Patent Publication Number: US-11379986-B2

Title: Surface color segmentation

Description:
This application is the national stage of International Application PCT/EP2018/083211, filed Nov. 30, 2018, which claims priority to European patent application 17306683.8, filed Dec. 1, 2017 
     TECHNICAL FIELD 
     The present invention relates to a method for segmenting a view and more particularly for segmenting light-field contents. 
     BACKGROUND 
     In image processing, image segmentation is a process of partitioning an image, or a view, into multiple segments, i.e. sets of pixels. The goal of segmentation is to simplify and/or change the representation of an image into something that is more meaningful and easier to analyze. Image segmentation is typically used to locate objects and boundaries (lines, curves, etc.) in images. More precisely, image segmentation is the process of assigning a label to every pixel in an image such that pixels with the same label share certain characteristics. 
     The result of image segmentation is a set of segments that collectively cover the entire image, or a set of contours extracted from the image. Each of the pixels in a region are similar with respect to some characteristic, such as intensity, or texture. Adjacent regions are significantly different with respect to the same characteristic(s). 
     In image segmentation it is usually assumed that all the surfaces of a scene are reflecting light in a perfectly diffuse or Lambertian manner. However, most existing surfaces are non-Lambertian surfaces. Examples of non-Lambertian surfaces are specular, glossy or mirror-like surfaces whose appearance may change depending on the point of view of the scene. 
     The present invention has been devised with the foregoing in mind. 
     SUMMARY OF INVENTION 
     According to a first aspect of the invention there is provided a computer implemented method for segmenting at least one view comprising:
         determining a color palette for said view, the number of colors of said color palette corresponding to a number of labels to be used for segmenting at least said view,   associating at least one pixel of the view to one of said labels as a function of a distance or difference between an actual color of said pixel and a color of a label.       

     The method according to an embodiment of the invention is not limited to images directly acquired by an optical device. These data may be Computer Graphics Image (CGI) that are totally or partially simulated by a computer for a given scene description. Another source of images may be post-produced data that are modified, for instance color graded, images obtained from an optical device or CGI. It is also now common in the movie industry to have data that are a mix of both image types acquired using an optical acquisition device, and CGI data. 
     Using the color palette for determining the number of labels to be used for segmenting the view provides a more robust estimation than other metrics used in the prior art such as k-means clustering. Furthermore, using the color palette for determining the number of labels does not require an interaction from a user for setting the number of labels. 
     The method according to an embodiment of the invention does not make the assumption that surfaces of objects in the view are perfect Lambertian reflectors by providing a surface color segmentation which takes into account the change in appearance due to the nature of the surfaces. 
     According to an embodiment of the invention, associating at least one pixel of the view to one of said labels consists of optimizing the energy function given by: 
     
       
         
           
             
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     where: ψ u  (i)=Σ c∈a,b |α c (x i )−f c (r i )| is a unitary potential, is a pairwise potential, and 
                 ψ   p     ⁡     (     i   ,   j     )       =       τ   ⁡     (     i   ,   j     )       ⁢           ⁢     exp   (     -              w   ⊙     (       f   ⁡     (     r   i     )       -     f   ⁡     (     r   j     )         )            2   2     2       )             
is a pairwise potential, and
 
Σ( i,j )=∥log(α( x   i ))−log(α( x   j ))∥ 1  
 
     and where f(r i )=[x′, y′, L, a, b] being a vector representing a pixel of the view, x′, y′ being the coordinates of the pixel in the view and L, a, b representing the color of the pixel; α c  (x i ) is a value of a color channel, α(x i ) is a color of a label, τ(i,j) a penalty for label compatibility, and w is a vector having five coordinates representing weights to be applied to each coordinates of f(r i ). 
     In such an embodiment, the unitary potential penalizes each pixel of the view which has a color very different from a color of a label and the pairwise potential forces pixels with similar feature vectors to have similar labels. 
     In an embodiment of the invention, the CIELab color space is used, but other color spaces may be used as well such as YUV, RGB, XYZ, YCbCr or YCpCt for example. 
     An optimization method used to optimize the energy function is for example the method disclosed in P. Krähenbühl and V. Koltun. Efficient Interference in Fully Connected CRFs With Gaussian Edge Potentials. In Advances in Neural Information Processing Systems, pages 109-117, 2011. 
     According to an embodiment of the invention, when the at least one view belongs to a light-field content, the method further comprises:
         selecting a reference view and at least another view from the light-field content, said color palette being determined from said reference view,   determining for the reference view and the other view at least one set of super-rays, a super-ray being a group of rays of light belonging to a same area of a scene with uniform color,   regrouping groups of pixels whose labels have similar color in a same set of pixels by determining if a set of super-rays intersects a boundary between said groups of pixels,       

