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... found however that this still does not produce edge maps which are clean enough for our purposes. Instead we have employed more sophisticated edge detection algorithms such as that proposed by Canny =-=[14]-=- and the SUSAN algorithm proposed in [15]. We haveachieved some success with both these methods; the results obtained here use the SUSAN edge detector. In this algorithm the image to be edge detected ...

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...nt for other artifacts of the imaging process (e.g., in [32] a four-sensor camera was considered and it was shown that, in this case, specularities could also be removed). We adopt a Lambertian model =-=[33]-=- of image formation so that if a light with a spectral power distribution (SPD) denoted Eð ; x; yÞ is incident upon a surface whose surface reflectance function is denoted Sð ; x; yÞ, then the respons...

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...they shouldn't be. Pragmatically then the results of this paper do not deliver photo-quality images. However, the technique might usefully subserve tasks such as tracking[16, 17] or object recognition=-=[18, 19]-=- where shadows are known to cause problems. 6 Conclusions In this paper we have presented a method for nding and removing shadows from images. Our method builds on two strands of prior research: light...

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... of illumination conditions. Using many images ensures that the problem is well-posed, but implies that the application of the method is quite restricted. The Retinex and Lightness algorithms of Land =-=[6]-=- and others [7], [8], [9], [10] can also be seen as an attempt to derive intrinsic reflectance images under certain restrictive scene assumptions. Specifically, those algorithms . G.D. Finlayson and S...

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...e lightness algorithms and factors such as specularities, shading, and shadows are ignored. A different approach to this problem is the so-called illuminant invariant approach [21], [22], [23], [24], =-=[25]-=-, [26], [27]. Instead of attempting to estimate the color of the scene illuminant, illuminant invariant methods attempt simply to remove its effect from an image. This is achieved by deriving invarian...

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...ue to material changes is a di cult problem and has a long history in computer vision research [2]. In addition, the investigation of shadows as cues for image understanding has an even older lineage =-=[3]-=-. Recently, the importance of understanding shadows has come to the fore in digital photography applications including colour correction[4] and dynamic range compression[5]. One possible solution to t...

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...sic reflectance image referred to as a lightness image. Estimating and accounting for the color of the prevailing scene illumination is a related problem which has received much attention [11], [12], =-=[13]-=-, [14], [15], [16], [17], [18], [19], [20]. In this body of work, the focus is not on deriving intrinsic reflectance images, but rather on obtaining a rendering of a scene as it would appear when view...

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...ing values obtained from neighboring nonshadow edge pixels. We also deal with the problem of integrability at this stage by including a step at each iteration to enforce integrability, as proposed in =-=[43]-=-. This iterative process is detailed below where t denotes artificial time: 1. Initialization, t 0, calculate: rx 0 kðx; yÞ t ! TS rx 0 kðx; yÞ;qsðx; yÞ ry 0 kðx; yÞ t ! TS ry 0 kðx; yÞ;qsðx; yÞ : 2...

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...hich are shadow free: that is to process images such that the shadows are removed whilst retaining all other salient information within the image. Recently, a study [6] aimed at lightness computation =-=[7]-=- set out a clever method to attenuate the e ect of shadows in an image. Unfortunately however, this method requires not just a single image, but rather a sequence of images, captured with a stationary...

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...they shouldn't be. Pragmatically then the results of this paper do not deliver photo-quality images. However, the technique might usefully subserve tasks such as tracking[16, 17] or object recognition=-=[18, 19]-=- where shadows are known to cause problems. 6 Conclusions In this paper we have presented a method for nding and removing shadows from images. Our method builds on two strands of prior research: light...

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...intrinsic reflectance image referred to as a lightness image. Estimating and accounting for the color of the prevailing scene illumination is a related problem which has received much attention [11], =-=[12]-=-, [13], [14], [15], [16], [17], [18], [19], [20]. In this body of work, the focus is not on deriving intrinsic reflectance images, but rather on obtaining a rendering of a scene as it would appear whe...

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...ms of shadows is to derive images which are shadow free: that is to process images such that the shadows are removed whilst retaining all other salient information within the image. Recently, a study =-=[6]-=- aimed at lightness computation [7] set out a clever method to attenuate the e ect of shadows in an image. Unfortunately however, this method requires not just a single image, but rather a sequence of...

