Separating Texture and Illumination forSingle-Shot Structured Light Reconstruction

Minh Vomvpo@cs.cmu.edu

Srinivasa G. Narasimhansrinivas@cs.cmu.edu

Carnegie Mellon University, Pittsburgh, PA, USA

Yaser Sheikhyaser@cs.cmu.edu

Abstract

Active illumination based methods have a trade-off be-tween acquisition time and resolution of the estimated 3Dshapes. Multi-shot approaches can generate dense recon-structions but require stationary scenes. In contrast, single-shot methods are applicable to dynamic objects but can onlyestimate sparse reconstructions and are sensitive to surfacetexture. In this work, we develop a single-shot approachto produce dense reconstructions of highly textured objects.Key to our approach is an image decomposition scheme thatcan recover the illumination and the texture images fromtheir mixed appearance. Despite the complex appearancesof the illuminated textured regions, our method can accu-rately compute per pixel warps from the illumination pat-tern and the texture template to the observed image. Thetexture template is obtained by interleaving the projectionsequence with an all-white pattern. Our estimated warpingfunctions are reliable even with infrequent interleaved pro-jection. Thus, we obtain detailed shape reconstruction anddense motion tracking of the textured surfaces. We validatethe approach on synthetic and real data containing subtlenon-rigid surface deformations.

1. Introduction

Structured light based shape reconstruction algorithmsare divided into two categories: multi-shot [4, 6, 15] andsingle-shot methods [7, 14, 17]. Multi-shot methods can es-timate per-pixel depth map for a wide range of objects usingtemporal coding of the illumination patterns but require thescene to be stationary during image acquisition. Single-shotmethods can work for dynamic objects by decoding the spa-tial structure embedded in the illumination pattern but gen-erate low spatial resolution reconstructions and are suscep-tible to the high frequency texture on the object surface (seeFigure 1 for examples).

In this work, we present a single-shot structured lightsystem that can estimate high spatial and temporal resolu-

Figure 1. Conventional single-shot structured light systems oftenfail for highly textured objects. The mixture of albedo variationsand high frequency illumination patterns makes it difficult to es-tablish reliable and dense camera-projector correspondences.

tion depth even for highly textured objects. The proposedmethod is single-shot in the sense that it does not use theilluminated images in the previous frames to temporally de-code the illumination pattern. Our system consists of onecamera and one projector. Any modern projector can gen-erate high frequency illumination patterns needed to esti-mate dense 3D shape. We decompose the mixed appear-ance in the observed image into the surface texture and theprojected illumination patterns. Because of this decomposi-tion, high resolution 3D shape of the object in the texturedregions can be reliably estimated. In addition, we obtaindense tracking inside the texture region in the presence ofthe illumination pattern.

To achieve the illumination-texture decomposition, wedevelop an optimization framework that estimates warps ofboth the illumination pattern and a reference texture tem-plate to compose the observed image. The texture templateis obtained by infrequently interleaving the projection se-quence with an all-white pattern. The warping functionsare computed starting from a sparse set of correspondencesbetween the camera and the projector. The results are greed-ily propagated into textured areas where spatial correspon-dences cannot be directly computed. Figure 1 shows severaltypes of surface texture that our method can handle.

Since the method computes warps to a template, it doesnot exhibit drift over time. Moreover, unlike conventionalsingle-shot structured light systems whose performancesdegrade as surface texture frequency increases, our method

1

achieves better decomposition accuracy with higher fre-quency texture. Finally, despite being presented for single-shot approaches, this method can also be used in conjunc-tion with multi-shot systems by spatially modulating the il-lumination patterns with a random pattern [18]. We demon-strate dense and accurate decomposition and reconstructionresults on both synthetic and real data with non-rigidly de-forming objects.

