Patent Application: US-201313764833-A

Abstract:
an image having m light sources , with m preferably equaling 2 or 3 , is segmented into different regions , each of which is lit by only one of the m light sources , by obtaining paired imaged with different filtering , for example a filtered and an unfiltered image , applying to the image pairs sets of m pre - computed mappings at the pixel or region level , and selecting the most appropriate . the rendering of the information in the image maybe adjusted accordingly .

Description:
we illustrate a method in accordance with one embodiment schematically in fig1 . pre - calculated mappings ( here represented by scalar multiplication factors 1 , ⅓ , and ½ ) are applied to unfiltered pixel values { 3 , 4 } to best match filtered counterparts { 1 , 2 }. here we have a very simple image with two regions which for the purposes of this example are represented by single numbers ( perhaps this image is the cast shadow of an aeroplane flying over the ground ). the top image i , has the region labeled ‘ 3 ’ representing a shadow . in this diagrammatic representation , we do not illustrate the algorithm using colour , which the method actually uses in practice . instead , we simplify to a single , scalar value at each pixel for illustrative purposes . in fig1 , the labels ‘ 1 ’, ‘ 2 ’, ‘ 3 ’, ‘ 4 ’, are the labels for each region and are also the pixel values : e . g ., in the shadow region of image i , the scalar value of the image pixels is the number 3 . a corresponding filtered image again with 2 regions is shown having regions ‘ 1 ’ and ‘ 2 ’ and is denoted as i f . for these scalar - values images , our pre - computed set sx of mappings from unfiltered to filtered pixel values are simply a set of n scalars , one for each of n lights . now suppose in this example we have predetermined a set of n = 3 mappings for 3 lights , and the mappings from unfiltered to filtered camera responses are given by the three scalars { 1 , ⅓ , ½ }. on the right - hand side of fig1 , the three possible mappings are shown : the first mapping is designated by ‘* 1 ’, where * 1 means we can multiply the image pixel by 1 to predict the corresponding filtered output , and so on . as there are three scaling factors ( in the general case these are mappings ) there are ‘ 3 choose 2 ’= n !/(( n − 2 )! 2 ! )= 3 !/( 1 ! 2 ! )= 3 possible combinations of two maps . in the diagram we label these map sets a , b and c . we now apply each of these mapping sets in turn . e . g ., if we test set a , consisting of the candidate mappings * 1 and * ⅓ , then we apply * 1 to the whole image i and then compare errors from the actually observed filtered responses i f , and then also apply * ⅓ to the whole image i and compare errors from i f . at the pixel level , for this mapping a , which of the two mappings , * 1 or * ⅓ , results in the least error at a pixel results in that pixel being labeled as associated with the first , or the second , mapping . ( associations of whole regions are described below .) we carry on as above with the alternate mappings b , meaning the scalar multiplier set {* ⅓ , * ½ }, and c , meaning the scalar multiplier set {* 1 , * ½ }. now we determine a method for deciding which mapping is the best , overall . if we follow the line labeled a we see the calculations involved in estimating the goodness of this map set . for the input pixel 3 in image 1 , from mappings set a we can apply a map of either * 1 or * ⅓ . applying each map in turn we arrive at the two leftmost leaf nodes in fig1 : we calculate the predicted filtered response we apply the map to the pixel value ) calculate error from the actually observed filtered image i f by subtracting that actual pixel response . in terms of the example we calculate : ( 3 * 1 − 1 ) and ( 3 * ⅓ − 1 ) ( equaling errors of 2 and 0 respectively for the error for pixels in region ‘ 3 ’ mapped to region ‘ 1 ’). since 0 is less than 2 , the mapping * ⅓ may be chosen as associated with this pixel . looking at the next leftmost pair of tree nodes , we go through the same procedure for the second pixel ‘ 4 ’. again in this case we see that * ⅓ better predicts the actual filtered outputs ( though , not exactly ). based on relation set a alone we could conclude that both pixels ‘ 3 ’ and ‘ 4 ’ are best mapped to the corresponding filtered counterparts using the same relation ,* ⅓ , and so at this stage we would conclude that both pixels were captured under the same light . if relation set a best modeled our data overall , then our hypothesis that there were two lights would be wrong ( only one relation and hence one light was found to be present ). parsing the rest of the tree , we can see that the middle relation branch ( relation set b ) results in the smallest total of absolute difference between predicted and actual responses . ( in this simple example the difference is actually exactly 0 ). moreover , we can see that pixels ‘ 3 ’ and ‘ 4 ’ are mapped with two different relations , * ⅓ and * ½ respectively . so , in this case we would conclude that each pixel is captured with respect to a different illuminant . of course , in an actual image processing task an image will have k pixels or regions . each pixel may typically be described by an rgb triplet , as may the corresponding filtered counterpart . the relations that predict how camera responses are mapped to filtered counterparts are multidimensional , not scalar , functions . for example the relations could be 3 × 3 matrix transforms or more complex non - linear maps . moreover , in practice there are many more maps ( n = 50 to 100 are used in our experiments ) than in fig1 and so there can be many more map sets to consider . but , in essence the computation is the same as outline above for fig1 . for every pixel , or region , in the image we find the map ( belonging to a set of 2 maps if we are considering m = 2 ) that best maps the rgb ( s ) to the filtered counterpart ( s ). we can then calculate a prediction error for the whole image . this process can be repeated for all possible map sets . the map set that best predicts filtered counterparts from image rgbs can then be used to directly partition the image into regions lit by different lights . in accordance with this disclosure pixels , or regions , assigned the same map will be assumed to be illuminated by the same light . if we do not happen to have available any pre - computed mappings from unfiltered to filtered responses , the chromogenic idea can still be used to obtain a best mapping between the two images and assigning the majority of pixels best transformed under the mapping found to one label , and all others to a second label . for example , a ‘ robust ’ statistical procedure can find the best mapping from one image to the other , provided that at least half the image ( half - plus - 1 pixel ) is approximately associated with that mapping . pixels not associated correctly are ‘ outliers ’ and belong to the second label . in fact , robust mapping can proceed in a hierarchical manner , going on to find the best mapping in just the second - label region , and going on to descend further until there is no good labeling for individual pixels . region - labeling may then be brought into play ( see below ). there is a subtlety in our approach : we use chromogenic theory only to find regions lit by different lights but do not estimate the colour of the lights themselves . this might appear a little strange . after all , each pixel , or region , is associated with a single relation and each relation is defined ( in a training stage ) to be the map that takes rgbs to filtered counterparts for a particular light . we might ( wrongly ) conclude that once we have identified which regions are lit by the same light that we also know the colour of the light for these regions . we do not know the light colours because chromogenic illuminant estimation tends to work best when there is a large colour diversity in a scene . often the total number of pixels found to be ( say ) in a shadow is a relatively small proportion of the total number of pixels in the image . in this case the best relation mapping rgbs to filtered counterparts might be for the wrong illuminant . this poses a problem if our goal was to estimate the colour of the light . but , here we seek to use the relations only as a means for discriminating between illuminants . chromogenic theory will now be discussed . let us denote light , reflectance and sensor as e ( λ ), s ( λ ) and qk ( λ ) where k indexes r , g , and b . for lambertian surfaces , image formation can be written as : where the integral may be evaluated over a the visible spectrum . it is useful to combine the triplet of sensor responses q k into a single vector , which we denote by q ( underscoring denotes a vector quantity ). where e i ( λ ), i = 1 . . . d e form an approximate basis set for illuminants , e j ( λ ), j = 1 . . . d s form an approximate basis set for surfaces , and weights ε i and σ j form the best fit for particular lights and surfaces to these basis sets . the image formation equations ( eq . ( 1 )) can be succinctly written as : where ( ε ) is a 3 × n matrix mapping reflectance weights to rgb responses . the kjth term of this lighting matrix may be given by : one formulation of the colour constancy problem is as follows : given a set of measured response vectors q , how can we recover the reflectance and illumination characteristics , i . e . recover σ and ε ? the linear model basis sets for light and reflectance , used in ( 2 ), are generally determined using principal component analysis [ 9 ] or characteristic vector analysis [ 10 ] in which case the model dimensions d e and d s are found to be 3 ( for daylights ) and 6 to 8 for reflectances . given that there are only 3 measurements at each pixel , these