On Simsun and Double Simsun Permutations Avoiding a Pattern of Length Three Abstract. A permutation σ ∈ Sn is simsun if for all k, the subword of σ restricted to {1, . . . , k} does not have three consecutive decreasing elements. The permutation σ is double simsun if both σ and σ −1 are simsun. In this paper we present a new bijection between simsun permutations and increasing 1-2 trees, and show a number of interesting consequences of this bijection in the enumeration of pattern-avoiding simsun and double simsun permutations. We also enumerate the double simsun permutations that avoid each pattern of length three.

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Modelling solute transport in soil columns using advective-dispersive equations with fractional spatial derivatives Solute transport in soils is commonly simulated with the advective-dispersive equation, or ADE. It has been reported that this model cannot take into account several important features of solute movement through soil. Recently, a new model has been suggested that results in a solute transport equation with fractional spatial derivatives, or FADE. We have assembled a database on published solute transport experiments in soil columns to test the new model. The FADE appears to be a useful generalization of the ADE. The order of the fractional differentiation reflects differences in physical conditions of the solute transport in soil. Advection and hydrodynamic dispersion are considered to be the dominant mechanisms of solute transport in the vadose zone, i.e. the variably saturated layer of soils and sediments between the soil surface and the aquifers [1] . The advection is associated with the average water flux or velocity. The hydrodynamic dispersion is conceptualised as a diffusion-like process and can be interpreted as the result of the Brownian motion of solute particles [2] . Under these assumptions, the parabolic advective-dispersive equation (ADE) . The ADE has served as the theoretical framework to model the fate and transport of chemicals, and to address critical environmental issues stemming from agricultural practices or waste disposal operations in last decades [1] . The ADE fails to capture some important features of solute transport in soils [3] [4] [5] [6] [7] [8] . On the one hand, the dispersion coefficient tends to increase with the distance of solute concentration observations. This is often mentioned as the scale effect on the dispersion process [9] . On the other hand, solute concentrations at the outlet of the soil columns approach expected asymptotic values slower than predicted by the ADE; the phenomenon is known as heavy tailing [10] [11] [12] . Such behaviour is sometime referred to as the anomalous or the non-Fickian dispersion.. The basic assumption of the ADE models for the transport of contaminants through soil is that the movements of solute particles are characterized by the Brownian motion [2] . The complexity of pore space in natural porous media makes the hypothesis of the Brownian motion far too restrictive in some cases. It has been suggested that, in the soil matrix, high velocity regions tend to be spatially continuous at all scales, and therefore a solute particle travelling faster than the mean is likely to do that over large distances. Similarly, slower particles are trapped in stagnant zones before they have a chance to move in the general direction of the flow. Invoking the notion of the Lévy motion can simulate this type of solute particle transport. The Lévy motion is a broader framework compared with the Brownian motion, and includes the persistence in movements of solute particles. Significant deviations from the mean are more likely to occur in Lévy motions than in the Brownian movement [13, 14] . These features make Lévy motion an attractive generalization of Brownian motion when describing solute transport in porous media [9, 15] . Brownian motion is a specific case of the Lévy motion.. Similarly to the ADE that can be derived assuming Brownian motion [2] , solute transport equations can be derived for Lévy motions [16] [17] [18] [19] [20] [21] [22] . These equations include fractional derivatives. The one-dimensional version of the fractional advective-dispersive equation (FADE) with symmetric dispersion is. ], the superscript a is the order of fractional differentiation, 1 < a 6 2, c is the for the right-sided fractional derivative. Here, m is the integer such that m À 1 < a 6 m, C is the gamma function and A and B are real numbers. Let us remark that in the case a = 2 the FADE reduces to the ADE.. The FADE as a model to simulate solute transport in soils has been applied to data from both laboratory and filed-scale experiments [20, 18, 9, [24] [25] [26] [27] [28] [29] . Laboratory data are obtained from the so called miscible displacement experiments, in which the tracer solution infiltrates into originally tracer-free soil columns, and the dependence of the tracer concentration at the outlet on time, or breakthrough curve (BTC), is measured during the infiltration.. Most of the applications of the FADE to the solute transport todate rely on analytical solutions of the initial value problem in the infinite domain. However, in many practical applications initialboundary value problems in a finite domain need to be considered and numerical solutions are required. Several methods had been developed to solve the FADE numerically in the past few years [30] [31] [32] 27, 33, 34, 28, 29] .. The objective of this work was to compare the performances of both the classical model (ADE) and the fractional one (FADE) using a mass-conserving boundary condition and the numerical solution. We used published breakthrough data from miscible displacement experiments. The FADE constitutes a broad framework that includes the ADE and considers solute particles undergoing motions that are more complex than Brownian motion. Differences in values of the parameter a presumably reflect differences in hierarchical geometries of soil pore spaces. The FADE has accurately simulated the breakthrough curves considered in this study. The values of a ran- ; B and C -measured (symbols [41] ) and simulated (solid lines) breakthrough curves of the high and low flow rates, respectively. The best fit was obtained for a = 2.0 in the case of high flow rates and a = 1.75 for the low flow case.