2. Related WorkActive illumination has been used to estimate shape es-

timation problem with major focus on designing coded pat-terns that are robust to occlusion, depth discontinuity, andalbedo variations [11]. A conventional structured light sys-tem has to choose appropriate illumination patterns depend-ing on its temporal or spatial resolution requirements. Sincemulti-shot methods can robustly generate high spatial reso-lution but require stationary scenes, motion compensationschemes have been developed to handle slowly moving ob-jects [16]. Another common approach is to interleave thepatterns for structure estimation with patterns optimized forcomputing motion [8].

On the other hand, single-shot methods sacrifice spa-tial resolution for high temporal resolution reconstruction.However, because of the spatial coding strategy, generallythese methods cannot deal with textured objects and theyare forced to rely on specific light patterns for differenttypes of surface texture. Koninckx et al. [9] mitigate theproblem by introducing a feedback loop that changes pat-terns according to errors in the decoding process. Yet, theyrely on heuristic rules to set the color codes depending ondifferent textured surfaces. In principle, this method treatsthe surface texture as a nuisance and designs illuminationpatterns robust to the texture. Conversely, our method con-siders the texture as an additional source of information thatneeds to be recovered along with the 3D shapes. To the bestof our knowledge, this is the first work to explicitly sepa-rate high frequency texture and illumination patterns in thecontext of structured light system.

Another solution for single-shot methods to handle ob-ject with both textured and textureless regions is to employmulti-view stereo systems. These systems treat the illumi-nation pattern itself as surface texture to assist the matching[19]. However, since this method requires at least two cam-eras with a projector in between, baseline between camerasis larger which makes correspondence estimation hard.

Our image decomposition method is similar in spiritto intrinsic image estimation [5, 12]. These works makesmoothness assumptions about the environment light (thesun, the sky, or indoor lights) and estimate the reflectanceand shading images from images captured by a single cam-era. Conversely, our work decomposes the high frequencyillumination patterns from the projector in the observed

mixed appearance. In addition, our method is specificallydesigned for single-shot structured light systems that con-sist of one camera and one projector.

3. Texture-Illumination DecompositionConsider an object being illuminated by a projector.

Similar to intrinsic image estimation, the brightness I(x, y)at location (x, y) in the observed image is modeled as a mul-tiplication of a texture image IT (x, y) and the illuminationimage IL(x, y) at that location:

I(x, y) = IT (x, y)IL(x, y). (1)

The texture image IT is the image observed when theprojector illuminates an all-white pattern on the object. Theillumination image IL is the incident lighting pattern. Equa-tion 1 is ill-posed because one has to solve for two un-knowns IT (x, y) and IL(x, y) from one equation. To han-dle this under-constrained problem, we require additionalknowledge of the reference templates for the illuminationand texture source and a proper per-pixel initialization ofthe unknowns. Since the illumination image is a projec-tion of the known projector pattern, this pattern serves asone of our references. The reference texture template canbe obtained by interleaving the projection sequence with awhite pattern. The initialization problem is solved by thegreedy correspondence growing algorithm [3]. We describethe method in detail below.

3.1. Mathematical Formulation of the Objective

Figure 2 shows a sequence of images of an object beingilluminated by the projector. Initially, the projector illumi-nates the scene with an all-white pattern so that the texturetemplate T is observed. The appearance of this template ITchanges according to the movement of the object. Becauseimage deformation is high dimensional and non-linear, an-alytic forms that describe consistent deformation behaviorover the entire image do not exist. Thus, we locally modelthis distortion by a warping function f and employ con-stant gain aT and offset bT to approximate for the intensitychanges between the two images due to changes in surfacenormals, light directions and ambient illumination:

IT (x, y) = aTT (f−1(x, y)) + bT , (2)

where f−1(x, y) is the inverse warping function of f thatmaps the coordinate of point (x, y) in the observed image toits corresponding location in the texture template T . Sim-ilarly, the illumination image IL is the projection of lightpattern L on the object and hence, is related to each otherby a set of local warping functions g. We assume the pro-jector has been photometrically calibrated and adopt a lin-ear model to relate the brightness of the pure illumination

