map. In such a case, one has to provide additional mem
IMAGE DATA PROCESSING METHOD FOR ory field in correspondence to coordinates outside of
COMPRESSING AN IMAGE BY the image field for accommodating these coordinate
APPROXIMATING CURVES USING A data. Such a procedure invites unwanted increase of
POLYNOMIAL 5 memory space or amount of information to be processed.
This application is a continuation of U.S. patent application Ser. No. 07/391,788, filed Aug. 9, 1989, now SUMMARY OF THE INVENTION abandoned. Accordingly, it is a general object of the present BACKGROUND OF THE INVENTION 10 invention to provide a novel and useful image process
The present invention generally relates to processing in? meth°d wherein the aforementioned problems are
of image data and more particularly to an image data eliminated.
processing method for compressing two-dimensional Another and more specific object of the present incurve image data and for expanding the information )5 vention is to provide an image processing method thus compressed. wherein a two-dimensional curve is compressed effecIn a field of image processing, a two-dimensional tively without losing smoothness of the curve when the curve image is usually decomposed into a number of curve is reproduced.
segments, and vectors are assigned in correspondence Another object of the present invention is to repro
to each of the segments. Thus, the curve is represented 20 duce an image which closely represents an original
by a number of vectors each corresponding to the seg- image from a compressed image data.
ment. In such a method, when the curve has a large Another object of the present invention is to provide
curvature, a large number of vectors are needed. Asso- a method of image data compression wherein determi
ciated therewith, information to be processed is in- natjon 0f control points for describing a given image is
creased, which causes a difficulty in transmission or 25 performed easily and automatically on a basis of origi
storage in memory. Further, such a method has a prob- na, image represented in a form of bit map.
lem of synthesizing a smooth curve as the synthesis of Another object of the present invention is to provide
the curve .s made on the basis of connection of a num- an image processing method for compressing an infor.
ber of these segments. mation of a two-dimensional curve by four independent
In order to avoid these problems, there has been ,n ,. .. . _ 4 . ¥ . . . ,
proposed to use the Bezier's equation for approximation 30 coordinate parameters, first one specifying an inma of the curve. According to this method, the curve is P0lnt °' the curve' sec0"d onf specifying a term.na approximated by the following equation: P0lnt ofJhe cuTMe'.thlrd one loca*ed on a tangential
passing through the initial point of the curve, and fourth
B(X.Y)=A(\-i)+iP(\-i)2i +iQ(\-i)i1+Eii (l) one located on another tangential passing through the
^ terminal point of the curve, wherein a line specified by
where B(X,Y) represents a coordinate of the two-di- the last two coordinate parameters maintains a tangen
mensional curve, A and E respectively stand for an tial contact with the curve, and further for reproducing
initial point and a terminal point of the curve, P' and Q' the image thus compressed according to an equation: respectively stand for an initial point and a terminal
point of a line which characterizes the shape of the 40 ...
curve and also tangential directions at points A and E, +W£?-W-3)£)(i-t);-+£
and t stands for a parameter specifying position of a
point on the curve between the point A and the point E. where A stands for the first coordinate parameter, E
The parameter t assumes a value zero (0) at the point A stands for the second coordinate parameter, P stands for
and a value one (1) at the point E. According to Eq.(l), 45 the third coordinate parameter, Q stand for the fourth
the curve is characterized by only four points A, E, P' coordinate parameter, c and d are predetermined coeffi
and Q'. cients, and t is a parameter between zero and one repre
FIGS. 1(A) and (B) show typical examples of such senting position of a point on the curve. According to
curves B1-B6, or ... wherein the shape of the the present invention, processing of the two-dimen
curve is determined by the coordinate of the initial 50 siona] curve becomes easy as the Jast menti0ned line
point A and the terminal point E as well as initial points connecting the third and fourth coordinate parameters
Pi'-P*' and terminal points Qi'-Q6, corresponding to maintains the tangential contact with the curve and the
the points P and Q . coordinate parameters defining the line are determined
J^,.0??,TM. ^JTMTM ... ... T^u « as an intersection of said line with a tangential of the Pl'Ql' P2 Q2 P3 Q3 . respectively connecting the 55 ^ h ^ ^ ^
points P, and Q, P2 and Q2, P3 and Qj . . . do not ^ ^ ^ f make contact with respective curves and because of . s _ *, t J? * „ . , this, there arises a problem in that the curve generated P°f/ the. ?"rve: The detection of these tangentials from given control points does not closely reproduce "eluding said line is easily performed automatically by the original image formed in a bit map. In relation with 60 edge detection. As the image reproduced by these four this, automatic contour coding or data compression of coordinate parameters according to the aforementioned the image becomes difficult as the curves which can equation makes a tangential contact with the line conclosely represent the image on the bit map has to be necting the third and fourth coordinate parameters, the specified by the control points which are not on the reproduced image closely represents the original image edge of the image. Further, when the curve is located 65 formed on a bit map. Further, the lines characterizing close to a marginal region of the image to be processed, the shape of the curve does not move outside of image there appears a case in which the points P' and Q' are field secured for the image and the memory space hithlocated outside of image field secured for storing a bit er'to necessary when the Bezier's equation is used for