     To capture larger scenes, the spacing between cameras of a camera-rig has to be larger. A wide space between cameras results in a sparse light-field. 
     Processing a light-field content relies on the derivatives in the angular domain to impose constraints or fit parametric models to extract surface properties. In the case of a sparse light-field the estimation of these derivatives may be unreliable forbidding the use of existing processing techniques designed for light-fields. 
     One drawback of sparse light-field is that the amount of information available in sparse light-field does not allow for rich surface prediction. In the case of non-Lambertian surfaces such as specular, glossy or mirror-like surfaces whose appearance may change depending on the point of view of the scene, the sparsity of a sparse light-field becomes critical. Indeed, a same glossy surface may have different colors in different views of the sparse light-field. In order to segment the surface of an object having a glossy surface into its different colors the differences between the views of the light-field need to be accounted for. 
     In order to overcome this drawback, the inventors of the present invention propose to over-segment the views of the sparse light-field into super-rays. This kind of over-segmentation provides a soft geometric decomposition of a scene. 
     The reference view corresponds to the central view of a camera rig, the other views correspond to the views taken from a camera located on each corner of the camera rig. Using these views enables the consideration of occlusions and view-dependent effects while keeping computational complexity low since only a small number views of the light-field are considered. A larger set of views may be selected in which case the computation complexity is higher but accuracy may be improved. 
     According to an embodiment of the invention, the method further comprises propagating parameters representative of said set of pixels to the other views of the light-field content. 
     Thus a user does not have to apply the segmentation technique to each view of the light-field independently. 
     According to an embodiment of the invention, determining if a set of super-rays B (c i , c k ) intersects a boundary between said groups of pixels c i , c k  consists of for a super-ray:
         determining a color coherence       

               β   p     =     exp   (     -              [       σ   ⁡     (       α   L     ⁡     (     x   i     )       )       ,     σ   ⁡     (       α   a     ⁡     (     x   i     )       )       ,     σ   ⁡     (       α   b     ⁡     (     x   i     )       )         ]          2     0.01       )           
where σ(α c (x i )) is a standard deviation in color channel c for a group of pixels {r i } inside a super-ray p,
 
     
       
         
           
             
               
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     q k ={i|r i ∈p∧(r i )=c k ∧c k ∈ϕ u (p)∧|c k |&gt;μ|p|}, where ϕ u (p) is the distinct group of pixels which are present in the super-ray,
         determining a fuzziness ρ p =max({λ p (c k )|c k ∈ϕ u (p)})   generating, based on these measures, a graph G=(V,E) where V is a set of nodes v i  which corresponds to a segment and E is a set of weighted edges,   determining a weight       

               w     i   ,   j       =       1     2   ⁢          B   ⁡     (       c   i     ,     c   k       )                ⁢       ∑     p   ∈     B   ⁡     (       c   i     ,     c   k       )           ⁢       ρ   p     ⁢           ⁢     ρ   p                 
where B(c i , c k )={p|c i , c k ∈ϕ u (p)∧c i ≠c k ∧p∈P(L)}
         Merging nodes if w i,k  is smaller than a given threshold.       

     According to an embodiment of the invention, prior to determining the color palette the method comprises:
         selecting an object in said reference image,   propagating said selected objects in the other views of the light-field content.       

     Another object of the invention concerns a device capable of segmenting at least one view comprising at least one hardware processor configured to:
         determine a color palette for said view, the number of colors of said color palette corresponding to a number of labels to be used for segmenting said view,   associate at least one pixel of the view to one of said labels as a function of a difference between an actual color of said pixel and a color of a label.       

