Identification of Image Noise Sources in Digital Scanner Evaluation

Transcription

1 Identification of Image Noie Source in Digital Scanner Evaluation Peter D. Burn and Don William Eatman Kodak Company, ocheter, NY USA ABSTACT For digital image acquiition ytem, analyi of image noie often focue on ource, uch a thoe aociated with quantum ignal detection and ignal-independent fluctuation. Other important noie ource reult in piel-to-piel enitivity variation that introduce repeatable pattern into the image data. In addition, becaue mot analye ue a nominally uniform taet area to etimate image noie tatitic, taet noie can often maquerade a noie introduced by the device under tet. We decribe a method for ditilling variou fied-pattern and temporal noie ource. The method ue everal replicate digital image acquired in regiter. In ome cae, however, evaluation of everal digital canner reveal can-to-can variation in the image regitration to the input tet taet. To overcome thi limitation, a modified noie etimation method i decribed. Thi include a tep to correct thi can-to-can miregitration. We alo how that, in ome cae, meaurement of temporal and fied-pattern noie ource can be achieved via the noie color covariance from a ingle tet image. Keyword: image noie, digital canner, image quality, fied pattern noie, noie cracking. INTODUCTION In the deign, election, and teting of image acquiition device it i often ueful to undertand the magnitude and nature of unwanted image fluctuation. For everal ource of thi image noie, a tatitical decription i appropriate. -3 For eample, the photon, or hot noie related to quantum detection i often modeled a a Poion ditributed proce. Other ource have both tochatic and predictable component. Piel-to-piel detector enitivity variation that introduce repeatable pattern into the image data may appear to be from unit to unit, but omewhat repeatable from can-to-can for a given canner. When evaluating digital canner, an additional ource of image noie i the tet taet ued in the meaurement. Thi can be due to, e.g., urface teture, cratche, or the microtructure of the printing technology ued. Becaue mot analye call for a nominally uniform image region over which image noie tatitic are to be obtained, taet noie can often maquerade a noie introduced by the device under tet. In a previou paper, 4 we decribed a method for ditilling variou fied-pattern and temporal noie ource. The method ue everal replicate digital image, acquired in regiter. A imilar ampling i included in a recent ISO tandard. 5 Practical evaluation of everal digital canner, however, can reveal can-to-can variation in the image regitration to the input tet taet. While thi i uually not a problem for normal product operation, it make the above method le accurate. Here we etend our previou method to accommodate thi characteritic and report on the ue of thee technique, ometime referred to a noie cracking. While the econd-order tatitic of the image noie (variance, rm) per piel are our primary interet, the propoed method can be etended to include the autocovariance or noie-power pectrum. -3,6 We tart with a ummary of the previou method.. MEASUEMENT OF NOISE COMPONENTS We can tate our objective a a variance component analyi 7 of everal noie ource from et of obervation (image data). A imple additive noie model, which eparate effective temporal and fied pattern noie (FPN) contribution, 8 i adopted. For a uniform image area, the variance i taken a the um of it component, +, () Proc. SPIE-IS&T Electronic Imaging Sympoium, SPIE vol. 594, pg. 4-3, 004

2 where i for the temporally uncorrelated (from image to image) noie ource, and i due to fied pattern component. We do not require all noie ource to be independent and additive; we are merely intereted in the effective component a in Eq. (). It hould be undertood that oberved image noie will uually vary with (mean) ignal level and color record. For digital camera and canner, the fied pattern noie can reult from everal ource. When teting a print canner, image fluctuation can be introduced by, e.g., the platen (gla), input taet, and imager. Thi lead to a breakdown of fied pattern noie variance, e.g., taet + platen + imager. () The procedure and analyi that follow are baed on the capturing and proceing of image data, which allow the uppreion of one or more of thee ource, o that the remaining ource can be etimated. The following notation i oberved whenever poible, {: V} i a et of replicate image array, gathered while varying parameter V. For eample, {: } i a et acquired by imple repeated canning varying only in time, {: taet} i a et acquired by moving the taet location between each ample image acquiition. An image data et i denoted by, p,, P piel, q,, Q line, r,, replicate. r. Data Collection In order to etimate the temporal and fied pattern noie variance component of Eq., a et of digital image i need, a hown in Fig.. Each digital image i a imple replicate with no change in hardware or oftware etting, or placement of the tet taet with uniform area. Thi image et, {: }, i patially regitered for a fied detector. 3 r replicate image q piel p line Figure. Set of image data ued to etimate fied pattern and noie component Thi data et can be ued to etimate the component of Eq., however, a econd et i needed to etimate the tatitic of the fied pattern noie component. The econd et, {y: taet}, i acquired while moving (tranlating) the tet taet a hort ditance between repeated image capture.. Fied Pattern and andom Noie Etimation The firt tep in the iolation of the (frame-to-frame temporal) image noie i to compute the overall variance for all piel value in the et of regitered replicate digital image, { }. Thi i done in two tep. After calculating the grand ample mean in Eq. 3, the ample variance i found PQ r p q r (3)