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Manifest types, modules, and separate compilation This paper presents a variant of the SML module system that introduces a strict distinction between abstract types and manifest types (types whose definitions are part of the module specification), while retaining most of the expressive power of the SML module system. The resulting module system provides much better support for separate compilation.

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Multi-level genetic algorithm (MLGA) for the construction of clock binary tree The clock signal and clock skew become more and more important for the circuit performance. Since there are salient shortcomings in the conventional topology construction algorithms for designing a clock network, the multi-level model of clock binary tree is built, and the binary tree construction algorithm of clock signal based on multi-level genetic algorithm (MLGA) is presented. The experiments on random test cases and standard benchmark test cases show that multi-level genetic algorithm can produce much better clock network design in most cases when compared with conventional heuristic algorithms. In synchronous systems, the circuit performance is directly proportional to its clock frequency. A clock net needs to be routed with great precision, since the actual length of the net path from its source point to sink points determines the maximum clock frequency on which a chip may operate. In addition, the clock signal must arrive simultaneously at all functional units with little or no waveform distortion [1] . With the development of VLSI technology, the circuit speed is limited more and more rigidly by two factors: 1) delay on the longest path through combinational logic, 2) clock skew, which is the maximum difference in arrival times of the clock signal at the units [2] . This is shown from the following inequality. A multi-level genetic algorithm for construction of the clock binary tree is presented in this paper, which may yield less pathlength results than that of the existing algorithms while the zero skew is achieved with a heuristic merging scheme. In the MLGA, the encoding, fitness, genetic operators, and multi-level model are addressed in detail. Other key techniques, such as merging scheme, odd nodes proposal, generation decreasing strategy, are also designed properly. From the experiments on random test cases and standard benchmark test cases, it can be concluded that the MLGA is able to produce much better results compared with conventional heuristic algorithms.

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Error Exponents for Maximum-Likelihood and Successive Decoders for the Gaussian CDMA Channel Abstract-Random-coding error exponents are derived for the Gaussian code-division multiple-access (CDMA) channel for the maximum-likelihood and optimum successive decoders. Error exponents not only specify the capacity region of the channel, which is known, but also give lower bounds on the rate of exponential decay of the average probability of error as a function of the block length of random codes. A comparison of the two decoders in terms of their error exponents is included. The capacity region of the symbol-synchronous Gaussian code-division multiple-access (CDMA) channel was obtained in [1] by applying the result on the capacity region of general discrete memoryless multiple-access channels in [2] and [3] . The implication is that it is possible to achieve arbitrarily reliable communication for any rate-tuple in the capacity region with multiuser coding and joint maximum-likelihood decoding (MLD). However, multiuser codes with sufficient structure to allow efficient maximum-likelihood decoding are far from being realized. Thus we also consider successive decoders, since these would be much simpler to implement than the MLD, and they allow us to sidestep the problem of finding good multiuser codes. Single-user codes can be chosen independently for each user. In particular, the Optimum Successive Decoder (OSD) for the Gaussian CDMA channel is known to achieve the total capacity (sum-rate) of the channel at any vertex of the capacity region [4] . Hence, as far as total capacity is concerned, there is no loss of optimality in using the OSD over the MLD.. In this correspondence, we analyze random-coding error exponents for the MLD and the OSD since error exponents provide more information than just the capacity region. For any rate-tuple inside the capacity region, they quantify (lower bound) the rate of exponential decay of the error probability of the decoder averaged over randomly chosen codes, thereby giving some indication of the error probability that might reasonably be expected of well-designed, finite-length codes. This allows us to make a finer comparison of the two decoders than does the total capacity measure (in terms of which the two decoders are equivalent) or even the capacity region. In particular, for rate-tuples that are common to the capacity regions of any two decoders, the error exponents would reveal the extent of the suboptimality of the OSD relative to the MLD.. We find that there are important instances in which the error exponents of the OSD and the MLD are equal. In cases where the OSD error exponents are significantly smaller than those of the MLD, we show in the two-user case that significant improvements in the error exponent cannot be achieved by extending successive decoding via rate splitting [5] to the CDMA channel.. The remainder of this correspondence is organized as follows. In Section II, the CDMA channel model is introduced and error exponents for the MLD are derived. Section III contains a derivation of the error exponents of successive decoders for the CDMA channel. Section IV compares the OSD and MLD error exponents, delineating sufficient conditions for equality. Section V contains concluding remarks.