large dimensions in the model cast doubt on the solubility of colour constancy . however , looking at ( 3 ) we can see that image formation is in reality predicated on a ( light dependent ) lighting matrix multiplying a reflectance weight vector . while we have no knowledge of as e ( λ ) or s ( λ ), we do see that the linearity of ( 1 ) is preserved : if we add two lights together we add the respective lighting matrices . it follows that the dimensionality of light and surface , viewed from the perspective of image formation , depends on how well a set of m , 3 × n lighting matrices interacting with n × 1 weight vectors model observed image rgbs . by reasoning in this way , marimont and wandell [ 111 dedemonstrated that a very good model of image formation is possible with only d e = 3 ( three lighting matrices ) and d s = 3 ( three degrees of freedom in reflectance ). this is encouraging because the model numbers are small . however , they are still generally not small enough to enable us to decouple light and reflectance . to see why , suppose we have a single illuminant and s reflectances , providing us with 3s measurements and 3s + 3 unknowns . even by observing that there is a scalar indeterminacy between surface lightness and illuminant brightness ( since they multiply each other ), so that the unknowns number 3s + 2 , this is still less than the number of known quantities : le ., 3s & lt ; 3s + 2 , suppose now , however , that we observe the s surfaces under two lights . we now have 6s measurements and more knowns than unknowns , 6s & gt ; 3s + 5 for two or more surfaces ( i . e ., 5 = 6 − 1 = two lights multiplied by 3 , minus the brightness indeterminacy ). indeed , a number of authors [ 12 , 13 , 14 ] have presented algorithms which can algebraically solve the colour constancy problem in this case . implicit to these approaches is the idea that rgbs are mapped across illumination by a 3 × 3 linear map : q 2 = ( ε 2 )[ λ ( ε 1 )] − 1 q 1 ( 5 ) finlayson [ 14 ] observed that because we can always generate the same rgbs ( through a judicious choice of sigma weights ) under any light , we can only hope to solve the two - light constancy problem if the 3 × 3 linear transform is unique . indeed , for most sensors , lights and surfaces , uniqueness was shown to hold in a simplified approximation model and the two - light constancy problem was thus shown to be soluble . however , one of the flaws in this approach is the requirement of having available images of the same surfaces seen under two lights , an impractical requirement in general . in chromogenic theory , rather than capturing a scene under two different lights we instead simulate a second light by placing a filter in front of the camera to generate an additional image . we can write the new filtered responses as where the superscript f denotes dependence on a coloured filter . from an equation - counting perspective we now have enough knowns to solve for our unknowns . we simply take two pictures of every scene , one filtered and one not . importantly , in [ 7 ] it was shown , assuming 3 degrees of freedom in light and surface is an accurate enough portrayal of nature , that the transform mapping rgbs to filtered counterparts uniquely defines the illuminant colour . this result led to the chromogenic theory of illuminant estimation . the algorithm works in 2 stages . in a preprocessing step we can pre - calculate the relations , one each for each of n illuminants , that map rgbs to filtered counterparts . for example , we find a set of n 3 × 3 matrix transforms . in the operation phase , we take a chromogenic pair of images — two images , one unfiltered and one filtered . the illumination is unknown for the new , testing pair . we can then apply each of the pre - computed relations , and the relation that best maps rgbs to filtered counterparts is used to index and hence estimate the prevailing illuminant colour [ 7 ]. a chromogenic method for illuminant estimation is described in the following two - stage approach . preprocessing : for a database of n lights e i ( λ ) and s surfaces s j ( λ ), calculate t j ≅ q i f q i + where q i + and q i f represent the matrices of unfiltered and filtered sensor responses for the s surfaces , under the ith light ; superscript ‘+’ denotes pseudo - inverse [ 15 ]. this generates a best least - squares transform , but the method is not limited to least - squares ( e . g ., robust methods could be used ), nor is the method limited to linear ( i . e ., matrix ) transforms , operation : given p surfaces in a new , test , image we have 3 × p measured image rgb matrices q and q f , then the task of finding the best estimate of the scene illuminant e est ( λ ) may be solved by finding the index i in our set of n illuminants that generates the least sum of squared errors : i est = art min ( err i ), ( i = 1 , 2 , □, n ), with err i =□ t i q − q f □ ( 9 ) it is worth