IL1

T IT2

L IL2

I1

IT1

I2

compose

g2

g1

compose

compose

compose

Time 1 Time 2 Time 0

f2

f1

initialize

Figure 2. Texture and illumination image decomposition. Thegreen texture region in the template T is warped to the pure textureimage ITi by the function fi. The red squares from the illumina-tion pattern L are mapped to the pure illumination image ILi bythe function gi. Properly composing the illuminated red squaresin ILi with the green region in ITi turns them into yellow squares,which constitute the mixture image Ii observed at time i. Noticethat spatially adjacent squares are likely to have similar warpingparameters. By using the estimated warping parameters of the pre-vious frame to initialize warps between the observed frame to itsreference templates L and T , the warping function can be reliablyestimated even with infrequent interleaving.

image to the projecting pattern:

IL(x, y) = aLL(g−1(x, y)) + bL, (3)

where g−1(x, y) is the inverse warping function of g thatrelates the point (x, y) to its matched in the illumination im-age L and aL, bL are constant gain and offset to compensatefor the brightness difference between the projector patternand the observed illumination. We use the inverse of f andg to avoid non-integer values when re-synthesizing the puretexture and illumination images from their prior templates.

To increase the robustness of the warping functions tolarge deformation, we set them to be locally affine and min-imize the following cost function for their shape parametersand the photometric compensation coefficients:

N∑k=−N

N∑l=−N

[IT (xk, yl)IL(xk, yl)− I(xk, yl)]2, (4)

over a patch of size (2N + 1)× (2N + 1) centered at point(x0, y0), where we want to decompose. These inverse warp-

ing functions are given as:

f−1(xk, yl) =

[x0 + p0 + (p2 + 1)k + p3ly0 + p1 + p4k + (p5 + 1)l

],

g−1(xk, yl) =

[x0 + q0dx + (q1 + 1)k + q2ly0 + q0dy + q3k + (q4 + 1)l

],

(5)

where (dx, dy) is the normalized vector representing thedirection of the epipolar line in the projector image, andq0..4, p0..5 are the affine warp parameters. Similar to stereomatching, we simplify the parameterization of g by con-straining it to lie on the camera-projector epipolar line. Weoptimize Equation 4 patch-wise using the Gauss-Newtonmethod.

3.2. Pixel-wise Initialization

Due to perspective distortion in the illumination imageIL and the large deviation from the texture template T forfast moving objects, good initial guesses for the warping pa-rameters are required to optimize equation 4. Even with ran-dom patterns [4], the repetitive nature of the spatial neigh-bor coding illumination pattern exacerbates the local mini-mum problem. We solve the initialization problem as fol-lows: start from the boundary of the textured regions andgreedily propagate the results to interior texture area. Weemploy the three steps to initialize points at the boundary.Step 1: Compute dense matching between camera and pro-jector using a greedy correspondence growing algorithm.This greedy growing strategy and the use of a random il-lumination pattern allows us to establish dense correspon-dences everywhere except for the textured surface regions.Here, the texture boundary is naturally defined as placeswhere spatial correspondences are not obtainable.Step 2: For a pixel that is close to the textured region bound-ary, we exhaustively search in its local neighbor for patcheson the illumination pattern and texture template that min-imizes the cost defined in Equation 4. Depending on themotion of the objects, the search range of pixels close to thetexture boundary is set a priory. Because of the deformationbetween patches in the templates and the ones in the puretexture and illumination images, patches in the templatesare pre-warped before being used to examine their contri-bution to the cost function. The warping parameters of theillumination pattern are initialized from its spatial neighborcomputed in step 1. Those of the texture templates are setto either its temporal neighbor if available or to the zero de-formation state.Step 3: Refine the best locations of the illumination andtexture patches by optimizing the cost function in Equation4 using a standard Gauss-Newton method.