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Efficient time domain threshold for sparse channel estimation in OFDM system A novel efficient time domain threshold based sparse channel estimation technique is proposed for orthogonal frequency division multiplexing (OFDM) systems. The proposed method aims to realize effective channel estimation without prior knowledge of channel statistics and noise standard deviation within a comparatively wide range of sparsity. Firstly, classical least squares (LS) method is used to get an initial channel impulse response (CIR) estimate. Then, an effective threshold, estimated from the noise coefficients of the initial estimated CIR, is proposed. Finally, the obtained threshold is used to select the most significant taps. Theoretical analysis and simulation results show that the proposed method achieves better performance in both BER (bit error rate) and NMSE (normalized mean square error) than the compared methods, has good spectral efficiency and moderate computational complexity. Orthogonal frequency division multiplexing (OFDM) technique is widely used in wireless communication system thanks to its advantages of high data Preprint submitted to AEU -International Journal of Electronics and CommunicationsOctober 13, 2013 transmission rate over multipath fading channel. In OFDM systems, accurate channel state information (CSI) is necessary for coherent detection at the receiver. Therefore, how to optimally use the precious limited communication system resources to obtain effective CSI is the main challenge in channel estimation field.. Channel estimation can be carried out in either frequency or time domain. In frequency domain, least squares (LS) and minimum mean square error (MMSE) are the most common channel estimation methods [1] . Generally, MMSE method can achieve better channel estimation performance than LS method, but MMSE method requires prior knowledge of channel statistics and noise variance. Moreover, it has an increased computational complexity [1, 2] . Comparatively, the complexity of LS is low and it is popular to combine LS method with different interpolation algorithms to realize effective channel estimation [2, 3, 4] . Among them, linear interpolation with lowest computational cost is the most classical one [2, 3, 4, 5, 6] . However, its performance relies on comparatively high percentage of pilots and it is vulnerable to noise, especially when the channel is sparse. For sparse channel, the channel impulse response (CIR) is characterized by a few dominant channel taps and majority of zero or nearly zero channel taps. In time domain, it is possible to estimate the sparse channel with limited number of pilots by fully considering the maximum channel length and the characteristics of channel sparsity. The most significant taps (MST) method, firstly proposed in [7] , is popular in estimating sparse channel. Following that, different thresholds [8, 9] have been proposed for MST based methods. However, all these methods have drawbacks. For example, a statistical threshold is derived for pilot aided sparse channel estimation in [8] , which needs prior knowledge of channel statistics and has reduced spectral efficiency. [9] uses twice of the noise power as threshold, which can hardly be optimal [6] . The noise standard deviation based threshold [10] is also not optimal [11] . In order to overcome the drawbacks of the above sparse channel estimation methods, recently, the theoretical optimal threshold is derived for sparse Rayleigh channel estimation in OFDM system [12] , which relies on the accurate knowledge of the channel tap power delay profile and the received pilot energy to noise ratio. In order to make the threshold more robust to communication environment, a sub-optimal threshold is proposed by assuming a uniform power delay profile [12] , which is proven to be robust with the true power delay profile and depends only on the received signal to noise ratio (SNR). This paper proposes a novel sparse channel estimation method with effective time-domain threshold. The proposed method depends only on the estimated noise standard deviation and needs no prior knowledge of channel statistics and noise standard deviation, it can realize effective channel estimation within a wide range of sparsity rate (the ratio of non-zero taps to the considered channel length) [13] .. The rest of this paper is organized as follows. In Section 2, the system model for sparse channel estimation in OFDM system is introduced and the noise statistics are analyzed. Based on the characteristics of the sparse channel, an effective time domain threshold is proposed for the improvement of channel estimation performance in Section 3. Some simulation results comparing the performance of the proposed method and other existing methods and the computational complexity analysis are provided in Section 4. Finally, conclusions are drawn in Section 5. Channel estimation methods with good estimation performance without requiring prior knowledge of channel statistics and noise standard deviation will significantly benefit the practical wireless communications. In