remarking that in the simplest approach the transform matrices may be defined by regression ( e . g ., the moore - penrose inverse uses least - squares regression ). therefore , illuminant relations , implemented as 3 × 3 matrices , may not perfectly transform rgbs to filtered counterparts . this modest imprecision has two consequences which bear on the method in accordance with the discussion below . first , to accurately estimate the best transform we may need a large test set of surfaces ( since we wish the relations to apply for all surfaces ). second , if we attempt to estimate the light colour for a small set of surfaces then we might wrongly estimate the illuminant : the best transform for a set of red patches might be different from the best transform for a large set of colours ( red , greens , white etc .). thus , when we run the chromogenic algorithm for an image that has only a small set of surfaces , we will find a relation , according to the algorithm presented above , but this relation may in fact index the wrong light colour . in one embodiment , for a given chromogenic image pair , i . e ., rgbs along with corresponding filtered counterparts , we can determine which pixels , or regions , are illuminated by the same lights . below we define our approach formally , assuming there can be in lights in an image . in practice m ≦ 2 will be appropriate for most images and therefore we set m = 2 when we outline the particular implementation of our algorithm that is discussed next . let us begin by assuming that for n lights we carry out the chromogenic preprocessing step and solve for the n relations that best map rgbs to filtered counterparts . here , however , we do not necessarily assume that the relation is a 3 × 3 matrix transform but rather , for generality , assume an arbitrary function f : ℑ 3 → ℑ 3 , where ℑ is the set of possible integers in a colour image ( for example , for 16 - bit colour channels , ℑ is the set [ 0 . . . 65 , 535 ]). suppose we now select an m - element subset r ⊂ . taking each pixel , or region , in turn we determine which of the relations best maps the rgb ( s ) to their filtered counterpart ( s ). once each pixel , or region , is assigned a single relation it is a simple matter to calculate how well the set of in relations r accounts for our data . of course there are many possible m - element subsets r ⊂ . mathematically , the set of all m element subsets of is denoted ( m ) and we call this set the m - set of . that r ∈ ( m ) which best describes the relation between image and filtered counterpart overall is then found through an optimisation procedure ( which is essentially a searching algorithm ). this effectively finds the m best mappings , and thus an m - level labeling of pixels . e . g ., in the case m = 2 this amounts to a binary labeling of pixels . this labeling could arise , for example , from shadowed and un - shadowed regions . before we can write down this optimisation mathematically , we need to introduce little more notation . let ={ f 1 , f 2 , . . . , f n } and let i k and i k f denote the kth pixel or region in the image and its filtered counterpart . the relation can be thought of as a mathematical function or computer algorithm that maps an image to filtered counterparts for a particular illuminant labeled i . thus , if f i , is appropriate for the image region i k , we would expect : for a given relation set r we have to assign to each pixel , or region , i k one of them relations f 1 , i ∈ 1 , 2 , . . . , n depending on which best predicts i k f . remembering that ( m ) denotes the set of all m - element subsets of , and letting i k ∈ 1 , 2 , . . . , m denote which of the m relations best applies at the kth pixel or region , we then must solve the following optimisation , which may be stated in general terms as : if i k is a single pixel then □, □ is some simple scalar function , e . g ., the sum of absolute values of vector components , or the square root of the sum of absolute values squared . if i k is a region there is scope to make □, □ a more robust measure , eg ., the median deviation . in the final step of the present method , we wish to identify different regions as belonging to different lights . after solving the optimisation ( 11 ), we arrive at the best overall m - element set of mappings r and the best set of pixel labels and i k k ∈ 1 , 2 , . . . , m . this can associate regions with labels for m lights directly by the relation indices i k as follows : all the pixels , or areas of pixels , where i k = 1 may be taken as having been imaged under the same light , indexed by ‘ 1 ’. similarly , all pixels or areas where i k = 2 are taken as under another light , index by ‘ 2 ’, and so on up to i k = m . to make our approach slightly more general we allow the goodness of fit operation to be carried out pixel - wise but will assign lighting labels on a region by region basis . suppose