     According to an embodiment of the invention, associating at least one pixel of the view to one of said labels consists in optimizing the energy function given by: 
     
       
         
           
             
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     where: ψ u (i)=Σ c∈a,b |α c (x i )−f c (r i )|; 
                   ψ   p     ⁡     (     i   ,   j     )       =       τ   ⁡     (     i   ,   j     )       ⁢           ⁢     exp   (     -              w   ⊙     (       f   ⁡     (     r   i     )       -     f   ⁡     (     r   j     )         )            2   2     2       )         ;   and                 τ   ⁡     (     i   ,   j     )       =              log   ⁡     (     α   ⁡     (     x   i     )       )       -     log   ⁡     (     α   ⁡     (     x   j     )       )              1           
and
 
τ( i,j )=∥log(α( x   i ))−log(α( x   j ))∥ 1  
 
     and where f(r i )=[x′, y′, L, a, b] being a vector representing a pixel of the view, x′, y′ being the coordinates of the pixel in the view and L, a, b representing the color of the pixel; α c (x i ) is a value of a color channel, α(x i ) is a color of a label, τ(i,j) a penalty for label compatibility, and w is a vector having five coordinates representing weights to be applied to each coordinates of f(r i ). 
     According to an embodiment of the invention, when the at least one view belongs to a light-field content, said hardware processor is further configured to:
         select a reference view and at least another view from the light-field content, said color palette being determined from said reference view,   determine for the reference view and the other view at least one set of super-rays, a super-ray being a group of rays of light belonging to a same area of a scene with uniform color,   regroup groups of pixels whose labels have similar color in a same set of pixels by determining if a set of super-rays intersects a boundary between said groups of pixels,       

     According to an embodiment of the invention, the parameters representative of said set of pixels are propagated to the other views of the light-field content. 
     Some processes implemented by elements of the invention may be computer implemented. Accordingly, such elements may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a “circuit”, “module” or “system’. Furthermore, such elements may take the form of a computer program product embodied in any tangible medium of expression having computer usable program code embodied in the medium. 
     Since elements of the present invention can be implemented in software, the present invention can be embodied as computer readable code for provision to a programmable apparatus on any suitable carrier medium. A tangible carrier medium may comprise a storage medium such as a floppy disk, a CD-ROM, a hard disk drive, a magnetic tape device or a solid state memory device and the like. A transient carrier medium may include a signal such as an electrical signal, an electronic signal, an optical signal, an acoustic signal, a magnetic signal or an electromagnetic signal, e.g. a microwave or RF signal. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments of the invention will now be described, by way of example only, and with reference to the following drawings in which: 
         FIG. 1  is a schematic block diagram illustrating an example of a device capable of executing the method according to an embodiment of the invention; 
         FIG. 2  is a flowchart representing the steps of a method for segmenting an image, or a view, according to an embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION 
     As will be appreciated by one skilled in the art, aspects of the present principles can be embodied as a system, method or computer readable medium. Accordingly, aspects of the present principles can take the form of an entirely hardware embodiment, an entirely software embodiment, (including firmware, resident software, micro-code, and so forth) or an embodiment combining software and hardware aspects that can all generally be referred to herein as a “circuit”, “module”, or “system”. Furthermore, aspects of the present principles can take the form of a computer readable storage medium. Any combination of one or more computer readable storage medium (a) may be utilized. 
     Table 1 summarizes the notations used throughout the following description of the different embodiments of the invention. 
     
       
         
           
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
             
            
               
                   
                 Light field 
                 L 
               
               
                   
                 Image plane 
                 Ω xy   
               
               
                   
                 Sensor plane 
                 Π uv   
               
               
                   
                 Number of views 
                 m × n 
               
               
                   
                 View 
                 L ij   
               
               
                   
                 Reference view 
                 L u     c   ,  v     c     
               
               
                   
                 Key views 
                 L′ = {L 00 , L  M0 , L u     c     v     c   , L 0N , L  M N } 
               
               
                   
                 Ray 
                 r = (x, y, u, v) 
               
               
                   
                 Super-ray 
                 p 
               
               
                   
                 Set of all super-rays 
                 P(L ) = {p} 
               
               
                   
                 Segment of a ray 
                 ϕ(r) 
               
               
                   
                 Color palette: 
                    (L u     c   ,  v     c   ) = {a 0 , a 1 , . . . , a k } 
               
               
                   
                 set of CIELab colors 
                   
               
               
                   
                 Label 
                 x 
               
               
                   
                 CIELab color of a label 
                 α(x) 
               
               
                   
                 Color channel of a label 
                 α c (X), c ϵ {L, a, b} 
               
               
                   
                 Energy for the CRF 
                 E 
               
               
                   
                 Feature vector of a ray 
                 f(r) = [x′, y′, L, a, b] 
               
               
                   
                 Label compatibility 
                 τ(i, j) 
               
               
                   
                 Unique segments 
                 ϕ u  (P) 
               
               
                   
                 per super-ray 
                   
               
               
                   
                 Color coherence 
                 β P  (c k ) 
               
