SExtractor Draft - METU Astrophysics

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28which leads to2 cos θ sin θ 0 (y 2 − x 2 ) + 2(cos 2 θ 0 − sin 2 θ 0 ) xy = 0. (20)If y 2 ≠ x 2 , this implies:xytan 2θ 0 = 2x 2 − y , (21)2a result which can also be obtained by requiring the covariance xy θ0 to be null. Over the domain[−π/2, +π/2[, two different angles — with opposite signs — satisfy (21). By definition, THETAis the position angle for which x 2 θis max imized. THETA is therefore the solution to (21) that hasthe same sign as the covariance xy. A and B can now simply be expressed as:A 2 = x 2 THETA, and (22)B 2 = y 2 THETA. (23)A and B can be computed directly from the 2nd-order moments, using the following equationsderived from (18) after some tedious arithmetics:( )A 2 = x2 + y 2 √+x 2 − y 2 2+ xy 2 , (24)22B 2 = x2 + y 22( )√−x 2 − y 2 2+ xy 2 . (25)2Note that A and B are exactly halves the a and b parameters computed by the COSMOS imageanalyser (Stobie 1980,1986). Actually, a and b are defined by Stobie as the semi-major andsemi-minor axes of an elliptical shape with constant surface brightness, which would have thesame 2nd-order moments as the analysed object.9.1.6 Ellipse parameters: CXX, CYY, CXYA, B and THETA are not very convenient to use when, for instance, one wants to know if aparticular <strong>SExtractor</strong> detection extends over some position. For this kind of application, threeother ellipse parameters are provided; CXX, CYY and CXY. They do nothing more than describingthe same ellipse, but in a different way: the elliptical shape associated to a detection is nowparameterized asCXX(x − x) 2 + CYY(y − y) 2 + CXY(x − x)(y − y) = R 2 , (26)where R is a parameter which scales the ellipse, in units of A (or B). Generally, the isophotallimit of a detected object is well represented by R ≈ 3 (Fig. 5). Ellipse parameters can bederived from the 2nd order moments:CXX = cos2 THETAA 2CYY = sin2 THETAA 2+ sin2 THETAB 2 =+ cos2 THETAB 2 =( 1CXY = 2 cos THETA sin THETAA 2 − 1 )B 2y 2√ ( ) (27)2x 2 −y 2+ xy 22x 2√ ( ) (28)2x 2 −y 2+ xy 22xy= −2√ ( ) (29)2x 2 −y 2+ xy 22
29¡ ¡ ¢ £ ¤ ¥ ¦ § ¨ © © ¢ £ ¤ ¥ ¦ § ¨ ¡ ¢ £ ¤ ¥ ¦ § ¨ © © ¨ B_IMAGEA_IMAGETHETA_IMAGEFigure 5: The meaning of basic shape parameters. THETA is negative here.9.1.7 By-products of shape parameters: ELONGATION, ELLIPTICITY15These parameters are directly derived from A and B:ELONGATION = A Band (30)ELLIPTICITY = 1 − B A . (31)9.1.8 Position errors: ERRX2, ERRY2, ERRXY, ERRA, ERRB, ERRTHETA, ERRCXX, ERRCYY,ERRCXYUncertainties on the position of the barycenter can be estimated using photon statistics. Ofcourse, this kind of estimate has to be considered as a lower-value of the real error since itdoes not include, for instance, the contribution of detection biases or the contamination byneighbours. As <strong>SExtractor</strong> does not currently take into account possible correlations betweenpixels, the variances simply write:ERRX2 = var(x) =ERRY2 = var(y) =∑σi 2 (x i − x) 2i∈S( ) ∑ 2, (32)I ii∈S∑σi 2 (y i − y) 2i∈S( ∑i∈SI i) 2, (33)15 Such parameters are dimensionless and therefore do not accept any IMAGE or WORLD suffix
Page 1: 1DraftSExtractorv2.1.3User’s guid
Page 4 and 5: 47 Weighting 227.1 Weight-map forma
Page 6 and 7: 62.2 Obtaining SExtractorThe easies
Page 8 and 9: 8BACK SIZE — integers (n ≤ 2) S
Page 10 and 11: 10INTERP TYPE ALL keywords (n ≤ 2
Page 12 and 13: 12VIGNET(15,15), yield arrays of nu
Page 14 and 15: 14Segmentation in SExtractor is ach
Page 16 and 17: 166.2 Filtering6.2.1 ConvolutionDet
Page 18 and 19: 186.2.4 Image boundaries and bad pi
Page 20 and 21: 206.4 DeblendingEach time an object
Page 22 and 23: 22are generally useless, except per
Page 24: 243. The CLEANing process (§??) ta
Page 27: 279.1.3 Position of the peak: XPEAK
Page 31 and 32: 31Positional errors are more diffic
Page 33 and 34: 33barycenter of the current SExtrac
Page 35: 35AAppendicesA.1 FAQ (Frequently As

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