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...ties, and interreflections, as well as changes due to local variation in the intensity or color of the illumination all make it more difficult to achieve basic visual tasks such as image segmentation =-=[1]-=-, object recognition [2], and tracking [3]. The importance of being able to separate illumination effects from reflectance has been well understood for a long time. For example, Barrow and Tenenbaum [...

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...as evidenced by the large literature on edge detection (see [44] for a review). For a more careful approach, we begin by applying a smoothing filter (specifically the Mean-Shift algorithm proposed in =-=[45]-=-) to both the original image and the 2D invariant image derived by exponentiating the invariant log image. This has the effect of suppressing features such as noise and high frequency textures so that...

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...nce image referred to as a lightness image. Estimating and accounting for the color of the prevailing scene illumination is a related problem which has received much attention [11], [12], [13], [14], =-=[15]-=-, [16], [17], [18], [19], [20]. In this body of work, the focus is not on deriving intrinsic reflectance images, but rather on obtaining a rendering of a scene as it would appear when viewed under som...

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... as the lightness algorithms and factors such as specularities, shading, and shadows are ignored. A different approach to this problem is the so-called illuminant invariant approach [21], [22], [23], =-=[24]-=-, [25], [26], [27]. Instead of attempting to estimate the color of the scene illuminant, illuminant invariant methods attempt simply to remove its effect from an image. This is achieved by deriving in...

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...s for 6 di erent patches, imaged under a set of di erent Planckian illuminants.sNow if sensors are fairly narrow-band (and if they are not they can be made more so via a spectral sharpening procedure =-=[10]-=-) then, for Planckian lights, changing the lighting colour simply amounts to moving the log-chromaticity colour vector along a direction multiplying a term which depends on the illuminant temperature ...

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...n conditions. Using many images ensures that the problem is well-posed, but implies that the application of the method is quite restricted. The Retinex and Lightness algorithms of Land [6] and others =-=[7]-=-, [8], [9], [10] can also be seen as an attempt to derive intrinsic reflectance images under certain restrictive scene assumptions. Specifically, those algorithms . G.D. Finlayson and S.D. Hordley are...

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...ns linear output without any image postprocessing) whose sensitivities are shown in Fig. 1b. Fig. 2a shows the color image as captured by the camera (for display purposes, the image is mapped to sRGB =-=[37]-=- color space)—a shadow is very prominent. Figs. 2b and 2c show the log-chromaticity representation of the image. Here, intensity and shading are removed but the shadow is still clearly visible, highli...

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...htness image. Estimating and accounting for the color of the prevailing scene illumination is a related problem which has received much attention [11], [12], [13], [14], [15], [16], [17], [18], [19], =-=[20]-=-. In this body of work, the focus is not on deriving intrinsic reflectance images, but rather on obtaining a rendering of a scene as it would appear when viewed under some standard illumination. Often...

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..., and subsequently remove shadows. The result is a 3-band colour image which contains all the original salient information in the image, except that the shadows are gone. We use the method set out in =-=[1]-=- to derive a 1-d illumination invariant shadow-free image. We then use this invariant image together with the original image to locate shadow edges. By setting these shadow edges to zero in an edge re...

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...algorithms and factors such as specularities, shading, and shadows are ignored. A different approach to this problem is the so-called illuminant invariant approach [21], [22], [23], [24], [25], [26], =-=[27]-=-. Instead of attempting to estimate the color of the scene illuminant, illuminant invariant methods attempt simply to remove its effect from an image. This is achieved by deriving invariant quantities...

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... a lightness image. Estimating and accounting for the color of the prevailing scene illumination is a related problem which has received much attention [11], [12], [13], [14], [15], [16], [17], [18], =-=[19]-=-, [20]. In this body of work, the focus is not on deriving intrinsic reflectance images, but rather on obtaining a rendering of a scene as it would appear when viewed under some standard illumination....

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...pixels being set to zero when they shouldn't be. Pragmatically then the results of this paper do not deliver photo-quality images. However, the technique might usefully subserve tasks such as tracking=-=[16, 17]-=- or object recognition[18, 19] where shadows are known to cause problems. 6 Conclusions In this paper we have presented a method for nding and removing shadows from images. Our method builds on two st...

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...dow edges to zero, we can no longer guarantee that the edge map we are integrating satisfies the integrability condition. For the edge map to be integrable, the following condition should be met (cf. =-=[42]-=-): ryrx 0 kðx; yÞ rxry 0 kðx; yÞ: ð27Þ The second problem is caused by the fact that to ensure shadows are effectively removed, we must set to zero, edges in quite a large neighborhood of the actual ...