               
                   
                 Fuzziness per 
                 λ P (c k ) 
               
               
                   
                 super-ray and segment 
                   
               
               
                   
                 Fuzziness 
                 ρ P   
               
               
                   
                 Edge weights 
                 w i,k   
               
               
                   
               
            
           
         
       
     
       FIG. 1  is a schematic block diagram illustrating an example of a device capable of executing the method according to an embodiment of the invention. 
     The apparatus  100  comprises a processor  101 , a storage unit  102 , an input device  103 , a display device  104 , and an interface unit  105  which are connected by a bus  106 . Of course, constituent elements of the computer apparatus  100  may be connected by a connection other than a bus connection. 
     The processor  101  controls operations of the apparatus  100 . The storage unit  102  stores at least one program to be executed by the processor  101 , and various data, including data of images captured and provided by a camera, parameters used by computations performed by the processor  101 , intermediate data of computations performed by the processor  101 , and so on. The processor  101  may be formed by any known and suitable hardware, or software, or a combination of hardware and software. For example, the processor  101  may be formed by dedicated hardware such as a processing circuit, or by a programmable processing unit such as a CPU (Central Processing Unit) that executes a program stored in a memory thereof. 
     The storage unit  102  may be formed by any suitable storage or means capable of storing the program, data, or the like in a computer-readable manner. Examples of the storage unit  102  include non-transitory computer-readable storage media such as semiconductor memory devices, and magnetic, optical, or magneto-optical recording media loaded into a read and write unit. The program causes the processor  101  to perform a process for segmenting an image according to an embodiment of the present disclosure as described with reference to  FIG. 2 . 
     The input device  103  may be formed by a keyboard  10 , a pointing device  11  such as a mouse, or the like for use by the user to input commands, etc. The output device  104  may be formed by a display device  12  to display, for example, a Graphical User Interface (GUI), images generated according to an embodiment of the present disclosure. The input device  103  and the output device  104  may be formed integrally by a touchscreen panel, for example. 
     The interface unit  105  provides an interface between the apparatus  100  and an external apparatus. The interface unit  105  may be communicable with the external apparatus via cable or wireless communication. In an embodiment, the external apparatus may be a camera. In this case, data images captured by the camera can be input from the camera to the apparatus  100  through the interface unit  105 , then stored in the storage unit  102 . In another embodiment, the device  100  receives Computer Graphics Image (CGI) data that are totally or partially simulated by a computer for a given scene description. Another source of data may be post-produced data that are modified, for instance color graded, images obtained from an optical device or CGI. It is also now common in the movie industry to have data that are a mix of both images acquired using an optical acquisition device, and CGI data. 
     In this embodiment the apparatus  100  is exemplary discussed as it is separated from the camera and they are communicable each other via cable or wireless communication, however it should be noted that the apparatus  100  can be integrated with such a camera. In this later case, the apparatus  100  may be for example a portable device such as a tablet or a smartphone embedding a camera. 
       FIG. 2  is a flowchart representing the steps of a method for segmenting an image, or a view, according to an embodiment of the invention. Such a method for segmenting an image applies both to classical 2D (2-dimensional) images and light-field images. 
     In a step  200 , the device  100  acquires or receives, depending on whether it is connected to a camera, an image I. In a first embodiment of the invention, the image I is a classical 2D image. In a second embodiment of the invention, the image I is a light-field image comprising a plurality of views. Such a light-field image may be acquired by a plenoptic camera or by a camera array also known as a camera rig. 
     When the image I is a light-field image, said light-field image is represented as a two-plane parametrization on ray space L(x, y, u, v), where a light ray r∈L passes through two parallel planes: the sensor plane Π uv , and the virtual camera plane or image plane Ω xy . L i,j (x, y) or L i,j  denotes a view of the light field that cuts the sensor plane of a camera at coordinates (u=i, v=j). A reference view of the light field is defined as L u     c     v     c    with 
               u   c     =         ⌊     m   2     ⌋     ⁢           ⁢   and   ⁢           ⁢     v   c       =     ⌊     n   2     ⌋             
for a sensor plane of size m×n.
 