this paper, an effective sparse channel estimation method based on LS is proposed in OFDM system. In this method, a novel effective time domain threshold 11 depending only on the effective noise standard deviation estimated from the noise coefficients obtained by eliminating the channel coefficients with an initial estimated threshold is proposed. Both theoretical analysis and simulation results show that the proposed method can achieve better performance in both BER and NMSE than the compared methods within a wide range of sparsity rate, has good spectral efficiency and moderate computational complexity. The proposed two-step threshold estimation technique is general, other threshold, like the suboptimal threshold proposed in [12] can be used in the same way as the universal threshold used in this paper.

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Overcoming Superstrictness in Line Drawing Interpretation Abstract-This paper presents a new algorithm for correcting incorrect line drawings-incorrect projections of a polyhedral scene. Such incorrect drawings arise, e.g., when an image of a polyhedral world is taken, the edges and vertices are extracted, and a drawing is synthesized. Along the way, the true positions of the vertices in the 2D projection are perturbed due to digitization errors and the preprocessing. As most available algorithms for interpreting line drawings are "superstrict", they judge these noisy inputs as incorrect and fail to reconstruct a 3-dimensional scene from them.The presented method overcomes this problem by moving the positions of all vertices until a very close correct drawing is found. The closeness criterion is to minimize the sum of squared distances from each vertex in the input drawing to its corrected position. With this tool, any superstrict method for line drawing interpretation is now practical, as it can be applied to the corrected version of the input drawing. Consider the pictures of the plane-faced alarm devices in ( fig. 1a ) and the line drawings extracted from them in fig. 1d . How can we tell whether these drawings represent correct projections of the spatial objects they come from? Even more, how can we reconstruct the 3D objects they represent? Answering these questions and producing an algorithm able to reconstruct a plane-faced object from its line drawing, with similar results as a human gets, has been one of the goals of Computer Vision and Artificial Intelligence since the early seventies.. Along the years, several methods have been proposed to test the correctness of line drawings and give their possible reconstructions [2] , [3] , [4] , [5] , [6] , [7] . These tests succeed in judging as incorrect such impossible figures as those in fig. 2 . However, even when the drawings come from a picture of a real scene, the tests usually judge them as incorrect, failing to derive a spatial reconstruction. To see why, consider the examples in fig. 1d , showing the projections of two truncated pyramids. These drawings can only be correct when the three edge lines , ¡ and ¢ meet at a common point, as this holds in any spatial reconstruction of the drawing ( fig. 1e ), and such conditions are preserved after projection. This is a general characteristic of all line drawings: they are only correct for very specific positions of the vertices, satisfying a number of concurrence conditions on triplets of lines [6] , [8] . Hence, as many geometric relationships between the vertices are lost due to digitization errors and L. Ros and F. Thomas are with the Institut de Robòtica i Informàtica Industrial (CSIC-UPC), Llorens Artigas 4-6, 2 planta, 08028 Barcelona, Catalonia (Spain). E-mails: llros@iri.upc.es and fthomas@iri.upc.es . This paper is an extended and updated version of [1] , presented at the ICRA'2001 conference. Up to the authors' knowledge, the literature offers two approaches to overcome the superstrictness issue: a drawing correction strategy due to Sugihara [5, chapter 7] and an explicit handling of uncertainty, due to Ponce and Shimshoni [21] , [22] .. Roughly speaking, Sugihara's correction method works as follows. Think about the truncated tetrahedron in Figure 4a . We see that fixing the heights of. is enough to determine the heights of the others, as we can use the coplanarity constraint of each face to derive them. However, the height of A G is overconstrained, as it can be deduced from both the coplanarity of D u and