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...g has an even older lineage [3]. Recently, the importance of understanding shadows has come to the fore in digital photography applications including colour correction[4] and dynamic range compression=-=[5]-=-. One possible solution to the confounding problems of shadows is to derive images which are shadow free: that is to process images such that the shadows are removed whilst retaining all other salient...

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...as: gradient ofchannel response kr 0 (x; y)k (9) Given the log-image edge map r 0 (x; y) we can de ne a threshold operator T to remove e ects due to illumination. In the original lightness formulation=-=[11]-=-, T thresholds out gradients of small magnitude: T (r 0 (x; y)) = 0 if kr 0 (x; y)k < threshold r 0 (x; y) otherwise 7 (10) Here our goal is not to remove illumination per se (we are not solving for c...

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...sing many images ensures that the problem is well-posed, but implies that the application of the method is quite restricted. The Retinex and Lightness algorithms of Land [6] and others [7], [8], [9], =-=[10]-=- can also be seen as an attempt to derive intrinsic reflectance images under certain restrictive scene assumptions. Specifically, those algorithms . G.D. Finlayson and S.D. Hordley are with the School...

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...itions as the lightness algorithms and factors such as specularities, shading, and shadows are ignored. A different approach to this problem is the so-called illuminant invariant approach [21], [22], =-=[23]-=-, [24], [25], [26], [27]. Instead of attempting to estimate the color of the scene illuminant, illuminant invariant methods attempt simply to remove its effect from an image. This is achieved by deriv...

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...; G; B : (1) If camera sensitivity Qk( ) is exactly a Dirac delta function Qk( )=qk ( , k), with qk the strength of the sensor qk = Qk( k), then Eq. (1) reduces to the simpler form k = E( k)S( k)qk : =-=(2)-=- Now suppose lighting can be approximated by Planck's law. E( ; T )= Ic1 ,5 e c 2 T , 1 ,1 Constants c1 and c2 equal 3:74183 10 ,16 Wm 2 and 1:4388 10 ,2 mK, respectively. The variable I controls the ...

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... to as a lightness image. Estimating and accounting for the color of the prevailing scene illumination is a related problem which has received much attention [11], [12], [13], [14], [15], [16], [17], =-=[18]-=-, [19], [20]. In this body of work, the focus is not on deriving intrinsic reflectance images, but rather on obtaining a rendering of a scene as it would appear when viewed under some standard illumin...

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...vious work requires only a single image. The approach is founded on an application of a recently developed method for eliminating from an image the colour and intensity of the prevailing illumination =-=[1, 8]-=-. The method works by nding a single scalar function of image an RGB that is invariant to changes in light colour and intensity i.e. it is a 1-dimensional invariant image that depends only on re ectan...

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...flectance image referred to as a lightness image. Estimating and accounting for the color of the prevailing scene illumination is a related problem which has received much attention [11], [12], [13], =-=[14]-=-, [15], [16], [17], [18], [19], [20]. In this body of work, the focus is not on deriving intrinsic reflectance images, but rather on obtaining a rendering of a scene as it would appear when viewed und...

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...or the underlying re ectance). We point out that a similar 'rule-based' approach to determining the semantics of edges (e.g. highlight edges vs material edges) has been proposed by Gevers and Stockman=-=[12]-=-. Though, that approach fails to account for shadows. After thresholding we should now have a gradient image where sharp changes are indicative only of material changes: there are no sharp changes due...

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...pixels being set to zero when they shouldn't be. Pragmatically then the results of this paper do not deliver photo-quality images. However, the technique might usefully subserve tasks such as tracking=-=[16, 17]-=- or object recognition[18, 19] where shadows are known to cause problems. 6 Conclusions In this paper we have presented a method for nding and removing shadows from images. Our method builds on two st...

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...age referred to as a lightness image. Estimating and accounting for the color of the prevailing scene illumination is a related problem which has received much attention [11], [12], [13], [14], [15], =-=[16]-=-, [17], [18], [19], [20]. In this body of work, the focus is not on deriving intrinsic reflectance images, but rather on obtaining a rendering of a scene as it would appear when viewed under some stan...