     One goal of the method according to embodiments of the invention is to find a set of segments Φ={c k } with coherent surface color across the multiple views of the light field. 
     In a step  201 , when the image I is a light-field image, the processor  101  of the device  100  selects key views L′ in the light-field image I. The key views are for example a reference view and at least another view from the light-field image, said color palette being determined from said reference view. In an embodiment of the invention, the key views L′ are the reference view and extrema views, which in the case of a camera rig correspond to views acquired by the cameras located on the corners of the camera rig, L′={L 0,0 , L m,0 , L u     c     ,v     c   , L 0,n , L m,n } since they cover the highest variability in terms of occlusions and color variations with view-point changes. 
     In a step  202 , the processor  101  determines for each of the key views L′ a set of super-rays P(L)={p}. A super-ray being a group of rays of light belonging to a same area of a scene with approximately uniform color and imaged in a plurality of views. The super-rays provide disparity values d(x, y, u, v) for each ray of light of the light-field image I. 
     The disparity values are then used to reparametrize all the rays of light of the light-field image I into the reference view. Consequently, each ray of light of the light-field image I may have new coordinates x′=x+(u−u c ) d(x, y, u, v) and y′=y+(v−v c ) d(x, y, u, v) in the reference view, where x, y, u, v are the former coordinates of the ray of light. 
     In an optimal step  203 , the processor  101  of the device  100  detects an input on the input device  103  which corresponds to a user selecting an object in the image I. Step  203  may be run on a classical 2D image or on a light-field image. 
     When the image I is a light-field image, the processor  101  propagates the selection to all the views of the light-field image using known propagation techniques such as the technique disclosed in M. Hog, N. Sabater and C. Guillemot. Super-rays for Efficient Light-Field Processing. IEEE Journal of Selected Topics in Signal Processing, 2017. 
     In a step  204 , the processor  101  determines a color palette  (L u     c     ,v     c   )={α 0 , α 1 , . . . , α k } of the image I. When image I is a light-field image, the processor determines the color palette  (L u     c     ,v     c   )={α 0 , α 1 , . . . , α k } of the reference view of the light-field image. The color palette  (L u     c     ,v     c   )={α 0 , α 1 , . . . , α k } may be determined using the method disclosed in J. Delon, A. Desolneux, J-L. Lisani and A. B. Petro. A Non-parametric Approach of Histogram Segmentation. IEEE Transactions on Image Processing, 16(1)/253-261, 2007. 
     The processor  101  then determines the number of labels to be used for segmenting image I since the number of labels corresponds to the number of colors of the color palette  (L u     c     ,v     c   )={α 0 , α 1 , . . . , α k }. 
     In a step  205 , the processor  101  associates the pixels of image I to one of said labels as a function of a difference between an actual color of said pixel and a color of a label. When image I is a light-field image, the processor executes step  205  on each of the key views selected during step  201 . 
     Associating said labels to pixels of image I consists of optimizing the energy function given by: 
     
       
         
           
             
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     where: ψ u (i)=Σ c∈a,b |α c  (x i )−f c (r i )| is a unitary potential, 
                 ψ   p     ⁡     (     i   ,   j     )       =       τ   ⁡     (     i   ,   j     )       ⁢           ⁢     exp   (     -              w   ⊙     (       f   ⁡     (     r   i     )       -     f   ⁡     (     r   j     )         )            2   2     2       )             
is a pairwise potential, and
 
τ( i,j )=∥log(α( x   i ))−log(α( x   j ))∥ 1  
 
     and where f(r i )=[x′, y′, L, a, b] being a vector representing a pixel of the view, x′, y′ being the coordinates of the pixel in the view and L, a, b representing the color of the pixel; α c  (x i ) is a value of a color channel, α(x i ) is a color of a label, τ(i,j) a penalty for label compatibility, and w is a vector having five coordinates representing weights to be applied to each of the coordinates of f(r i ). 
     In such an embodiment, the unitary potential penalizes each pixel of the view which has a color very different from a color of a label and the pairwise potential forces pixels with similar feature vectors to have similar labels. 
     An optimization method used to optimize the energy function is for example the method disclosed in P. Krähenbühl and V. Koltun. Efficient Interference in Fully Connected CRFs With Gaussian Edge Potentials. In Advances in Neural Information Processing Systems, pages 109-117, 2011. 
     In a step  206 , the processor  101  regroups groups of pixels whose labels have similar color in a same set of pixels by determining if a set of super-rays intersects a boundary between said groups of pixels. Step  205  produces a color segmentation of image I which may be over-segmented, due for example to shadows or high-lights. This may impact the final segmentation of image I. 
     To overcome this issue, step  206  is executed. To merge segments of image I which corresponds to a same surface. Since the processor  101  uses information related to the super-rays while executing step  206 , this step is only executed when step  202  is executed. 
     Determining if a set of super-rays B(c i , c k ) intersects a boundary between said groups of pixels c i , c k  consists in computing for each super-ray:
         the color coherence       

