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the general problem of the fully automatic star detecting algorithms on the ccd images is the successful recognition of real star images or star - like sources in general from other types of objects and defects .
these false objects originate from non - ideal characteristics of the ccd instrument ( noise , bad column and hot pixels ) or from the environment ( nebulae , galaxy or cosmic ray events known as cosmics ) .
the frequent requirement is to find real star images on a diffuse background or in a crowded star field .
therefore , the detecting algorithm can not use a simple intensity comparing principle , because the intensity of non - stellar objects can be comparable to star intensities .    a number of different methods for the automatic star detection on astronomical images has been used during the last two decades . for example ,
the method based on wavelet transforms applied to satellite rosat image processing was published by damiani  et  al .
@xcite . the automatic search and classification
were implemented in focas routine by valdes  et  al .
@xcite . the pc  vista by trefers and richmod  @xcite is a package for photometry with a simple algorithm for star detection . the well - known program daophot by stetson  @xcite contains two parameters @xmath0 and @xmath2 and a highly robust algorithm for star detection .
the determination of these parameters originates from specific characteristics of the sources on ccd images , but both parameters are not sensitive enough to resolve stars and cosmics on the ccd images exposed in focus of a space telescope and/or camera such as the omc experiment on - board integral ( hermsen and winkler  @xcite ) .
the large part of the information describing the detected object is included in its intensity profile , but the profile varies widely with weather , telescope focus , etc . changes .
the intensity distribution can not be described by an analytical function , because it depends on many non - controllable factors .
fortunately , the real measured profiles are ( in the first approximation ) close to the two - dimensional gaussian profile both for the ground - based ( moffat  @xcite ) and space telescopes .    from this point of view
, we can easy distinguish between the hot pixel ( a  single pixel with very different intensity compared to surrounding pixels ) and the real star .
the star image with the gaussian profile is usually spread over several pixels . for illustration ,
the typical 1-dimensional profiles of the star and of the hot pixel are shown in figures  [ fig1 ] and [ fig2 ] .
the maximum intensity of the object @xmath3 is at the pixel @xmath4 .
the center of the star is at position @xmath5 where summations are evaluated over a small area around the central pixel @xmath4  for example over @xmath6 pixels .
this notation is also used below .
approximation of the observed intensity by the two - dimensional gaussian profile is the next step of our algorithm @xmath7/2 h^2 } + \ , b\ ] ] the parameter @xmath8 is the estimated maximum of the star profile , @xmath9 is the local sky background .
the parameter @xmath10 is the width of the typical star and its numerical value must be known _ a priori_. the stars are axis - symmetrical objects according to this formula .
note , that the @xmath8 parameter is equivalent to , but not quite identical with the stetson s
parameter @xmath11 ( integer values are used for @xmath12 , i.e. @xmath13 ) . if we suppose that the statistical distribution of the observed intensity has a normal distribution , we can use the least square method @xmath14 for the estimation of the unknown @xmath8 and ( further unused ) @xmath9 .
further , we can estimate the central intensity @xmath15 from the maximum intensity @xmath3 by subtracting the local background intensity @xmath16 from @xmath3 : @xmath17 where @xmath18 ( @xmath19 are arbitrary weights ) and compare its numerical value in parameter @xmath0 : @xmath20 the figures  [ fig1 ] and [ fig2 ] indicate the typical values of this parameter .
its value is in agreement with the inequality @xmath21 for the star and with @xmath22 for the hot pixel .
we can hence deduce the range of the parameter @xmath0 as @xmath23 for the star .
the cosmic ray events frequency on the ccd images exposed at a ground - based observatory is low and , moreover , its profiles are narrower than the star profiles
. the image processing algorithm can then easily resolve the images of the stars and those of the cosmic - ray events .
but ccd images from satellites contain a higher number of the cosmic - ray event tracks and the numerical value of the @xmath0 parameter , computed for the stars , is close to the numerical value for cosmics .
the construction of the confidentiality test for its distinguishing with only the @xmath0 parameter is not possible .
the star isophotes of the ideal images have the shape of concentric circles , but the cosmics or the bad columns are represented in general by ellipses with the major semi - axis at some angle to the @xmath24 coordinate .
the mathematical description of an object in image is derived from this characteristics .
the most effective way is the description of the object by its 2nd moments @xmath25 and @xmath26 where the summations are evaluated over the same small area around @xmath4 .
now , we can compute the lengths of the object semi - axes as the eigenvalues problem .
its lengths satisfy the equation @xmath27 resolving of this equations for @xmath28 gives the sizes of semi - axes as @xmath29\ ] ] the numerical values of its parameters ( lengths of semi - axes ) are different for elongated object , but approximately the same for stars .
with respect to their character we define the parameter @xmath30 the limits of this parameter are :    * @xmath31 , the star case * @xmath32 , the cosmics case * @xmath33 , the bad column case , @xmath1 parameter is then equivalent to the @xmath2 parameter of stetson  ( 1987 )    the parameter @xmath1 describes the shape of the object .
the circular objects are interpreted this way as stars and the very elongated object as cosmic - ray events or bad columns .
note , that the @xmath1 parameter represents direct generalization of the @xmath2 parameter described in stetson  ( 1987 ) .
the @xmath2 parameter is capable of measuring elongation only parallel to rows or columns of the image .
it was intended to identify bad rows or columns , not cosmics .
