# Last edited on 2011-07-06 19:01:48 by stolfilocal Table I should be placed at the top left of page 2. We suggest removing the line "TABLE I" from the header of this table, leaving only the header "MAIN SYMBOLS USED" (since it is not really a table, but only an index of sorts), and renumbering the other tables accordingly. EVERYWHERE : Replace "tg" by "t.g" (non-raised dot, with t in math-italic and "g" in boldface math-italic). EVERYWHERE : Move the down-arrow symbol closer to the folowing letter ("g" or "s"). EVERYWHERE : Variables "tbest" and "dbest" should be wholly in text-italic. EVERYWHERE : Replace "tbestg" by "tbest.g", with "tbest" in text-italic and g in bold math-italic. Abstract "find a pixel of a reference object of known" >> "find a pixel of reference object, of known" "Our method is faster than known previous solutions" >> "Our method is faster than previous known solutions" "the search can be efficiently solved with" >> "the search can be efficiently solved with" 1 - Introduction "The problem of " : Text within <> should be in italic. "(VLPS) was considered in [15], [25] and [31]." >> "(VLPS) was considered by Horn et al. [15], Silver [25], Woodham [31], and others." "which are all taken" >> "all taken" "with different lightings but with the same pose and the same viewpoint" >> "with different lightings but with the same pose and viewpoint" "perpendicular to a surface element, which is" >> "perpendicular to the surface element which is" "the third dimension (i.e depth) ... " >> "the third dimension (depth)" " (BRDF)" : Text within <> should be in italic. "surface with normal n, which is viewed" >> "surface with normal n, viewed" " (we include the geometric" >> ". (We include the geometric " " BRDF itself)." >> " BRDF itself.)" "The problem of VLPS has attracted" >> "The VLPS problem has attracted" "by [5],[6],[24], and [26]." >> "by Barski and Petrou [5], Shen et al. [6], Sun et al. [24], and Basri et al. [26]." A. Example-Based VLPS In the variant : Text within <> should be in italic.s "VLPS, which is introduced in [33], the BRDF" >> "VLPS, introduced by Woodham [33], the BRDF" "of a reference object, i.e, a sample object" >> "of a reference object---a sample object" (--- is m-dash) "color, where each image reference object G_i" >> "color---where each reference image G_i" "that all images S_1...S_m have" >> "that all images S_1,...S_m have" "also assume linear light sampling so that" >> "also assume linear light sampling, so that" "if all visible scenes and reference-object" >> "if all visible scene and reference-object" "q must be multiples of some BRDF \beta as follows:" >> "q must be multiples of some BRDF \beta:" "are the " : Text within <> should be in italic.s "or the" >> "or... "" : Text within <> should be in italic.s "the scene and the reference-object surface" >> "the scene and reference-object surfaces" "albedo of the reference object g*[q] and the normal direction g->[q] must" >> "albedo g*[q] and the normal direction g->[q] of the reference object must" "albedo, which is preferably" >> "albedo, preferably" "However, almost any BRDF B will do" : remove indentation " and distant light sources so " >> " and distant light sources, so " "The later provide illumination-independent of" : Text within <> should be in italic.s B. Fundamental Equations " normal n). Specifically" >> " normal n). Specifically," "Here, each L_i is the implied" : Text within <> should be in italic.s "Factor" >> "The factor" (also remove indentation) "is " : Text within <> should be in italic.s "in the sense that" >> ", in the sense that" "(p or q) but only on direction u->" >> "(p or q) but only on the direction u->" "except for albedo s*[p] and albedo g*[q]." >> "except for the albedos s*[p] and g*[q]." "as the" >> "the" " (OVs)" : Text within <> should be in italic.s " must be varied sufficiently to break" >> "must be sufficiently varied to break" "well as with shadows.. : Text within <> should be in italic.s "occur (however" >> "occur. However, " shadows" : Text within <> should be in italic.s "still a problem)." >> "still a problem." C. Table Lookup Step "As pointed out in [14]" >> "As pointed out by Hertzmann and Seitz [14]" "to matching the " : Text within <> should be in italics. "Note that position q" >> "Note that the position q" "to normal g->[q] and" >> "..to the normal g->[q] and the" " \gamma[q]" : Text within <> should be in italics. "by a " : Text within <> should be in italics. "set of triplets as follows:" >> "set of triplets" "then becomes the closest match table lookup problem, where" >> "then becomes a , where" (text within <> should be in italics) "we look for element" >> "we look for the element" "of table T that minimizes" >> "of T that minimizes" "to scan table T," >> "to scan the table T," "track of the closest matching" >> "track of the closest-matching" "accurate results, table T" >> "accurate results, T" D. Previous Work "For instance, in [21]," >> "For instance, Nayar