we compute an assignment of n regions indexed by k , k = 1 , 2 , . . . , n in an image . many algorithms exist for such a task ; such an algorithm is referred to as a segmentation procedure . let i kj denote the jth pixel in the kth region . we can now , initially , assign the relation labels i kj by minimising the following region - driven statement : we can now assign labels to entire regions based on the fits to the underlying pixels : here , function bestlabel ( ) must choose which label to assign to region k , of all the up to m labels assigned to pixels i kj in region k . an obvious candidate for function bestlabel ( ) is the mode function , e . g ., if i k has 100 pixels and , of those 100 , 90 have a relation label i , then the mode is also i and the overall label for the region should also be i . another candidate would be that label minimising the overall error in mapping unfiltered to filtered pixels , in that region k . we remark that minimising ( 11 ) or ( 12 ) can be computationally laborious . the computational cost is proportional to the cardinality of the set ( m ). if , say , there are 50 relations in ( a reasonable number to account for the range of typical lights [ 16 ]) then the cardinality of the m - set ( m ) is [ 50 !/( m ! ( 50 - m )!] which for m = 2 , 3 , 4 , 5 is equal to 1225 , 19600 , 230300 and 2118110 . a brute force search is only really possible for small m , i . e . m = 2 or m = 3 . if , of course , we allow all possible maps to be in ( e . g . all possible 3 × 3 matrices ) then our solution strategy will follow classical optimisation theory ( and not the combinatorial approach suggested above ). in the optimisation approach we would start with an initial guess of m good transforms and then seek to update these incrementally by minimising a cost function . for example , we might employ the widely used gradient descent method . these differential optimisations tend to find locally , as opposed to globally , optimal solutions . heuristic techniques such as simulated annealing might be used to find a global optimum . to complete this section , we suggest other modifications of the basic algorithm which can be used for illuminant detection . first , though , we have presented the basic theory assuming three rgb sensors and three filtered counterparts , other embodiments cover the case where we have six arbitrary sensor response functions ( they need not be a filter correction apart ). in this case the relation f ( ) best maps the first three sensor responses to the second three . further we can allow other means of arriving at multidimensional response data . for example our method can detect shadows given a normal rgb image and a second image taken where a flash is used to illuminate the scene . in general , methods in accordance with this disclosure can be applied to any capture condition which might be written as ; where q k ( λ ) might be a sensor response function or a sensor multiplied by a filter transmittance . setting — accurately models the effect of adding flash light to a scene and is also covered by the present invention . the number of sensors is also not important in the present embodiments . indeed , given a q sensor camera , our method will still work if p of the sensor responses , recorded for different lights and surfaces , are related to the remaining q − p responses by some function f ( ). in the embodiment presented in detail above , q = 6 and p = 3 , but equally q and p could be any two numbers where p & lt ; q : q = 7 and p = 2 , or q = 3 and p = 1 . the last case draws attention to the fact that for a conventional rgb camera , we can relate the blue responses to the red and green responses in the manner described above . and , even though the relationship is less strong ( e . g . the fit in ( 9 ) will have significant error ), the method will still provide a degree of illumination detection . also , the means by which we relate the first p responses to the remaining q − p responses ( for a q response camera ) can be written in several general forms . in the method described above , where q = 6 and p = 3 , the unfiltered responses are related to filtered responses by a 3 × 3 matrix transform . more generally , this map could be any function of the form f : 3 → 3 ( a function that maps a 3 - dimensional input to a 3 - dimensional output ). for an arbitrary q ( number of sensors ) and p ( number of dependent responses ), the mapping function f : 3 → 3 . we also point out that we can generalise how we compute the distances that we have thus far written as □ f ( i k q − p )− i k p □, where i q − p and i p denote the first q − p and remaining p responses and the subscript k indexes the kth pixel or region ). we can do this in two ways . first , we can use an arbitrary definition of the magnitude function □, □, e . g ., it could be the standard euclidean distance , or , it could be any reasonable distance