= 1.0 cm    ( 8,8 ) ( 8,8 )
in this section we describe the use of the parameters mentioned in previous sections to analyze the simulated image of the star field . the image ( see fig .  [ fig3 ] )
is generated as the simulation of the field of view of the omc ( optical monitoring camera ) prepared for the esa satellite integral .
the psf function of the stars in the image is defined as the two - dimensional gaussian profile with 70% of the light energy in the central pixel , according to the psf of the flight optics .
this results in @xmath34 for the stars in the simulated image , while their centers are uniformly spread over the unit interval .
there are also some other sources in the image , namely the bad column , hot pixels and a few cosmics ( see fig .
[ fig3 ] and table  [ tab ] ) .
the image is critically under - sampled .
the image left - bottom corner has coordinates @xmath35 and right - top one @xmath36 in pixels .
the bad column is situated at @xmath37 .
the hot pixels occupy positions @xmath38 , @xmath39 , @xmath40 , @xmath41 and the centers of the three cosmics appear at @xmath42 , @xmath43 , @xmath44 .
all other sources represent real stars .
the intensity of the sky is @xmath45 with the gaussian noise @xmath46 ( all intensities in arbitrary units ) .
object no .  4 ( star ) and object no .  1 ( hot pixel ) were used for construction of the profiles shown in fig .
[ fig1 ] and  [ fig2 ] .
the computed characteristics for the selected sources in the simulated image are listed in table  [ tab ] .
the center of the object is at coordinates @xmath12 , see formulae ( [ e1 ] ) , the intensity peak at pixel @xmath4 is related to @xmath15 according to ( [ e2 ] ) .
the moments computed from ( [ e3 ] ) and ( [ e4 ] ) are @xmath47 , @xmath48 , @xmath49 and the parameter @xmath8 is obtained by minimization of the sum ( [ e5 ] ) .
the last three columns contain the values of the parameters @xmath50 and @xmath1 .
the values of the numerical differences of the @xmath0 parameter for star and hot pixel are small because @xmath10 is small , but the upper bound at 1 separates stars and hot pixels to obviously different groups
. the values of the @xmath2 parameter demonstrate small difference between cosmics and stars . on the contrary the values of the @xmath1 parameter of the stars ( or hot pixels ) and of the cosmics as well as that of the bad columns
are clearly incompatible .
.the parameters of objects in the simulated image ( legend : no . 1  hot pixel , no . 2  bad column , no .
3  cosmics , no . 4  star ) . [ cols=">,>,>,>,>,>,>,>,>,>,>,>",options="header " , ]
the two parameters @xmath0 and @xmath1 described in this paper are widely applicable to the robust detection of the star - like sources in images provided by array detectors .
the primary reason for deriving the parameters was the development of a reliable automatic algorithm for the recognition of stars on ccd images .
we can choose following criterion for this purpose it the intensity of the central pixel of the examined object is above an arbitrarily defined level of significance ( threshold ) and the object lying far from the edge of the frame .
then        we might specify a range of the @xmath0 and @xmath1 parameters for a star centered on a pixel as @xmath51 , @xmath52 .
the range of @xmath0 for a star centered on the edge between two pixels decrease to @xmath55 and one for a star centered on the corner of four pixels decrease to @xmath56 , but the range for @xmath1 increase to @xmath57 in this both cases .
i am grateful to r. hudec , t. rezek and b. lencov for their correction of the manuscript and many helpful comments .
this work has been supported by the czech ministry for education and youth , project nr .
es  036 kontakt .
we have done many of computation at supercomputing center of masaryk university in brno .
the hst image originates from the hst archive at the space telescope institute .
two parameters are developed to analyze the ccd images from ground - based and/or space telescopes . 
 the first parameter , deduced from the intensity profile of the object @xmath0 , is useful to resolve stars and hot pixels . 
 the second parameter @xmath1 distinguishes the stars from the background cosmic - ray events using geometric characteristics defined by its shapes . 
 the parameters are applied to a simulated omc / integral image and a hst image .