et al. [21] considered" "known position, was considered but" >> "know position, but" "In [28], linear " >> "Tagare and Figueiredo [28] allowed linear" "Lambertian forestcatter (glossy) and backscatter BRDFs was allowed but" >> "Lambertian, forestcatter (glossy), and backscatter BRDFs but" "of three images, i.e., each" >> "three images, each taken" "In [12] and [29], heuristics was used to" >> "Hayakawa [12] and Yuille and Snow [29] used heuristics" "image and pixels where there were shadows" >> "image and pixels in shadows" "lines is [17]." >> "lines that of Kay and Caelli [17]." "However, unreferenced techniques" >> "However, techniques without reference objects" "than the actual slopes and therefore" >> "than the actual slopes; and therefore" "spanning hypercube" >> "spanning the hypercube" "each reference-object OV" >> "each reference-object observation vector" "was stored (Woodham" >> "was stored. Woodham" "normalize the OVs)." >> "normalize the OVs" "size of the grid, i.e," >> "size of the grid:" "nearest point algorithms" >> "nearest-point algorithms" "use the " : Text within <> should be in italics. "(ANN) of [3]." >> "(ANN) algorithm of Arya et al. [3]." "the " : Text within <> should be in italics. "(LSH) in [16]." >> "(LSH) method of Indyk and Motwani [16]." "the method" : Text within <> should be in italics. "in [7]." >> "of Bentley et al. [7]." "m-dimensional nearest neighbor search" >> "m-dimensional nearest-neighbor search" 2 - Fast Table Searching With 2-D Bucketing A. Shape of the Signature Table "where l is the " : Text within <> should be in italics. "as follows:" >> "" (delete) "Note that function l that" >> "Note that the function l, that" "lighting signatures is defined" >> "lighting signatures, is defined" "by formula (4) are the continuous" >> "by formula (4) are continuous" "one-to-one embedding of hemisphere" >> "one-to-one embedding of the hemisphere" "diameter of K, i.e., as seen" >> "diameter of K, as seen" B. The 2-D Grid Scheme "unit vectors u v" >> "unit vectors u,v " "Point b and vectors u and v define the 2-D affine" >> "The point b and the vectors u and v define a 2-D affine" "subspace P of Rm and the" >> "subspace P of Rm, the" "" : Text within <> should be in italics. "centered on point b, has" >> "centered on the point b, has" "we build, i.e., for each" >> "we build, for each" "the grid, the linked >> "grid, a linked" " B[i,j]" : Text within <> should be in italics. "of all table entries" >> "with all table entries" "T, whose" >> "T whose" "corresponding " : Text within <> should be in italics. "all signatures tg in list B[i,j]" >> "all signatures t.g in the list B[i,j]" "and the " : Text within <> should be in italics. "The 2-D shape of T" >> "The two-dimensional shape of T" "each other even if" >> "each other, even if" "in Sections II-C-II-E." >> "in Sections II-C through II-E." C. Bucket-Grid Searching "It then scans list" >> "It then scans the list" "not be in bucket B[i,j], i.e, even" >> "not be in bucket B[i,j]---even" (m-dash) "allow us to skip over quickly buckets that cannot contain possibly" >> "allow us to quickly skip over buckets that cannot possibly contain" "table (step 8), i.e.," >> "table (step 8); i.e.," (semicolon) "condition (11) the condition." : Text within <> should be in italics. D. Bucket Search Order and Early Return "in the grid which, as" >> "in the grid---which, as" "to be scanned can contain possibly a" >> "to be scanned can possibly contain a" "In this formula, dist" : Remove indentation "two cells, which is seen as" >> "two cells, seen as" "We conclude that bucket" >> "We conclude that a bucket" "all vectors (\delta_i, \delta_j) within |\delta_i|,|\delta_j|< N, which is sorted " >> "all vectors (\delta_i,\delta_j) with |\delta_i|,|\delta_j| < N, sorted " "each displacements" >> "each displacement" " (see Fig. 4)." >> ". See Fig. 4." E. Analysis "worst case, i.e., when" >> "worst case, when" "proportion to N^2 because" >> "proportion to N^2, because" "decreasing d cancel mostly each other so" >> "decreasing d mostly cancel each other; so" " (see Table III and Fig. 20)." >> ". See Table III and Fig. 20." F. Extension for Color Images "the color OVs" >> "the " (Text within <> should be in italics.) "yields the separate albedo" >> "yields a separate albedo" "image, i.e., the" >> "image, the" " of" : Text within <> should be in italics. " (see Fig. 16)." >> ". See Fig. 16." 