two axes dismus a cattura de movimento 44 11

12 Determination of the pose of a oca set of axes Determination of the instantaneous bone pose usin the reconstructed instantaneous position of marers y c ppendix z 1. Definition of a pane 2. Definition of two orthoona axes on that pane 3. The third axis is orthoona to the former two axes dismus a cattura de movimento 45 This oca frame is referred to as marer-custer technica frame dismus a cattura de movimento 46 Determination of the poses of the marer-custer technica frames y c Determination of the poses of the marer-custer technica frames y c Minima set up: three non-ained marers y c Redundant set up y c y 3 mathematica operator yc y >3 mathematica operator yc x x z z p ij [ p p p ]; i 1,..., c; j 1,..., xij position vectors yij zij cj orientation vector [ θ θ ]; j 1,..., dismus a cattura de movimento 47 t cj position vector [ t t t ]; j 1,..., cxj θ cxj cyj cyj czj czj p ij [ p p p ]; i 1,..., c; j 1,..., xij position vectors yij zij cj orientation vector [ θ θ ]; j 1,..., dismus a cattura de movimento 48 t cj position vector [ t t t ]; j 1,..., cxj θ cxj cyj cyj czj czj 12

13 Determination of the poses of the marer-custer technica frames y c Redundant set up y >3 mathematica operator y c yc fine dea ezione # 5 x z p ij [ p p p ]; i 1,..., c; j 1,..., xij position vectors yij zij cj [ t t t ]; j 1,..., orientation matrix R ; j 1,..., dismus a cattura de movimento 49 t position vector cxj cj cyj czj dismus a cattura de movimento 50 TENOLOGIE PER L RIILITZIONE The riid body Università dei Studi di Napoi "Federico II Facotà di Ineneria orso di Laurea in Ineneria iomedica ppendix riid-body pose determination y Prof. ureio appozzo Dipartimento di Scienze de Movimento Umano e deo Sport Laboratorio di ioineneria x Istituto Universitario di Scienze Motorie - Roma dismus a cattura de movimento 51 z dismus a cattura de movimento 52 13

14 Point position vectors Frame unity vectors determination y p p p y p p j j ( p p ) p p x x z dismus a cattura de movimento 53 z dismus a cattura de movimento 54 Frame unity vectors determination Frame unity vectors determination y p p p j i i ( p p ) j ( p p ) j y z j i i j x x z dismus a cattura de movimento 55 z dismus a cattura de movimento 56 14

15 Frame orientation-matrix and position vector determination Frame orientation-matrix and direction cosines R i j y p z x j i R t i j p c z y z j x i i xx yx zx x R y z j x x x xy yy zy xy yy zy xz yz zz xz yz zz z dismus a cattura de movimento 57 dismus a cattura de movimento 58 Frame orientation-vector determination Reationship between orientation matrix and orientation vector x y z x zy zz x xy xz R x yy yz [ ] θx θy θz xa ya z a xb zayb zazb xb xayb xazb a a a a a R b x b yay b yaz [ ] b b θbx θby θbz Given two frames a and b y z j i x z dismus a cattura de movimento 59 a b tn θ θ 2sinθ θ θ 2sinθ θ θ 2sinθ a bx a by a bz \ [( ) + ( ) + ( ) ] zayb ( ) zayb ( ) xazb ( ) yaxb yazb yazb zaxb xayb xaxb xazb + dismus a cattura de movimento 60 yayb zaxb + zazb 1 yaxb xayb

16 In summary In summary Given the marer position vectors in the oba frame: p p p The orientation of a riid body can therefore be described by a position vector y p z p p We were abe to estimate the position and orientation vectors of the oca frame (marer custer frame): t c c [ tcx tcy tcz] [ θ θ θ ] cx cy cz y z c or by an orientation matrix R z x In addition, the orientation matrix has been presented and its reationship with the orientation vector found. dismus a cattura de movimento 61 z x dismus a cattura de movimento 62 The end of ppendix dismus a cattura de movimento 63 16