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A hierarchical semantic-based distance for nominal histogram comparison . A hierarchical semantic-based distance for nominal histogram comparison. Data and Knowledge Engineering, Elsevier, 2013, 87, pp.206-225. 10.1016/j.datak.2013 Abstract-We propose a new distance, devoted to the comparison of nominal histograms equipped with a dissimilarity matrix providing the correlations between the bins. The computation of this distance is based on a hierarchical strategy, progressively merging the considered instances (and their bins) according to their semantic proximity. For each level of this hierarchy, a standard bin-to-bin distance is computed between the corresponding pair of histograms. In order to obtain the proposed distance, these bin-to-bin distances are then fused by taking into account the semantic coherency of their associated level. From this modus operandi, the proposed distance can handle histograms which are generally compared thanks to cross-bin distances. It preserves the advantages of such cross-bin distances (namely robustness to histogram translation and histogram bin size), while inheriting from the low computational cost of bin-to-bin distances. Validations in the context of geographical data classification emphasize the relevance and usefulness of the proposed distance. These different indexes have been used to quantitatively evaluate the clustering results obtained with HSBD and to compare them to the results obtained with classical bin-to-bin distances. We present hereafter both local and global evaluation results. The local evaluation results obtained on the three datasets are presented in Figure 6 . From these graphs, one can see that the F-measure scores obtained for each extracted class are always higher when the K-MEANS algorithm is run with the HSBD distance instead of its corresponding bin-to-bin distance D bin . In particular, the best scores have been obtained when the HSBD distance is run with the Manhattan D L1 distance as sub-distance, while the worst scores have been obtained when HSBD is run with the χ 2 as sub-distance. However, the scores obtained with the χ 2 as sub-distance remain always higher than those obtained by using only standard bin-to-bin distances. Such local evaluation results mean that the HSBD distance enables to enhance the precision and the recall of the results.. The global evaluation results obtained on the three datasets are presented in Table 6 . They lead to the same observations as previously. Best global evaluation scores obtained are always higher when the K-MEANS algorithm is run with the HSBD distance instead of its corresponding bin-to-bin distance D bin .. Furthermore, the best scores have been obtained when the HSBD distance is run with the D L1 sub-distance.. From these different results, one can see that the proposed distance outperforms the classical bin-to-bin ones when comparing semantic nominal histograms. Finally, such validations, in the context of geographical data classification, emphasize the relevance and usefulness of HSBD for data mining tasks. In this work, we consider the comparison of possibly large datasets where data are characterized by nominal histograms for which (semantic) proximity information between the bins can be provided. In order to illustrate such histograms, let us go back to the example depicted in Figure 1 (a). Each bin of the histogram represents the proportion of a kind of fruit which is an instance of the semantic concept FRUIT. Since Lemon and Orange are both citrus fruits, the instance Lemon could be considered as closer to the instance Orange than the instance Plum. It is then possible to evaluate semantic similarities between the bins composing these nominal histograms. In this context, it can be advisable to take into account such kinds of semantic similarities to improve the comparison of these histograms. On one hand, the bin-to-bin distances are well fitted to process large datasets, in particular thanks to their low computational cost. Nevertheless, by definition, such distances cannot consider the semantic proximity between the different bins. (In particular, they suffer from both problems of histogram translations and bin size changes.) For instance, let us consider the three shopping carts C 1 , C 2 , C 3 , provided in Table 1 . Their fruits can take values in {Lemon, Quince, . . . , Plum}. Then, the composition of a shopping cart C i can be modelled by a histogram H i (#Lemon, #Quince, . . . , #Plum) where #x denotes the number of occurrences of the instance x in the shopping cart C i . With a standard bin-to-bin distance, for instance the Manhattan one d L1 , there is the same distance between H 1 and H 2 than between H 1 and. ). However, C 1 is semantically closer to C 3 than to C 2 because C 1 and C 3 are both citrus fruits shopping carts.. On the other hand, cross-bin distances, which compare more exhaustively both corresponding and noncorresponding bins, enable to consider the semantic proximity between the different bins. Practically, this can be done by assigning, to each pair of instances, a weight (i.e., a numerical value) modelling the de- L em o n Q u in ce A p p le G ra p ef ru it A p ri co t P ea r P ea ch C h er ry O ra n g e P lu m. gree of semantic proximity between the compared instances. For instance, in the shopping cart example, the weight associated to the couple of instances (Lemon, Orange) should be lower than the one associated to the couples (Lemon, Plum) or (Orange, Plum).. The counterpart of such strategies is the quadratic cost induced by these multiple bin comparisons. Based on these considerations, it appears that, when comparing nominal histograms, the handling of semantic proximity between their instances seems incompatible with a low computational cost. In this work, we propose a new distance addressing this issue. Its computation is based on a hierarchical strategy, progressively merging the considered instances (and their bins) according to their semantic proximity. For each level of this hierarchy, a standard bin-tobin distance is computed between the corresponding pair of histograms. In order to obtain the proposed distance, these bin-to-bin distances are then fused by taking into account the semantic coherency of their associated level. From this modus operandi, the proposed distance preserves the advantages of cross-bin distances (namely robustness to histogram translation and histogram bin size), while inheriting from the low computational cost of bin-to-bin distances. 