Peer reviewed eScholarship.orgPowered by the California Digital Library University of California largest absolute correlations with the label. However, he or she verifies the correlations (with the label) on the holdout set and uses only those variables whose correlation agrees in sign with the correlation on the training set and for which both correlations are larger than some threshold in absolute value. The analyst then creates a simple linear threshold classifier on the selected variables using only the signs of the correlations of the selected variables. A final test evaluates the classification accuracy of the classifier on the holdout set. Full details of the analyst's algorithm can be found in section 3 of (17). In our first experiment, each attribute is drawn independently from the normal distribution N(0,1), and we choose the class label y ∈ f−1; 1g uniformly at random so that there is no correlation between the data point and its label. We chose n = 10,000 and d = 10,000 and varied the number of selected variables k. In this scenario no classifier can achieve true accuracy better than 50%. Nevertheless, reusing a standard holdout results in reported accuracy of >63 ± 0.4% for k = 500 on both the training set and the holdout set. The average and standard deviation of results obtained from 100 independent executions of the experiment are plotted in Fig. 1A, which also includes the accuracy of the classifier on another fresh data set of size n drawn from the same distribution. We then executed the same algorithm with our reusable holdout. The algorithm Thresholdout was invoked with T = 0.04 and t = 0.01, which explains why the accuracy of the classifier reported by Thresholdout is off by up to 0.04 whenever the accuracy on the holdout set is within 0.04 of the accuracy on the training set. Thresholdout prevents the algorithm from overfitting to the holdout set and gives a valid estimate of classifier accuracy. In Fig. 1B, we plot the accuracy of the classifier as reported by Thresholdout. In addition, in fig. S2 we include a plot of the actual accuracy of the produced classifier on the holdout set.In our second experiment, the class labels are correlated with some of the variables. As before, the label is randomly chosen from {-1,1} and each of the attributes is drawn from N(0,1), aside from 20 attributes drawn from N(y·0.06,1), where y is the class label. We execute the same algorithm on this data with both the standard holdout and Thresholdout and plot the results in Fig. 2. Our experiment shows that when using the reusable holdout, the algorithm still finds a good classifier while preventing overfitting.Overfitting to the standard holdout set arises in our experiment because the analyst reuses the holdout after using it to measure the correlation of single attributes. We first note that neither cross-validation nor bootstrap resolve this issue. If we used either of these methods to validate the correlations, overfitting would still arise as a result of using the same data for training and validation (...

a) Scene (b) Direct Component (c) Global Component Figure 1: (a) A scene lit by a single source of light.The scene includes a wide variety of physical phenomena that produce complex global illumination effects. We present several methods for separating the (b) direct and (c) global illumination components of the scene using high frequency illumination. In this example, the components were estimated by shifting a single checkerboard pattern 25 times to overcome the optical and resolution limits of the source (projector) and sensor (camera). The direct and global images have been brightness scaled by a factor of 1.25. In theory, the separation can be done using just 2 images. When the separation results are only needed at a resolution that is lower than those of the source and sensor, the separation can be done with a single image. AbstractWe present fast methods for separating the direct and global illumination components of a scene measured by a camera and illuminated by a light source. In theory, the separation can be done with just two images taken with a high frequency binary illumination pattern and its complement. In practice, a larger number of images are used to overcome the optical and resolution limitations of the camera and the source. The approach does not require the material properties of objects and media in the scene to be known. However, we require that the illumination frequency is high enough to adequately sample the global components received by scene points. We present separation results for scenes that include complex interreflections, subsurface scattering and volumetric scattering. Several variants of the separation approach are also described. When a sinusoidal illumination pattern is used with different phase shifts, the separation can be done using just three images. When the computed images are of lower resolution than the source and the camera, smoothness constraints are used to perform the separation using a single image. Finally, in the case of a static scene that is lit by a simple point source, such as the sun, a moving occluder and a video camera can be used to do the separation. We also show several simple examples of how novel images of a scene can be computed from the separation results.

Many vision tasks such as scene segmentation, or the recognition of materials within a scene, become considerably easier when it is possible to measure the spectral reflectance of scene surfaces. In this paper, we present an efficient and robust approach for recovering spectral reflectance in a scene that combines the advantages of using multiple spectral sources and a multispectral camera. We have implemented a system based on this approach using a cluster of light sources with different spectra to illuminate the scene and a conventional RGB camera to acquire images. Rather than sequentially activating the sources, we have developed a novel technique to determine the optimal multiplexing sequence of spectral sources so as to minimize the number of acquired images. We use our recovered spectral measurements to recover the continuous spectral reflectance for each scene point by using a linear model for spectral reflectance. Our imaging system can produce multispectral videos of scenes at 30fps. We demonstrate the effectiveness of our system through extensive evaluation. As a demonstration, we present the results of applying data recovered by our system to material segmentation and spectral relighting.

Abstract