function ( e . g . such as one of the minkowski family of norms ). second , we observe that if f ( i k q − p )≈ i k p , then this implies that the q vector lies in a particular part of q - dimensional space . for example , f ( ) is a p ×( q − p ) matrix transform then the q vector of responses must lie on a q − p dimensional plane embedded in q space . thus , rather than computing a relation f ( ) directly and then calculating □ f ( i k q − p )− i k p □ we could instead calculate the distance of the q vector of responses to a q − p dimensional plane . it follows we might rewrite our fitting function as : □ p ( i k )− i k □ where p projects the q vector onto some q − p dimensional plane . subtracting the projected vector from the original then makes a suitable distance measure . we can extend this idea still further and write □ p ( i k )− i k □≡ p ⊥ ( i k )□ projects the q vector of responses onto the p dimensional plane orthogonal to the q − p dimensional plane where we expect i k to lie . more generally , we might calculate he measure p ( i k ) where p is a function that returns a small number when the response vector is likely for the illuminant under consideration . here p could , for example , be some sort of probabilistic measure . in one embodiment we determine the fit , or likelihood , that a given q - vector of responses occurs for a given light in a preprocessing step . this might be the 3 × 3 matrices best mapping rgbs to filtered counterparts for a given training set . alternatively , for the other embodiments discussed we could pre - calculate the best relations of the form f : p − q → p . or , if we use the position of the response vectors directly , then we could pre - calculate the best fitting plane or pre - calculate a probabilistic model which ascribes a likelihood that given q vectors occur under different lights . however , we note that that the fit , or likelihood , that a given q - vector of responses occurs for a given light can be computed within a single image by using the image statistics and this is also covered by this disclosure . for example , for the case of 3 × 3 linear maps taking rgbs to filtered counterparts and where there are lust two lights present in a scene , we might find the pair of transforms that best accounts for the image data ( one of the pair is applied at each pixel according to which light is present ) by using robust statistics . we find the best 3 × 3 matrix that maps at least 50 % of the image plus one pixel to corresponding filtered counterparts . the remaining pixels can be treated as outliers and can be fit separately . the inliers and outliers can determine which part of the image are lit by the different lights . our experiments indicate good illuminant detection in this case . further , all the different combinations of distance measures , and fitting functions described above , could , in principle , be trained on the image data itself , using standard techniques . to summarise , in methods according to the present disclosure when the position of the q vector of responses measured by a camera depends strongly on illumination and weakly on reflectance we can use the position in q space to measure the likelihood of this response occurring under that light . this likelihood can be calculated in many ways including testing the relationship between the first q − p responses to the last p responses ( using linear or non linear functions and any arbitrary distance measure ). equally , the position of the q vector can be used directly and this includes calculating the proximity to a given plane or by a computing a probabilistic or other measure . the information that is needed to measure whether a q vector is consistent with a given light can be pre - calculated or can be calculated based on the statistics of the image itself . there will now be described a method , working with real images , of finding image regions lit by two illuminants . arguably , the m = 2 case is the most interesting and most common case . many scenes are lit by a single light or by two lights . often in the outdoor environment there is a single light . as well , there are often two lights : the sun + sky ( non - shadow ) and the sky alone ( shadow ). similarly , indoors at night we may light the room by a single incandescent bulb . yet , during the day many office environments are a combination of artificial light from above the desk and natural light coming through the window . indeed , it is hard to think of normal circumstances when m is much larger than 2 . let us , thus , implement the algorithm given in eq . ( ii ) for the m = 2 case . we begin by creating the set , which in this example consists of fifty 3 × 3 matrix transforms . these transforms were calculated by imaging a standard colour reference chart ( the macbeth colorchecker [ 17 ]) under 50 lights one at a time , with and without a coloured filter , using a nikon d70 