3 - Tests "size and shape and allow us" >> "size and shape. They also allow us" "defects such as" >> "defects---such as" (m-dash) "either 422x422" >> "namely 422x422" "\kappa = #T/N^2 6%" >> "\kappa = #T/N^2 of 6%" "conversion for both tests for visualization purposes and " >> "conversion in both tests---for visualization purposes, and" "file saracchini" >> "file ~saracchini" (tilde symbol at mid-letter level) A. Tests With Synthetic Images "ray tracer in [8], which was from" >> "ray tracer [8], from" "The source-to-scene" : Join with paragraph above. "of the scene, which was large enough to" >> "of the scene---large enough to" "entire scene, and the " >> "entire scene; and the" (semicolon) "Fig. 7 shows the" : Start new paragraph before "Fig. 7". "Fig. 8 shows" : Join with paragraph above. "Fig. 11 shows" : Start new paragraph before "Fig. 11". "Fig. 11 is not" : Join with paragraph above. "Fig. 11 depicts accurately" >> "Fig. 11 accurately depicts" "of T from plane P." >> "of T from the plane P." "our claim that set" >> "our claim that the set" "Tables I and II shows" >> "Table II shows" "The columns are the " >> "The columns are: the" (colon) "2.5-GHz-clock" >> "2.5 GHz clock" "8-GB random access memory device; the" >> "8 GB of RAM. The" (or "8 GB of random-access memory. The") B. Tests With Photos of a Real Scene "TABLE I" : Move table to top left corner of page 2. "with matte-white enamel" >> "with matte white enamel" "black paper to block" >> "black paper, to block" "W50), which is mounted" >> "W50), mounted" "in a 8 cm x 16 cm" >> "in an 8 cm x 16 cm" "quality JPEG at" >> "quality JPEG format at" "small defects in the" >> "small defects of the" "defects had a relatively" >> "defects had relatively" "map, which is obtained by" >> "map, obtained by" "of the sticks and the second one, by" >> "of the sticks, and the second one by" C. Comparison With k-D Tree Nearest Neighbor "algorithm in [7]." >> "algorithm [7]." "Both methods are equally" >> "Our method and the k-D tree method are equally" "faster than both, although" >> "faster than the other two, although" "input images, i.e., from" >> "input images: from" (colon) "photos to a factor" >> "photos, to a factor" "signatures, i.e., both" >> "signatures, both" "displace usually" >> "usually displace" "removed further" >> "further removed" D. Comparison With ANN and LSH "is the LSH, as used in [34]." >> "is the LSH [34]." "According to Zhong and Little" >> "According to the authors" "used in [14]." >> "used by Hertzmann and Seitz [14]." "LSH method of [16]." >> "LSH method of Indyk and Motwani [16]." "implemented by [2]" >> "implemented by Andoni and Indyk [2]" E. Effect of image Noise "1) the seach time; 2) the accuracy ... 3) the accuracy" >> "(1) the search time; (2) the accuracy ... (3) the accuracy" Items 1) through 5) : Un-indent the text. "1)" >> "(1)" ":" : Text within <> should be in italics. "1Even.." >> "Even" "2)" : Delete the item number. "resolution (see Fig. 21) (since" >> "resolution. See Fig. 21. Since" "for the outliers)." >> "for the outliers." "3)" >> "(2)" ":" : Text within <> should be in italics. "4)" : Delete the item number. "5)" >> "(3)" ":" : Text within <> should be in italics. "integrator of [23] (however" >> "integrator of Saracchini et al. [23]. (However" "to this paper)." >> "to this paper.)" 4 - Conclusion and Future Work Remove topic 3 and 7 Remove enumeration of topics. Set italic font in the title of the topics ("Multiple materials","Spatially variable materials", "Height field error", "Nonuniform lighting", "Projected shadows", "Alternative grid projections") "18, radius" >> "18, the radius" "smaller than distance" >> "smaller than the distance" "1)" : Remove item number and un-indent text. ":" : Text within <> should be in italics. "and a grid structure" >> "and its grid structure" "each table and select" >> "each table, and select" "2)" : Remove item number and un-indent text. ":" : Text within <> should be in italics. "BRDF is a linear" >> "BRDF is a variable linear" "3)" : Remove item number and un-indent text. "in [14]), manifold" >> "by Hertzmann and Seitz [14]), the manifold" "4)" : Remove item number and un-indent text. ":" : Text within <> should be in italics. "5)" : Remove item number and un-indent text. ":" : Text within <> should be in italics. "signature s so that" >> "signature s, so that" "6)" : Remove item number and un-indent text. ":" : Text within <> should be in italics. "The large remaining" >> "The largest remaining" "start searching, particularly" >> "start searching --- particularly" "7)" : Remove item number and un-indent text. "One could remove easily" >> "One could easily remove" Biographies Rafael Saracchini "degree from Fluminense" >> "degree from the Fluminense" "working toward the Ph.D" >> "working toward a Ph.D" "State University of Campinas, Campinas, Brazil" >> "State University of Campinas, Brazil" "His research" : Join with paragraph above. "photometric Stereo" >> "photometric stereo" Jorge Stolfi "M.Sc. degrees" >> "M.Sc. degree" "from University" >> "from the University" "He is currently" : Join with paragraph above. "Computing, University of Campinas, Campinas, Brazil" >> "Computing, State University of Campinas, Brazil" ", and image processing and applications" >> ", image processing, and applications" Helena Leitão "Federal University of Rio de Janeiro, Rio de Janeiro, Brazil" >> "Federal University of Rio de Janeiro, Brazil" "Fluminense Federal University, Rio de Janeiro, Brazil" >> "Fluminense Federal University, Niterói, Brazil"