               β   p     =     exp   (     -              [       σ   ⁡     (       α   L     ⁡     (     x   i     )       )       ,     σ   ⁡     (       α   a     ⁡     (     x   i     )       )       ,     σ   ⁡     (       α   b     ⁡     (     x   i     )       )         ]          2     0.01       )           
where σ(α c (x i )) is a standard deviation in color channel c for a group of pixels {r i } inside a super-ray p,
 
     
       
         
           
             
               
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     q k ={i|r i ∈p∧ϕ(r i )=c k ∧c k ∈ϕ u (p)∧|c k |&gt;μ|p|}, where ϕ u (p) is the distinct group of pixels which are present in the super-ray,
         the fuzziness ρ p =max({λ p (c k )|c k ∈ϕ u (p)}).       

     Then, based on these measures per super-ray, a graph G=(V,E) where V is a set of nodes v i  which corresponds to a segment, i.e. V={v i =c i } and E is a set of weighted edges, where two nodes are neighbors when they are connected in a 4-neighborood in an image plane of the light-field image. 
     A weight w i,j  is given by 
               w     i   ,   j       =       1     2   ⁢          B   ⁡     (       c   i     ,     c   k       )                ⁢       ∑     p   ∈     B   ⁡     (       c   i     ,     c   k       )           ⁢       ρ   p     ⁢           ⁢     ρ   p                 
where
 
     B(c i ,c k )={p|c i , c k ∈ϕ u (p)∧c i ≠c k ∧p∈P(L)} which is the super-ray which intersect the boundaries between segments c i , and c k . The nodes are merged if w i,k  is smaller than a given threshold. For example, in an embodiment of the invention, w i,k &lt;0.02. 
     In step  207 , the processor  101  propagates the merging determined during step  206  to all the views of the light-field image using known propagation techniques. 
     The method according to the invention may provide an image representing the segmentation of image I, i.e. an image in which each segment has a color corresponding to its label or a data file in which in pixel of the image I is associated to a segment and its label. 
     The segmentation of the image I obtained after executing the method according to an embodiment of the invention may be used as input data for an intrinsic light-field decomposition method. 
     Intrinsic decomposition is process of reverse-engineering the process of image formation. More particularly, any pixel recorded by a camera corresponds to light having reflected off a surface in a scene. Intrinsic decomposition splits an image I into a first component representing the reflectance R of the imaged surface, and a second component S representing the illumination incident upon that surface so that I=R⊙S. this is an under-constrained problem in classical 2 mages as well as in light-field images for which I=L. 
     In light-field images however, a same scene point is imaged in different views from different vantage points. The broader the baseline of the light-field image the more potential for analysis said light-field image offers in this respect. Using the segmentation method according to the different embodiments of the invention enables a meaningful intrinsic decomposition. 
     Using the segmentation resulting from the execution of the method according to an embodiment of the invention in the decomposition enable to obtain a gray-scale shading component s=log S by minimizing a linear system of equations according for example to the method disclosed in E. Garces, A. Munoz, J. Lopez-Moreno, and D. Gutierrez. Intrinsic Images by Clustering. Computer Graphics Forum (Proc. EGSR), 31(4), 2012. 
     As a consequence of having segmented the light-field image, there is only one unknown left per segment c k , so that it possible to impose shading smoothness constrains between pairs of neighboring segments: 
     
       
         
           
             
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     where c k  and c l  are neighboring segments in the light-field image plan, and the shading components s k  and s l  are computed as: 
     
       
         
           
             
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     Where r k  refers to a reflectance color. Further  ι   k  is the average value for all the rays within a segment k. This optimization may be solved globally in closed-form for the entire light-field image as the number of unknowns is significantly reduced by working with segments instead of rays. Then the light-field image reflectance R is determined as per pixel and per channel division: R=LØS. 
     Although the present invention has been described hereinabove with reference to specific embodiments, the present invention is not limited to the specific embodiments, and modifications will be apparent to a skilled person in the art which lie within the scope of the present invention. 
     Many further modifications and variations will suggest themselves to those versed in the art upon making reference to the foregoing illustrative embodiments, which are given by way of example only and which are not intended to limit the scope of the invention, that being determined solely by the appended claims. In particular the different features from different embodiments may be interchanged, where appropriate.