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...tness algorithms and factors such as specularities, shading, and shadows are ignored. A different approach to this problem is the so-called illuminant invariant approach [21], [22], [23], [24], [25], =-=[26]-=-, [27]. Instead of attempting to estimate the color of the scene illuminant, illuminant invariant methods attempt simply to remove its effect from an image. This is achieved by deriving invariant quan...

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...nges due to local variation in the intensity or color of the illumination all make it more difficult to achieve basic visual tasks such as image segmentation [1], object recognition [2], and tracking =-=[3]-=-. The importance of being able to separate illumination effects from reflectance has been well understood for a long time. For example, Barrow and Tenenbaum [4] introduced the notion of “intrinsic ima...

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...ng an intrinsic reflectance image referred to as a lightness image. Estimating and accounting for the color of the prevailing scene illumination is a related problem which has received much attention =-=[11]-=-, [12], [13], [14], [15], [16], [17], [18], [19], [20]. In this body of work, the focus is not on deriving intrinsic reflectance images, but rather on obtaining a rendering of a scene as it would appe...

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...at there is not a simple relationship between the shape and width of sensors and the degree of invariance, so that the suitability of sensors is best judged on a camera by camera basis. In other work =-=[39]-=-, it has been shown that it is possible to find a fixed 3 3 linear transform of a given set of sensor responses so that the 1D image representation derived from the transformed sensors has improved il...

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... illumination removed and, thus, it is in effect an intrinsic reflectance image. To recover a color representation closer to that in Fig. 3b, we must put the illumination back into the representation =-=[41]-=-. Of course, we don’t want to add illumination back on a pixel-by-pixel basis since this would simply reverse what we have just done and result in an image representation which once again contains sha...

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...ns. Using many images ensures that the problem is well-posed, but implies that the application of the method is quite restricted. The Retinex and Lightness algorithms of Land [6] and others [7], [8], =-=[9]-=-, [10] can also be seen as an attempt to derive intrinsic reflectance images under certain restrictive scene assumptions. Specifically, those algorithms . G.D. Finlayson and S.D. Hordley are with the ...

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...in (5) instead of a particular p and still retain our straight line dependence. Log-color ratios then live on a plane in three-space orthogonal to u ð1; 1; 1Þ T and form lines exactly as in Fig. 1a =-=[35]-=-. We have derived this 1D illuminant invariant representation under quite restrictive conditions (though the conditions on the camera can be relaxed to broad-band sensors with the addition of some con...

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...ws as cues for image understanding has an even older lineage [3]. Recently, the importance of understanding shadows has come to the fore in digital photography applications including colour correction=-=[4]-=- and dynamic range compression[5]. One possible solution to the confounding problems of shadows is to derive images which are shadow free: that is to process images such that the shadows are removed w...

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...roduce edge maps which are clean enough for our purposes. Instead we have employed more sophisticated edge detection algorithms such as that proposed by Canny [14] and the SUSAN algorithm proposed in =-=[15]-=-. We haveachieved some success with both these methods; the results obtained here use the SUSAN edge detector. In this algorithm the image to be edge detected is rst smoothed by convolution with a ker...

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...ferred to as a lightness image. Estimating and accounting for the color of the prevailing scene illumination is a related problem which has received much attention [11], [12], [13], [14], [15], [16], =-=[17]-=-, [18], [19], [20]. In this body of work, the focus is not on deriving intrinsic reflectance images, but rather on obtaining a rendering of a scene as it would appear when viewed under some standard i...

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...in Section 2, the effect that departures from the theoretical case have on the resulting 1D invariant representation. A more detailed discussion of these issues can also be found in other works [28], =-=[31]-=-. It is also important to point out that, for some images, the process of transforming the original RGB representation to the 1D invariant representation might also introduce some undesirable artifact...

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...f the original image) so that the image remains shadow-free but is closer in color to a 2D representation of the original image. This 2D image representation is similar to a conventional chromaticity =-=[30]-=- representation (an intensity invariant representation) but with the additional advantage of being shadow-free. Finally, we show how to recover a full-color 3D image representation which is the same a...

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...luminant invariant representation under quite restrictive conditions (though the conditions on the camera can be relaxed to broad-band sensors with the addition of some conditions on the reflectances =-=[36]-=-) and it is therefore reasonable to ask: In practice, is the method at all useful? To answer this question, we must first calculate the orthogonal projection direction for a given camera. There are a ...