Owing to the use of the previously computed texturewarping parameters in step 2, our warping functions canrobustly warp observed patch to its reference template thatis temporally far away. Hence, only infrequent projection

of the interleaving white frame is needed and the obtainedresults have high temporal resolution. This strategy is anal-ogous to the approach of Tian and Narasimhan et al. [13]who use less distorted patches to estimate globally optimalsets of warping parameters.

In spite of the greedy correspondence growing strategy,erroneous guesses can not propagate long as monitored bythe cost function in Equation 4. Hence, our method avoidboth the global ambiguity of the illumination pattern andbeing stuck in regions where occlusion, surface disconti-nuity, or severe foreshortening occurs. Our method showsgood recovery from non-decomposable regions in the pre-vious frames. Since only a few seed points are needed ini-tially, the good correspondences can be quickly propagatedto non-decomposable regions in the earlier frames.

4. ResultsWe validate the performance of our approach on both

synthetic and real cloth sequences containing a range oftexture frequencies. The non-rigidity of cloth makes densedecomposition and shape reconstruction challenging. Weshow the results for sequences in which the all-white patternis projected once in 30 frames. For all of our experiments,this interleaving interval gives good trade-off between thetemporal resolution of the results and speeds of the movingobjects. We also fix the patch size to be 19×19. The 3Dshapes are estimated by triangulating the correspondencesobtained after the decomposition. We split the region ofinterest into sub-regions and independently execute themin parallel to take advantage of the multi-core architectureof modern computer. Currently, our algorithm can decom-pose on average 4112 points every second on a Quad-corei7 CPU (3.6 GHz).

4.1. Illumination pattern

Figure 3 shows our static bandpass random binary illu-mination pattern [4]. The size of the speckle in this patterncan be tuned to provide suitable contrast for illuminatingobjects of different size. Fiducial checkerboard markers areuniformly seeded at every 32 pixels inside this pattern toprovide set of sparse spatial correspondences. These cor-respondences are computed using template matching alongepipolar lines. Because the distance between these markersis usually magnified in the camera image, these markers donot cause ambiguities in the propagation process.

4.2. Synthetic Data

Our synthetic cloth composed of 64,000 vertices is gen-erated using the OpenCloth engine [10] and can deform insubtle and non-rigid ways. The camera and projector reso-lution are set to 1920×1080 and 1280×800, respectively.

Figure 4 shows the decomposition result on the syn-thetic bear cloth sequence. We intentionally have the tex-

Figure 3. Part of the illumination pattern. The fiducial markersare embedded into the random pattern to provide a sparse set ofcorrespondences between the camera and the projector.

ture of the bears to be very similar to the illumination pat-tern. This extreme case severely violates the assumptions ofany methods powered by independent component analysisor smoothness prior. Thus, such methods are not applicable.Conversely, our method recovers the pure texture and illu-mination images that well resemble the groundtruth. Thesmall noticeable defect in frame 2 does not expand and isfixed in frame 18. Hence, there is little-to-no drift in theestimated warping functions.

Figure 5 shows the decomposed images, the 3D shape aswell as the flow from the observed image to the referencetemplate obtained from texture warping functions. Withoutour separation, the correlation score between the projectorpatch and its corresponding patch in the observed image isvery low in the textured regions. The depths estimated inthese regions are eliminated, which results in large holes inthe 3D shape. By separating the pure texture and illumi-nation images, the proposed method successfully estimatesthe 3D shape with the exceptions of regions where severeforeshortening occurs.