3.1.1 Bin-to-bin distances As stated above, bin-to-bin distances consider a histogram as a fixed-dimensional vector and only compare the contents of the corresponding bins of the histograms. To compare these bins, it is possible to use various metrics/distance functions. The most commonly used are (non-exhaustively):. In the sequel, they are denoted as D L1 , D L2 , D ∩ , and D χ 2 . For two histograms H(A) and H(B) with v bins, these distances can be formulated as:. These distances present specific properties, the respective advantages and drawbacks of which are discussed in [11] .. As they only compare corresponding histogram bins, and then ignore the correlations between neighboring bins, bin-to-bin distances are fast to compute and can be used to measure similarities for large datasets. Moreover, they do not require any ordering or similarity relations among the bins, and can then be used to compare both nominal or ordinal histograms. However, they suffer from the translation problem: a small translation of the histogram values may significantly affect the histogram distance. Furthermore, bin-to-bin distances are deeply linked to the bin size of histograms: a too coarse binning will not have a sufficient discriminative capacity while a too fine one will separate similar/correlated features in different bins which will not be matched. The cross-bin distances enable to overcome these limitations.

O O O O O B I O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Dynamic media arts programming in impromptu Dynamic software systems for generative art have particular requirements around rapid development and manipulation of ideas and real-time computational processes. Impromptu is an innovative new programming environment created by Andrew Sorensen, and is designed to facilitate the fluid flow of creative ideas and their expression in software. It has been used for our recent projects, including a variety of Collaborative Music Jamming Systems, because it supports creative processes by leveraging the audio, graphic and video capabilities of the modern operating system within a dynamic programming environment. In our projects collaboration is supported through a synthesis of media types, numerous communication protocols, and facilities for inter-system communications and control. The demonstration will show these environments and how Impromptu supported their development. Dynamic Media Jamming environments enable users to interact with generative music and visual systems to perform audio-visual works, typically in the style of electronic dance music and VJing. User's become metacreators by adjusting generative system parameters through a variety of graphical and physical controller interfaces. These systems require a development environment with rich media capabilities, reliable timing and the ability for rapid development and easy modification. The environments we have developed are in the context of interaction design research and thus the ability to iteratively refine the systems in response to usability feedback is particularly important. Impromptu has proven to be an effective tool for this development.. Impromptu is a Mac OS X programming environment for composers, sound artists, VJ's and graphic artists with an interest in live or interactive programming. Impromptu is a Scheme language environment. Scheme is a member of the Lisp family of languages.. Time plays a major role in the Impromptu environment which allows accurate real-time scheduling of events and code blocks. Impromptu is a dynamic environment designed for the creation and manipulation of running programs in live performance and can also be used for computational arts installations, and developing interactive media experiences. The development of dynamic Media Art works, such as the collaborative jamming systems created by the researchers, is made easier by development environments that share the priorities of media artists. Impromptu is a dynamic software development environment for Mac OS X, version 10.4 +, that has been optimized for time-based, interactive works. The features and interface of Impromptu have been designed to allow the artist/developer to rapidly create, test and modify their computational ideas. Information about the dynamic media jamming environments mentioned here is available from http://acid.net.au and Impromptu is available for free download from http://impromptu.moso.com.au.