3 PQ P Q p q r ( ) r. (4) Note that in Eq. 4 each piel (obervation) i treated a independent. The fied pattern noie, however, ha been oberved time for each image piel location. Thi ugget that an inter-image averaging may be ueful in identifying thi noie ource. Thi i accomplihed by, r r, for all p, q (5) where i an array of mean value. Thi array can provide an etimate of the fied pattern noie variance, however, a direct etimate of the temporal noie variance i firt obtained via the inter-image ample variance array. Thi i given by, ( r ) Thi array i then ued in a pooled etimate of the temporal noie variance, where ^ indicate an etimate. r P Q p q, for all p, q. (6) ˆ, (7) PQ The fied pattern variance etimate i computed from the array of Eq. 3 and 7 ˆ ( ), (8) PQ p q where the double ummation term i the mean-quared error of the array of inter-image mean, and the lat term of the HS enure that an unbiaed etimate i computed, a hown in the Appendi. The two etimated noie variance can then be combined to ee to what etent Eq. hold for the imaging ytem under tudy, ˆ? +, where ˆ. ˆ ˆ.4 Fied Pattern Noie Component Etimation If a eparation of canner and taet-induced fied pattern noie variance i deired, the econd et of digital image can be ued. ecall that each digital image in {y: taet} wa captured over the ame canner platen area and with the ame region of the canning detector array, but with hifted taet. The inter-record average of thee image, therefore, will provide a meaure with reduced noie and FPN due to the taet. Thu the fied pattern noie due to the imager i etimated uing a procedure imilar to that of Eq. 7 and 8. Firt the grand mean, y, and mean and variance array are computed y ( y r y ) ; y y r r r A pooled variance etimate of the um of taet FPN and component i PQ y P Q p q y.. (9) The fied pattern noie variance for the imager (detector, optic and platen) i found from the mean-quared fluctuation acro the mean array, corrected a in Eq. 8 for the bia due to the and taet noie ource

4 y ˆ imager ( y y). (0) PQ p p The FPN variance due to the taet i ˆ taet ˆ ˆ imager. () The following characterize the imaging ytem noie component ˆ ˆ imager ˆ noie fied pattern fied pattern from imager, optic and platen temporal..5 Eample Several gray Munel matte paper ample were ued a uniform area on a tet taet. Several replicate digital image were collected with oftware driver parameter et conitent with general print canning operation (e.g., 4 bit color, gamma., 300 piel per inch). Five digital image (5) were choen a et {: } in the above noie ource etimation procedure. Figure how the reult for thirty patche for the green color record, each with a different mean ignal level. Note that particularly for high mean value, the oberved image noie i dominated by fied pattern image fluctuation. A a tet of whether Eq. hold for thi canner, the fied pattern temporal variance value were added and the reulting MS value compared with that for the noie. The reult, hown in Fig. 3, were in agreement, indicating than Eq. approimately hold for thi device..5 fied pattern temp. MS noie mean ignal Figure. Meaured, fied pattern and MS noie for a dek top canner uing temporal method (unit are digital ignal value, 0-55)

5 .5 + MS noie mean ignal Figure 3. Comparion of noie and the combined (in quadrature) fied pattern and temporal ource for a dek top canner uing temporal method 3. MODIFIED METHOD The above method for ditilling the variou image noie ource for image acquiition ytem ha been ued uccefully. For everal ytem which include a moveable imager aembly, uch a dektop canner with a linear detector array, minor tranlation error from can-to-can make the acquiition of the regitered data et {: } difficult. The ame ituation occur in high peed document and film canner. One olution i to creen the digital image for minimal miregitration and elect thoe mot compatible with the analyi. In ome cae thi i not practical. Note that mot minor, uually one-dimenional, image tranlation i normally of no importance during canning operation, ince replicate can are rarely compared in thi way. 3. Data and Analyi Since the intent of mot device meaurement i to conducted meaurement in itu, rather than in an unrealitic (tationary) fiture, the challenge wa to modify the above method to accommodate thi ituation. A olution i to firt detect the magnitude of the can-to-can tranlation, and then to re-regiter the replicate image array with repect to the input taet feature. Figure 4 how an outline of the modified procedure, which we will now decribe in detail. Input replicate image Grand ample mean and ample variance Inter-image mean, variance array, and pooled variance Align replicate image by phae correlation Grand ample mean, and ample variance Inter-image mean, variance array, and pooled variance Etimated noie component Figure 4. Step in the modified method Conider the et of replicate image array, where each i now ubject to a tranlation error with repect to the input tet taet. In the notation ued above, thi et i {: taet}. We will ue many of the ame tep, tarting with computing the grand ample mean,, and variance,, uing Eq. 3 and 4. A before, we then compute the inter-

