Image data processing method for compressing an image by approximating ...

1 2

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

5 6

For the case of the second curve portion S2, the letter wherein the curve SO comprises a curve portion

initial point P2 is located on an extension of a line Q1A2 SO\ corresponding to the curve portion SI of FIG. 3

connecting the point Ql and the point A2 as is clearly and a curve portion SCb corresponding to the curve

illustrated in FIG. 3, and therefore, the coordinate of portion S2 of FIG. 3 and the curve SI comprises a curve

the point P2 can be obtained by the coordinate of the 5 portion SIi and a curve portion SIi. Similarly to the

point A2 in combination with a distance s2 of the point case of FIG. 3, the curve portion SO] is represented by

P2 measured from the point A2. the points Al and A2 as well as points POl and QOl

The position of the point P2 thus represented in terms corresponding to the points Pi and Qi, and the curve

of the distance S2 is then converted to x- and y-coordi- portion SO2 is represented by the points A2 and A3 as

nates by using a general relation x=s.cos0 and y=s.- 10 well as points P02 and Q02 corresponding to the

sin0, where 6 stands for an angle defined between the points P2 and Q2. Further, the curve portion SIi is

line connecting the points and the abscissa as defined in determined by the initial point Al as well as points PI1,

FIG. 3 and s stands for the distance between the two QI1 and a terminal point A4 which correspond to the

points. By using the distance data s which is a scaler parameters A, P, Q and E of Eq.(2) respectively. The

quantity, one can reduce the information to be pro- 15 curve portion Shis determined by the initial point A4

cessed as compared to a case in which the coordinate of and terminal point A3 as well as points PI2 and QI2

the poipts is represented by vectors each comprising which correspond to the parameters A, P, Q and E of

two components. Eq.(2). Note that the points Al, PI1, QI1 and A4 defines

Alternatively, one may obtain the coordinate of the a quadrangle PIIQ1IA4 in which the curve portion SI 1

points by using a data set comprising a distance data and 20 inscribes, and the points A4, PI2, QI2 and A3 defines a

an argument data of a point with respect to an immedi- quadrangle A4PI2Q12A3 in which the curve portion

ately preceding point. Thus, the coordinate of the point SI2 inscribes. As the data compression for the curve

P2 for example is obtained by adding the x- and y-coor- portions SOi, SO2, SI 1 and SI2 are identical to that of

dinates to the corresponding coordinates of the point the curve portions SI and S2 already described with

Ql which in turn are obtained by adding the x-and 25 reference to FIG. 3, further description will be omitted,

y-coordinates obtained similarly to the x- and y-coordi- When these curves are reproduced according to Eq.(2)

nates of the point PI. When adopting this method, one or (3), area surrounded by the curves SO and SI is filled

may quantize the argument data into sixteen directions by dots as usual.

for example, each separated by 22.5 degrees. In this FIG. 5 shows a raster-vector conversion procedure case, the argument can be digitized by four bit data and 30 for compressing an image data according to Eq.(2) or the information to be processed is further reduced. (3). Referring to the drawing, the image to be cornWhen synthesizing the curve, Eq.(2) is used for each pressed is read by raster scanning and the like in a step of the curve portions and the coordinate of the dots 101, whereby the read image is stored in a pattern memused for displaying the curve portions SI and S2 are ory in a form of a bit map. Next, a contour of the pattern calculated with a sufficient density. The dots thus ob- 35 is extracted from the bit map in a step 102 by edge tained are connected by line segments. It is needless to filtering and the like, and the contour thus obtained is say that the more the number of dots, the more the divided into a number of line portions and curve porsmoothness of the line is improved. As the curve repro- tions on the basis of curvature detection in a step 103. In duced by Eq.(2) always makes tangential contact with a step 104, the line portions extracted in the step 103 is the line PQ defined by the control points P and Q, the 40 compressed into a vector data comprising coordinates reproduced curve from the points A, E, P and Q closely of the initial point and terminal point and the curve represents the original font. portions is compressed into a vector data comprising When decomposing a font into a number of curve coordinates of the four parameters A, E, P and Q of portions having different curvatures and line portions Eq.(2) or Eq.(3). The vector data thus obtained is then having different lengths, the curve is once divided into 45 stored in a memory as shown in a step 105. a number of unit vectors and the segmentation of the When the image data compression method of the curve into the curve portions and the line portions is present invention is applied to a facsimile transmission performed by detecting the change in the direction of system, the vector data is transmitted to a reception side the unit vectors. where the original image is recovered according to a In order to avoid unwanted excessive use of memory 50 vector-raster conversion procedure shown in FIG. 6. or transmission band arising when applying Eq.(2) or Referring to FIG. 6, the vector data is read out in a step Eq.(3) involving four parameters to a case where the 201 from a memory storing the received vector data and curve includes a substantial proportion of line portions, the contour of the curve portion is reproduced in a step it is preferred to separate the line portion from the 202 according to Eq.(2) or Eq.(3). The contour of the curved portion by detecting the directional change of 55 line portion is reproduced from the coordinate of its the unit vector or the curvature. The line portion thus initial point and terminal point as already described. In separated is then represented by the two points corre- a step 203, the overall contour of the original image is sponding to the initial and terminal points. recovered by connecting the contours thus reproduced FIG. 4 shows the data compression of the letter "tsu" Further, an area surrounded by the contour of the for an actual case in which the letter has a finite thick- 60 image thus recovered is filled by dots in a step 204 and ness. After the edge detection of the font "tsu", an edge a bit map of the dots thus obtained is stored in a pattern pattern shown in FIG. 4 is obtained. When the font is memory in a step 205. The bit map thus obtained is represented in a form of bit map, the edge pattern is not converted to a visual image by a printer and the facsimsmooth but comprises a number of steps. For the sake of ile transmission of the image is completed, simplicity and clarity of the illustration, representation 65 It should be noted that the vector data may be repreof the edge pattern by stepped line is omitted. The letter sented by a radial distance and an argument measured comprises a first curve SO defining an outer contour from a reference point instead of representing by the and a second curve SI defining an inner contour of the ordinary x- and y- coordinate as already described.