To quantify the decomposition error, we compare thecorrespondences obtained after the decomposition withthose estimated on the synthesized pure illumination andtexture images. The pure illumination image is created byprojecting the illumination pattern onto a textureless cloth.Texture image is obtained by texturemapping the cloth withbinarized Perlin-noise pattern generated by error-diffusiondithering and projecting white light on the cloth. This bi-narized random pattern is known to give accurate trackingresults [1, 8]. We compute spatial correspondences betweencamera and projector on the pure illumination image andtemporal correspondences on the pure texture image usingthe method in [2]. These correspondences are the best pos-sible estimation at a given frame and hence serve as groundtruth. We define our error metric as the normalized error indecomposing texture and illumination images:

1

N

√(xi − xi

W)2 + (

yi − yiH

)2, (6)

where N is the number of points inside the texture re-gions, (xi, yi), and (xi, yi) are the ground truth and the es-

Decomposed illumination at frame 18

Ground truth illumination at frame 18

Observed image and its magnified mixed

appearance region at frame 18

Ground truth illumination at frame 2 Ground truth texture at frame 18 Ground truth texture at frame 2

Decomposed illumination at frame 2 Decomposed texture at frame 18 Decomposed texture at frame 2

Observed image and its magnified mixed

appearance region at frame 2

Figure 4. Decomposition of the texture and illumination images of the synthetic bear cloth sequences. The interleaving pattern is projectedevery 30 frames. The same region of the bear in the two images is magnified to show how its intricate appearance changes over time whenit is illuminated by the projector. Because of cloth folding, bear appears smaller in the vertical direction. Visually, the illumination imagesexperiences higher deformation than the texture images. The noticeable defect in the decomposition at frame 2 has been fixed in frame 18.

timated correspondence locations, respectively. Dependingon whether the error of the illumination or texture is beingevaluated, (W,H) could be either the resolution of the pro-jector or camera image.

Figure 6 shows the performance of our method on thebear and flowery cloth sequences. The bear cloth has higherfrequency texture than the flowery cloth. With longer in-terleaving sequences, larger deformation in the image de-grades the algorithm performance. The texture decomposi-tion error and the fraction of correspondences estimated forflowery sequence are not as good as for the bear sequence.This indicates that the algorithm performs better with higherfrequency texture. The explanation for this phenomenon issimilar to the optical flow problem: tracking highly texturedsurfaces suffers from less drift. Notice that because of the

coherent structure of the bear, the algorithm fails when theentire texture boundary cannot be estimated reliably whichresults in the abrupt drop in the fraction of estimated cor-respondences. Nevertheless, the initial illumination decom-position error for the flowery sequence remains competitiveto the bear sequence until influence of the decomposed tex-ture error overwhelms the overall result.

4.3. Real Data

We conduct several real experiments with different clothdeformation and different texture frequencies. For all of ourexperiments, the scenes are illuminated using a 1280×800DLP View Sonic projector and the images are acquired bythe Canon XH-G1s HD 1920×1080 camera operating at30fps. The camera and projector are calibrated using the

3D shape computed

with texture decomposition

Observed image Decomposed texture Reference template

Estimating depth error with

respect to the ground truth

Depth map computed with

texture decomposition

Depth map computed without

texture decomposition

Texture flow

Figure 5. Decomposition of the texture and illumination images from a synthetic flowery cloth sequence with interleaving pattern projectedevery 30 frames. The depth map estimated after removing the texture not only shows its completeness over depth map obtained withouttexture removal but its high accuracy with respect to ground truth depth. The displacement of the texture regions with respect to thereference template is also estimated from the decomposition results.

(b)

(d) (c)

(a)

Figure 6. The accuracy and robustness of the decomposition withrespect to the interleaving period. (a) The median distance fromthe current frame to the reference template and the accumula-tive median displacement over frames (b) Percentage of camera-projector correspondences obtained in the textured regions (c)Normalized illumination error (d) Normalized texture error. Theerror is evaluated only for points inside the textured regions and iscomputed by Equation 6.

method of Vo et al [15]. As in the synthetic dataset, weproject an all-white frame every 30 frames. The results arepresented without any post-processing.

