Inessa Gracheva and Andrey Kopylov - Image Processing Algorithms with Structure Transferring Propertie on the Basis of Gamma-normal Model
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The document discusses image processing algorithms utilizing the gamma-normal model to improve results in various applications such as haze removal and edge refinement. It analyzes the joint conditional probability density and introduces a fast global image denoising algorithm leveraging nonstationary statistics. Additionally, it compares computational efficiencies and outputs experimental results highlighting the effectiveness of the proposed methods.
Inessa Gracheva and Andrey Kopylov - Image Processing Algorithms with Structure Transferring Propertie on the Basis of Gamma-normal Model
- 1. Image processing algorithms with structure transferring proper4es on the basis of gamma-‐normal model Gracheva Inessa, gia1509@mail.ru, Kopylov Andrey, and.kopylov@gmail.com, Russia, Tula, Tula State University, AIST Conference, Yekaterinburg, 2016
- 2. Related Work ( , )tY y t T= ∈ ( , )tX x t T= ∈ Analyzed Image Processing Result 1 2 1 1 2 2{ ( , ): 1,..., , 1,..., }T t t t t N t N= = = = We will consider an analyzed image and processing result as, respectively, the observed and hidden components of the two-component random field (X, Y ). ( , )tY y t T= ∈ ( , )tX x t T= ∈
- 3. Probabilis4c Data Model Joint conditional probability density: where is the variance of the observation noise. A priori joint distribution: where is factors of the unknown local variability of the sought for processing result; V is the neighborhood graphs of image elements having the form of a lattice. 1 2 1 2 2 ( )/2 ( )/2 1 1 ( | , ) exp( ( ) ) (2 ) 2 t tN N N N t T Y X y xδ δ π δ ∈ Φ = − −∑ 1 2 2 1/2 ,( )/2 1 1 1 ( | , ) exp ( ) 2 (2 ) t t t t V tN N t t T X x xδ δλ δλ π ʹ′ ʹ′ʹ′ ʹ′ ʹ′ʹ′∈ ∈ ⎛ ⎞ Ψ Λ ∝ × − −⎜ ⎟ ⎛ ⎞ ⎝ ⎠ ⎜ ⎟ ⎝ ⎠ ∑ ∏ δ=)( 2 teE tλ 1 N1t1 1 N2 t2
- 4. Gamma-‐Normal Model 2 1 2 (1/ | , , ) (1/ ) exp (1/ ) 2 t t t µ δµ λ γ λ δ λ µ λ λ δµ + ⎛ ⎞ ∝ −⎜ ⎟ ⎝ ⎠ 2 1)1( 2)/1(, 1)1( )/1( λ µδ δµλ λ µδ λ ++ = ++ = tt VarE 1 1 1 ( | , , ) exp ln 2 t t T t G δ λ µ λ λ δµ λ λ∈ ⎡ ⎤⎛ ⎞ Λ = − +⎢ ⎥⎜ ⎟ ⎝ ⎠⎣ ⎦ ∑ Gamma-distribution of the inverse factors :tλ/1 with mathematical expectations and variances: A priori distribution density: Joint prior normal gamma-distribution: ( , | , , ) ( | , ) ( | , , )H X X Gδ λ µ δ δ λ µΛ = Ψ Λ Λ , 2 2 ' '' ', '' ( , | , ) argmin ( , | , , ), 1 1 ( , | , , ) ( ) ( ) (1 )ln . X t t t t t t T t t V t X J X Y J X Y y x x x λ µ λ µ λ λ µ λ λ µ µ Λ ∈ ∈ ⎧ Λ = Λ ⎪⎪ ⎨ ⎧ ⎫⎡ ⎤ ⎪ Λ = − + − + + +⎨ ⎬⎢ ⎥ ⎪ ⎣ ⎦⎩ ⎭⎩ ∑ ∑ ) ) Bayesian estimate of :( , )X Λ Gracheva I., Kopylov A., Krasotkina O.: Fast global image denoising algorithm on the basis of nonstationary gamma-normal statistical model. Communications in Computer and Information Science. Springer. 542, 71-83 (2015).
- 5. New Formula4on of the Problem He K., Sun J., Tang X.: Guided Image Filtering. IEEE Trans. on Pattern Analysis and Machine Intel. 35(6), 1397-1409 (2013). Analyzed Image Guided Image ( , )tY y t T= ∈ ( , )g g tX x t T= ∈ ( , )tX x t T= ∈ ( , , , ) arg min ( | , , , ) X X Y J X Yµ µΛ = Λλ λ ( , , ) arg min ( | , , )g g X J Xµ µ Λ Λ = Λλ λ Processing Result
- 6. 1 2 1 1 2 2{ ( , ): 1,..., , 1,..., }T t t t t N t N= = = = Image haze removal problem: Analyzed Image Processing Result Guided Image ( , )tY y t T= ∈ ( , )tX x t T= ∈ ( , )g g tX x t T= ∈ HDR image compression problem: Edge refinement of an image: Examples of Problems
- 7. Structure-‐Transferring Proper4es 2 ' '' ' (1/ )( ) 1/ ( , , ) 1 1/ g g g t t t x x X λ µ λ λ µ λ µ − + = + ) ( , )t t TλΛ = ∈ )) ( , )g g tX x t T= ∈ ( , )tX x t T= ∈ ( , )tY y t T= ∈ The estimates of factors represent the edges of objects in the guide image . This makes it possible to transfer structure from the guide image to the output image , even if the analyzed image is smooth. ( , )g g tX x t T= ∈ 2 2 ' '' ', '' ' ( , ) argmin ( , | , , ) 1 argmin ( ) ( ) . X t t t t X t T t t V t X x t T J X Y y x x x λ µ λ∈ ∈ = ∈ = Λ = ⎧ ⎫ = − + −⎨ ⎬ ⎩ ⎭ ∑ ∑ ) )
- 8. Edge Refinement of an image ( , )g g tX x t T= ∈ ( , )tY y t T= ∈ ( , )t t TλΛ = ∈ )) ( , )tX x t T= ∈
- 9. Image Haze Removal 3 Ra ∈ g t t t x a x a x − = +% ( , )t t TλΛ = ∈ )) ( , )g g tX x t T= ∈ ( , )tY y t T= ∈ ( , )tX x t T= ∈% % ( , )tX x t T= ∈
- 10. Compression HDR ( ( ))t t tx y x mean xα= − + ) ) % α is contrast sensitivity and will compress contrasts for values<1,0. ( , )tY y t T= ∈ ( , )g g tX x t T= ∈( , )tX x t T= ∈
- 11. Experimental Result Comparison experimental results on structure-transferring filtering. a) Original image; b) Binary mask; c) Our algorithm; d) Guided filter; e) Fast Guided filter; f) In the zoom-in patches, our algorithm compare with the Guided filter and the fast Guided filter.
- 14. Computa4on Time Computation time of Guided filter, fast Guided filter (with s = 2), fast Guided filter (with s = 4) and our algorithm for processing of images of different sizes.
- 15. THANK YOU FOR ATTENTION!