camera ( which outputs linear ( raw unprocessed ) images ). the 50 lights were chosen to be representative of typical lights that are encountered every day and included : blue sky only , blue sky + sun , overcast sky , fluorescent light and incandescent illumination . the macbeth colorchecker has 24 different coloured patches and so we solved for each 3 × 3 transform by regressing the 24 unfiltered rgbs onto the filtered counterparts , now we run the algorithm . in the first pass , we can start by making use of a pixel - based optimisation algorithm , using eq . ( 11 ): we calculate the 2 - set ( 2 ): the set of all subsets of with 2 elements . because there are 50 transforms there are ‘ 50 choose 2 equals 1 , 225 combinations . for a given relation set r containing a particular pair of 3 × 3 matrices , we test which matrix best maps each image pixel to the filtered counterpart . as we do so , we calculate the discrepancy , or error , between the mapped rgbs and the actual filtered responses . we repeat this process over all 1 , 225 combinations of two lights ( and hence mappings ); we determine that one pair of transforms , one of which is applied at each pixel , that best maps the unfiltered to filtered image overall . fig1 illustrates this process where there are just 3 relations ( mappings ) and instead of matrices the relations are simple scalar multipliers . fig2 shows typical results of an optimisation eq . ( 11 ) applied at the pixel level . fig2 ( a ) shows the original image ; since it has shadows there are clearly two lights present in the scene . it represents noisy , pixel - based detection . because a single transform is applied to each pixel , we can view the output of this process as a binary image . denoting the matrix transform that best fits the data as ‘ 0 ’ ( for the 1st transform ) and ‘ 1 ’ ( for the second transform ), we show our estimate of the illuminations present in the scene in fig2 ( b ). while it is clear that we have some correspondence between shadowed and non - shadow regions , and therefore our algorithm is working , the output is far from perfect . it looks like the correct answer , but appears corrupted by a high degree of noise . now let us apply the region - based label assignment given by optimisation eq . ( 12 ) followed by eq . ( 13 ). using the mean shift algorithm [ 18 ], or any similarly edge - preserving segmentation algorithm , we can calculate an initial segmentation of an image . fig3 ( a ) shows the segmentation arrived at by the standard mean shift algorithm . it will be noted that there are many regions in the image : that is , we have over - segmented the image vis - a - vis our present objective , namely disambiguating shadowed from non - shadowed regions . this is important to note , as we wish to be sure that the segmentation of the input image has not merged regions which are lit by different lights ( the degree of segmentation is controllable using parameters that the mean shift algorithm uses , and this applies to other edge - preserving segmentation algorithms as well ). fig3 ( b ) is the result of a region - based illuminant detection procedure . we start with the output given in fig2 ( b ). in conjunction with the regions obtained using the mean shift segmentation in fig3 ( a ), we then go on to assign output labels as in eq . ( 13 ). in this variant , for each region we count the proportion of ‘ 0 ’ s and ‘ is ’ and assign the majority number to the entire region . the result shown in fig3 ( b ) makes it clear that we have obtained an excellent segmentation of the lights present in the scene . fig3 represents a dean determination of shadow areas . importantly , we have found this simple approach to illumination detection reliably delivers good results . thus , we have disclosed a method for segmenting illumination in images . the method can use pre - determined transforms of pairs of images from unfiltered to filtered versions , where a chromogenic filter is utilised . to determine a segmentation with m or fewer illuminant labels , sets of m mappings can be applied at the pixel or region level to the image pairs , to best generate an assignment of labels . alternatively , if no pre - calculated mappings are available , m or fewer assignments of labels can be determined by regression or similar method applied to the image pairs in a hierarchical manner . the region - based approach generates cleaner illumination segmentations , in general . where reference is made in this specification to a filtered and an unfiltered image , this includes images with differing filtering characteristics . one can use instead two filtered images with different filtering . alternatively one can simply use two different cameras , for example cameras of different makes . in a specific example , a conventional digital camera and a camera with a yellow filter are used . 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