Outline. Seamless Image Stitching in the Gradient Domain. Related Approaches. Image Stitching. Introduction Related Work

Transcription

1 Outlne Seamless Image Sttchng n the Gradent Doman Anat Levn, Assaf Zomet, Shmuel Peleg and Yar Wess ECCV 004 Presenter: Pn Wu Oct 007 Introducton Related Work GIST: Gradent-doman Image Sttchng GIST GIST Imlementaton detals Iteratve Otmzaton Exerments & Dscusson Panoramc Vew Obect Parts Image Sttchng Related Aroaches Combne ndvdual mages havng some overla nto a comoste mage Commonly used for generatng anoramc mages + Otmal seam algorthm Otmal seam [3,,4] Otmal seam curve that fts to the mnmal dfference Transton smoothng Featherng [6] or alha blendng Weghted combnaton wth coeffcent functons of dstance [] [6] Vsual artfcal edges at the seam due to the dfferences n Camera gan Scene llumnaton Geometrcal msalgnment 3 Pyramd Blendng [7] Dfferent alha masks n dfferent frequency bands Otmzaton rocess Posson Image Edtng [0] Otmzaton over the gradent doman Gradent-doman Image Sttchng(GIST) 4

2 Photometrc nconsstences Comarson of Sttchng Methods Requrement Good sttchng (seamless) The mosac should be as smlar as ossble to the nut mages, both geometrcally and hoto-metrcally. The seam between the sttched mages should be nvsble. Qualty measurement s oerated n gradent doman. Horzontal msalgnments Vertcal msalgnments 5 6 GIST: Gradent Image STtchng GIST: Otmzng a cost functon over Image Dervatves E ( Iˆ ; I, I, W ) = d ( Iˆ, I, τ ω, W ) + d ( Iˆ, I, τ ω, U W ), where d ( J, J, φ, W ) = W ( q) J ( q) J ( q) GIST: Gradent Image STtchng GIST: Sttchng Dervatve Images I I I I Comute deratves:,,, x y x y Form a feld F = ( F, F ), where x y I I I I Fx, Fy are formed wth sttchng, and, x x y y (Featherng, Pyramd blendng, or otmal seam) mnmze d ( I, F, π, U ) = U ( q) I ( q) F( q) q π f x 7 8

3 GIST Proertes Imlementaton Whch method to use? GIST under l s recommended GIST under l Solvng through FFT d ( J, J, φ, W ) = W ( q) J ( q) J ( q) GIST under l V.S otmal seam Same results n geometrc msalgnments condton GIST > otmal seam f no erfect seam, e.g. hotometrc nconsstences GIST under l V.S GIST under l GIST under l Featherng of the gradent mages (GIST) under l (soluton of Posson Equaton) l : tendng to mx the dervatves and hence blurrng n the overla regon. l : tendng to behave smlarly to the otmal seam methods. 9 GIST under l Solvng through Lnear Programmng Unform ntensty shft (nut mage, mosac mage) l Iteratve otmzaton Intal the soluton mage I Iterate untl convergence: For all x,y n the mage, d ( J, J, φ, W ) = W ( q) J ( q) J ( q) Mn : ( z + z ) Subect to : Ax + ( z + z ) = b, x 0, z 0, z 0 I( x +, y) Dx ( x, y), I ( x, y) + Dx ( x, y), I( x, y) * medan( { }) I ( x, y + ) Dy ( x, y), I ( x, y ) + Dy ( x, y ) 0 Dfferences wth Posson Edtng GIST use the gradents of both mages n the overla regon. The otmzaton s done under dfferent norms Performance + Overcome global nconsstences + Overcome Msalgnments - Seed - Convergence Image-ntensty methods V.S. Gradent-doman methods Double edge 3

4 Sttchng Panoramc Vew Sttchng Panoramc Vew (a) Otmal seam (b) Featherng (c) Pyramd blendng (d) Otmal seam (gradent) (e) Featherng (gradent) (f) Pyramd blendng (gradent) (g) Posson edtng (h) GIST under l (a) Otmal seam (b) Featherng (c) Pyramd blendng (d) Otmal seam (gradent) (e) Featherng (gradent) (f) Pyramd blendng (gradent) (g) Posson edtng (h) GIST under l 3 4 Sttchng Panoramc Vew Sttchng Panoramc Vew (a) Otmal seam (b) Featherng (c) Pyramd blendng (d) Otmal seam (gradent) (e) Featherng (gradent) (f) Pyramd blendng (gradent) (g) Posson edtng (h) GIST under l (a) Otmal seam (b) Featherng (c) Pyramd blendng (d) Otmal seam (gradent) (e) Featherng (gradent) (f) Pyramd blendng (gradent) (g) Posson edtng (h) GIST under l 5 6 4

5 Sttchng Obect Parts Sttchng Obect Parts Orgnal comoston GIST under l GIST under l Pyramd (gradent) 7 GIST under l GIST under l Pyramd (gradent) Pyramd (mage) 8 5