Figure 7 shows our results on the dogs and flag se-quences. Despite the simple image formation model, ourapproach can handle complex appearances of real worldtextured objects illuminated by the projector. We believethis is due to the local block decomposition strategy which

Kinect RGB 3D shape

Figure 8. 3D shape from the Kinect. Note that smoothing filtershas been applied to generate the mesh from raw point cloud data.

is robust to global lighting variation. As shown in the flagsequence, while the texture decomposition could be incom-plete, especially for low frequency textured objects, thequality of the decomposed illumination is less affected bythe texture frequency. Due to the relatively large size of thetextured region, the 3D shape of this folding cloth cannotbe obtained by hole-filling or interpolation algorithms. De-spite the mixed appearance, the texture flow estimated withrespect to the reference template is also obtained.

Figure 8 shows the 3D shape obtained from the Kinectsensor. For fair comparison with the performance of pro-posed method shown in the T-shirt sequence in Figure 7,the same subject is standing at a similar distance to the sen-sor. Visually, the quality 3D shape from our method out-performs that of the Kinect. It is noteworthy that unlesssmoothing filter is applied to raw Kinect results, the meshgeneration fails as the surface normal computed from rawpoint cloud is noisy.

4.4. Texture Flow vs. Illumination Flow

Besides the motion of the textured regions, there is alsoan apparent motion due to the illumination pattern. As il-lustrated in Figure 9, the flow direction of the illumination

3D shape obtained with

texture decomposition : view 2

Observed image Decomposed texture Texture flow

3D shape obtained without

texture separation

3D shape obtained with

texture decomposition: view 1

3D shape obtained with

texture decomposition : view 2

Observed image Decomposed texture Texture flow

3D shape obtained without

texture separation

3D shape obtained with

texture decomposition: view 1

Figure 7. Decomposition of the texture and illumination images from real cloth sequences. The interleaving pattern is projected every 30frames. After the decomposing process, the 3D shape can be obtained in the textured regions. No post-processing is applied. Applyinghole-filling methods on the 3D shape estimated without texture decomposing cannot yield appealing results because of the relatively largetextured regions. Despite the mixed appearance, the texture flow faithfully shows how the cloth is moving.

pattern and the texture are remarkably different from eachother. Unlike the motion flow which presents the movementof points on the object surface, the observed illumination isthe projection of the ray emanating from the light sourceand hence, its flow field must move only on the epipo-lar line of the camera-projector system. Furthermore, this

flow field encodes the changes in depths of rays emanatingfrom the light source that hit the object. Because establish-ing spatial correspondences between camera and projectoris much more difficult than estimating temporal correspon-dences, especially in the wide baseline scenario, any struc-tured light system can gain benefit from the temporal co-

Illumination flow Illumination flow Texture flow Texture flow

Figure 9. Observed motion flow and illumination flow when a moving textured object is illuminated by point light source. While thedirections of texture flow follow the movement of the object, the directions of the illumination flow are constrained to be on the camera-projector epipolar line. The figure is best viewed in the electronic version.

herency of the illumination flow. Future work will inves-tigate different approaches to incorporate illumination flowconstraint into structured light reconstruction algorithms.

5. DiscussionWhile we only show results on a single deforming ob-

ject, our algorithm is applicable to general scenes contain-ing multiple objects. As long as the seed points, i.e. corre-spondences established in textureless region, are availableon the object, these correspondences can propagate to theentire object. Nevertheless, because of the nature of thepatch decomposition approach, our algorithm cannot han-dle well the textured regions at the occluding boundary.

For objects with completely high frequency texture, theproposed algorithm will fail. Yet, such cases are rare andmost objects have a mixture of low and high frequencytexture regions (see Figure 5). While our approach mayalso fail for objects with low frequency texture, the camera-projector correspondence can be established to reconstruct3D shape. This shape information can be exploited to sepa-rate the texture out of the observed image.

Since the interleaving sequence is dependent on the mo-tion of the object, the interleaving period has to be adaptedto different applications. Nevertheless, in an era 60-fps con-sumer grade camera, there is no need to interleave everyframe, especially for daily human activity.

Acknowledgement: This research was supported inparts by an ONR Grant N00014-11-1-0295, an NSF GrantIIS-1317749, and a NSF Grant No. 1353120.

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