6 image mean,, and variance, array by Eq. 5 and 6. From the variance array, the pooled variance i computed for all piel a in Eq. 7, however; ince the input taet i not regitered with thi data et, thi inter-image pooled variance include both temporal and taet variation. The pooled variance i PQ P Q p q. () ˆ + ˆ ttae. The mean-quared fluctuation acro the inter-image mean array i computed, thi i taken a equal to the um of three term, PQ p q PQ p q, (3) uing the reult of the Appendi. ˆ ˆ taet ˆ imager + +, A hown in Fig. 4, the net tep i to tranlate the image array in {, taet} o that each i in regiter with repect to the input taet. Thi can be done uing a phae correlation 9 approach in either the patial domain or by dicrete Fourier tranform. Detail of thi approach will not be dicued here, ecept to note that the method can be ued to detect and report image miregitration prior to tranlating the array. The aligned verion of the image data et will now not be aligned with repect to the imager in the canner under tet, and we will ue thi in the analyi. The alligned data et, we denote a {y: imager}. A before, we compute the inter-image mean, y y, and variance, array by Eq. 5 and 6. From the variance array, the pooled variance i computed for all piel a in Eq. 7, however, ince the imager i now not regitered with thi data et, thi inter-image pooled variance include both temporal and imager variation, o the mean pooled variance, a in Eq., i ˆ ˆ y + imager. (4) A before, we compute the ample variance acro the inter-image mean array, a in Eq. 3 i the um of three term ˆ imager ˆ taet + +. (5) ˆ y For the above modified method, the following noie variance etimate are taken a characterizing the ytem under tet, ˆ imager y ˆ taet y ˆ ˆ ˆ imager taet.

7 4. SIMPLIFIED COLO COELATION METHOD 4. Data and Etimation Procedure While the original noie ditillation method i intended to be mot general, a we have een the requirement for the input image data may not alway be met for digital canner. The modified method, with the addition of the automated patial regitration tep can accommodate the evaluation of mot digital canner. For field ue, however, it i not alway convenient to collect a erie of replicate image. The earch for a implified method baed on ingle tet image led to an invetigation into the ue of the inter-record noie covariance. Conider the cae where a neutral gray taet i canned for the purpoe of noie evaluation. If the imager or taet were ubject to fied pattern noie ource, we would epect a correlation between fluctuation in the red, green and blue color record. We oberve thi when canning photographic film, where the tructure of the film grain introduce both patial and color correlation into the image fluctuation. Inkjet print alo can impart uch noie correlation. If we have a three-color digital image, the (33) color covariance matri, in common notation given by Σ b rr rb gg gbr rb gb, bb which ha i unique element. The diagonal element are the variance value, rr r, etc. A for the MS noie (variance), the covariance matri for image noie will often vary with mean ignal level. For nominally uniform image data, the covariance matri can be etimated element-by-element by the ample covariance, e.g., ( r r )( g g ) ˆ ; r r, g g PQ p q PQ p q PQ p q (6) where the red, green and blue image array are r g, b., Several apect of an image acquiition ytem can influence the noie color correlation. Unwanted miing of the three color-record, crotalk, at the detector or during ignal readout can introduce or modify the off-diagonal element of the matri. In addition, ignal miing via a matri or 3-D look-up table operation, a part of normal image proceing will modify the matri. 0 The preence of inter-color fied pattern noie will alo influence the color variance matri. For digital canner with little to no color ignal miing or color channel miregitration, it wa uggeted that the etimated color covariance matri could provide a meaure of fied pattern noie due to the input taet Since the amplitude of image noie oberved in digital image i uually different in each of the color record, we choe to ue the normalized form of the covariance matri, to etimate the relative amount of variation (fraction of the variance). The element of the correlation matri are caled a c, and the diagonal element are unity. The fraction of the variance component in the red image record due to the green and blue record wa taken a, c and c, repectively. One etimate of the temporal variance in the red record, therefore, i rb rr gg ˆ r ˆ r ( c ). (7)

