Recognition of polyhedrons with a range finder

A r e c o g n i t i o n procedure w i t h a range f i n d e r presented i n t h i s paper i s developed f o r the eye of the i n t e l l i g e n t robo t s t u d i e d i n the E l e c t r o t e c h n i c a l L a b o r a t o r y . The range f i n d e r employs a v e r t i c a l s l i t p r o j e c t e r which p r o j e c t s a . l i g h t beam on the o b j e c t s . Whi le the beam is moved in a f i e l d of v iew, the p i c t u r e at each i n s t a n t is p icked up by a TV camera. The d i s t a n c e to each p o i n t can be obta ined by means of t r i g o n o m e t r i c a l c a l c u l a t i o n . The r e c o g n i t i o n procedure us ing thus obta ined i n f o r mat ion is f r e e from the e f f e c t s o f the arrangement and shadow of o b j e c t s . 1 . I n t r o d u c t i o n The r e c o g n i t i o n of 3 -d imens iona l ob j ec t s and the measurement of t h e i r parameters are necessary f o r i n t e l l i g e n t robots t h a t man ipu la te o b j e c t s on the basis o f v i s u a l i n f o r m a t i o n . The recog n i t i o n procedure* of po lyhedrons based on the l i n e drawing of a scene has been (1) (2) (3) h e r e t o f o r e d e v e l o p e d . ( 1 ) , ( 2 ) , ( 3 ) H o w e v e r , e x t r a c t i o n o f a l i n e drawing i s d i f f i c u l t , and if even one edge of an o b j e c t is i n c o r r e c t l y d e t e c t e d , the o b j e c t may be (4) recognized as a q u i t e d i f f e r e n t one. Bes ides, the c o n s t r a i n t o f the p o s i t i o n , the arrangement and the shape of the ob jec t s are necessary f o r the measurement of their 3-dimensional positions and sizes. In order to measure the 3-dimensional position direct ly, a range finder has been studied, and two typical methods have been developed up to now. One is to project a spot l ight and detect i ts (5) reflecting l ight , and the other is based on the stereoscopic view. The former takes a long time to got the range of many points of objects because it requires the rotation of a spot beam for the measurement of each point. The latter requires a great deal of calculation to determine the corresponding points of the two pictures. The method presented here employs a vert ical s l i t projector and a TV camera to pick up i ts reflected l ight . By rotating a projector from the le f t to the right, the distance of many points in a f ield of view is obtained quickly. 2. Construction of a range finder The range finder employed in this study projects a l ight beam through a vertical s l i t in a projector at a constant distance from a TV camera as shown in F ig . l . While the projector is rotated, pictures are sampled by a TV camera at predetermined instances and the information related to each picture and a corresponding s l i t beam angle is stored. If each position of a s l i t in the picture is determined from a stored picture, then i ts 3-dimensional position can be calculated by means of trigonometry. The input of picture data is controlled by a computer as shown in Fig.2, and the video signal of each picturee is converted into (7) a digi tal signal by a preprocessor. This preprocessor divides the frame of a camera into 256 x 256 picture elements, Session No. 3 Scene Analysis II General Papers 81 and 64 x 64 elements are sampled in one scanning time. 3. Recocrmtion of polyhedrons The recognition procedure of polyhedrons based on a set of picture data and s l i t beam angles involves ( l ) determination of s l i t positions, (2) composition of lines, (3) composition of planes , (4) determination of the position of planes, and (5) composition of polyhedrons. In ( l ) (3), only picture data are used; in (4), the 3-dimensional position of the plane is obtained with s l i t beam angles. In (5), the objects are recognized based on the interrelation of planes. There is an alternative process of estimating the distance to the surface for each point and then analyzing the two dimensional f ield of distance to find surface. This method takes a long time for calculation of the distance for evely point. The process presented here calculates only the end points of lines to determine the psoition of planes. Each procedure is described in detail in the fo i l owing. (1) Determination of s l i t positions Each picture corresponding to a s l i t beam angle is stored in binary form where each picture element is 1 if the l ight intensity is above the threshold, and 0 otherwise. At f i r s t this picture is smoothed to eliminate the effect of noise caused by a vidicon camera or a preprocessor. Let the binary picture element be denoted by the mutrix element C( i , j ) , the output of smoothing operation C ' ( i , j ) is the majority of C ( i , j ) , C(i, j l ) and C( i , j+ l ) . By examining elements C ' ( i , j ) along the j th row, from among the sequences whose element successively takes value 1, the longest sequence is selected, and i ts position is established as the center of the sequence. This operation is carried out for every j, and then a s l i t position is denoted by the sequence of points I ( j ) . Fig.4 i l lustrates the sequence of points for each s l i t position of a picture. (2) Composition of lines If polyhedrons are placed in the background that consists of planes, a projected s l i t image is generally composed of lines as shown in Fig.5. In the image, a discontinuous terminal point of a line corresponds to a discontinuous boundary point of a plane and an intersection of two lines corresponds to a boundary point of two adjacent planes. In the f i r s t step for composition of lines from the sequence of s l i t points I ( j ) , discontinuous points are found and each set of l ( j ) whose elements are regarded as continuous is l is ted. A set of s l i t points {T(j), J=J s~ Je} constitutes a line or several adjacent lines. The next step is , therefore, to find the number of lines included in a set of s l i t points, and the terminal points and the equation of each l ine. At f i r s t a sequence of I ( j ) which constitutes a line segment is found. This sequence {I ( j i ) , J i=J_ 3 ,J_ 2 , j_ 1J o , J-1' J2' J3} must satisfy the following two equations: 82 Session No. 3 Scene Analysis II General Papers line is found. This algorithm is , as shown in Fig.6, to track the s l i t point, sequentially correcting the equation of a l ine. Fig.7 shows the result of the tracking and Fig.8 shows the lines thus obtai ned. (3) Composition of planes This operation groups linos obtained in (2) into classes whose element constitutes a plane. If s l i t images are sampled at constant time intervals, then the images of the sl i ts projected on the same plane form nearly parallel lines at constant intervals. Adjacent lines which correspond to s l i t beam angles are grouped into the same class, and then the lines in a class are again d i vided into different classes based on their intervals. After this operation, each class of lines constitutes a plane. The principle of the above two classif i cation algorithms is about the same as that of tracking in (2); i .e. , at f i rs t find the segment of a plane and then examine the next line if it belongs to the plane unti l the boundary line of the plane is found. (4) Determination of the positions of planes A class of lines obtained in (3) does not precisely compose a plane because of errors in various phases of the procedure. In this stage, the 3-dimensional position of each plane is calculated from the class of lines and their corresponding s l i t beam angles. Let a plane consist of n lines and the equation of the plane be denoted by bx + c = 0. Let L(x., b, c) denote the Euclidian distance between the plane and a point x. on the i th l ine, then L(x i , b, c) can be easily calculated. Let the integral of L (x., b, c) be defined as (3) The coefficients of the equation of the plane, b and c, are determined by the least squares method so that the following value J is minimized.