8 However, a econd etimate i provided by the red-blue correlation, ˆ ˆ r r ( c ) (8) Combining thee two value in a imple average provided an etimate of the temporal noie variance in the red color record, and the correponding etimate of the fied pattern noie, rb c + crb ˆ r r, (9) c + crb ˆ ˆ ˆ r r r r. (0) It hould be noted that, if needed, we could alo correct thi etimate for the correlation between green and blue color record in the etimate of the red fied pattern noie. 4. Eample Figure 5 compare the color correlation and original temporal method for MS noie etimation. Image proceing and regitration aumption for the two technique were verified. The tet taet contained a erie of gray uniform patche, and wa canned uing a dektop canner at 600 piel per inch ampling. The reult from the correlation method and a ingle tet image were conitent with thoe from the temporal noie cracking method with 5. A in thi eample, we oberve that the correlated noie etimation reult have more variability than thoe from the temporal method. The general concluion regarding the fraction of noie due to temporal ource, however, are conitent. 3.5 correlated temporal MS noie mean ignal Figure 5. Comparion of implified color correlation method and original temporal method for etimating the MS noie of a dek top canner

9 5. CONCLUSIONS Image capture and data proceing method for meauring the tatitic of component noie ource for digital canner have been preented. Thi information i ueful for product comparion, performance verification, fied pattern correction evaluation and taet noie pecification. The tatitical analyi of variance approach can be applied to multiple regitered data et in a way that identifie temporal and repeated image fluctuation due to the digital canner being teted, and bia introduced to the tet taet being ued. In addition, two abbreviated method have alo been dicued. The modified method can be ued for ytem when regitration with an input tet taet i impractical. When teting on a ingle digital image i deired, we have alo hown that in ome cae, the color noie correlation can alo be ued to eparate temporal and fied pattern noie tatitic. Application of thee method to actual canner howed good agreement between eplicit noie calculation and thoe inferred from the imple additive model ued. In everal cae, oberved fied pattern component were found to dominate ytem noie performance. EFEENCES. P. D. Burn, Image Signal Modulation and Noie Characteritic of Chae-Coupled Device Imager, Proc. SPIE, 07, pp. 44-5, C. S. McCurnin, L. C. Schooley, and G.. Sim, Chae-Coupled Device Signal Proceing Model and Comparion, J. Electronic Imaging,, pp , P. J. Kane, T. F. Bouk, P. D. Burn and A. D. Thompon, Quantification of Banding, Streaking and Grain in Flat Field, Proc. PICS Conf., IS&T, pp , P. D. Burn and D. William, Ditilling Noie Source for Digital Capture Device, Proc. IS&T PICS Conf., IS&T, pp. 3-36, ISO 5739:003, Photography Electronic till picture camera Noie meaurement, ISO/TC4, (003). 6.. Shaw, Satifying Simultaneou eolution and Noie Criteria in Digital Image, Proc. PICS, IS&T, pp. 7-74, E. Walpole and. H. Meyer, Probability and Statitic for Engineer and Scientit, nd Ed., MacMillan Publihing, New York, 978, pp G. C. Holt, Electro-Optical Imaging Sytem Performance, JCD Publihing, Winter Park, FL, 995, pp E. DeCatro and C. Morandi, egitration of Tranlated and otated Image Uing Finite Fourier Tranform, IEEE Tran. Pattern Analyi and Intell., PAMI-95, pp P. D. Burn and. S. Bern, Error Propagation Analyi for Color meaurement and Imaging, Color eearch and Application,, pp , 997. APPENDIX: UNBIASED ESTIMATION OF FIXED PATTEN VAIANCE Let the data et {: } reult from the ampling of the um of independent and fied pattern normal variable, where µ r ε + ε r µ 0; ε (a) (a)

10 The firt term of the HS Eq. a i due to the fied pattern and the econd term the component. Note that for any ingle image piel value, ε i oberved once at each piel. We form by computing the ample mean at each piel r r + r ε, for all p, q. (a3) r Thi allow u to reduce the influence of (temporal) fluctuation on the etimate of Thi can be addreed by conidering the tatitic of. Uing Eq. a, but not eliminate it. µ + ε if we aume that each replicate image i an independent obervation of variance by computing the mean-quared variation acro the array r (a4). We now etimate the fied pattern PQ p q PQ p q. From Eq. a4 and a we ee that the epected value of thi etimate i where we rely on r E [ ] ε + +, being the um of independent normal variable. The econd term repreent the bia that i a decreaing function of. An unbiaed etimate of the fied pattern variance i found by ˆ ˆ, where the temporal variance etimate i given in Eq. 7. Equation 8 and 5 ue thi reult.