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Quantum universality by state distillation Quantum universality can be achieved using classically controlled stabilizer operations and repeated preparation of certain ancilla states. Which ancilla states suffice for universality? This "magic states distillation" question is closely related to quantum fault tolerance. Lower bounds on the noise tolerable on the ancilla help give lower bounds on the tolerable noise rate threshold for fault-tolerant computation. Upper bounds show the limits of threshold upperbound arguments based on the Gottesman-Knill theorem.We extend the range of single-qubit mixed states that are known to give universality, by using a simple parity-checking operation. For applications to proving threshold lower bounds, certain practical stability characteristics are often required, and we also show a stable distillation procedure.No distillation upper bounds are known beyond those given by the Gottesman-Knill theorem. One might ask whether distillation upper bounds reduce to upper bounds for single-qubit ancilla states. For multi-qubit pure states and previously considered two-qubit ancilla states, the answer is yes. However, we exhibit two-qubit mixed states that are not mixtures of stabilizer states, but for which every postselected stabilizer reduction from two qubits to one outputs a mixture of stabilizer states. Distilling such states would require true multi-qubit state distillation methods. Stabilizer operations, consisting of Clifford group unitaries and Pauli operator measurement and eigenstate preparation, suffice for generating interesting, highly entangled quantum states. By the Gottesman-Knill theorem, however, they are efficiently classically simulatable and not quantum universal [AG04] . What more does one need to obtain quantum universality? A sufficient additional operation is any one-qubit unitary that is not a Clifford up to overall phase [Shi03] . Almost every n-qubit unitary also suffices. Much less is known, however, about which non-unitary quantum channels, such as noisy gates, suffice for universality together with stabilizer operations. If we assume that the quantum operations are under the adaptive control of a universal classical computer, then this question turns out to be a special case of a broader problem:. Magic states distillation problem. For which quantum states ρ does stabilizer operations plus repeated preparation of ρ imply quantum universality?. If repeated preparation of ρ and stabilizer operations gives universality, we say for short U(ρ). The problem of characterizing the states ρ for which U(ρ) holds has its main application in quantum fault tolerance. For fault-tolerance schemes based on stabilizer codes, encoded stabilizer operations are the easiest operations to implement. Magic states distillation allows extending these operations to a full universal set, provided that noisy enough states ρ satisfy U(ρ). Conversely, limits on when U(ρ) can hold can also give limits on fault-tolerance schemes.. In this paper, we extend the range of single-qubit mixed states ρ that are known to give universality, by using a simple parity-checking operation. However, the question of fully characterizing those single-qubit states ρ for which U(ρ) holds remains open. For multi-qubit pure states, the question U(ρ)? reduces to the same question for single-qubit pure states. Unfortunately, though, as a second result we show that this question for mixed multi-qubit states ρ generally does not reduce to the single-qubit problem. We also study the applications of magic states distillation to quantum fault-tolerance schemes. In particular, these applications in practice will require certain stability properties, and we present a stable distillation procedure. Magic states distillation is important both because it describes the power of stabilizer operations, in terms of what more is necessary for achieving full quantum universality, and because of its application to quantum fault tolerance. We have given improved magic states distillation procedures, reducing the set of single-qubit mixed states ρ for which U(ρ) is unknown. We have also introduced the multi-qubit magic states distillation problem, and proved that it does not reduce to the singlequbit case. We have used magic states distillation to prove that two noise threshold upper bounds are in fact tight.. There remain many open problems, including most of those described in earlier papers [BK05, Rei05] . Are there two-qubit nonstabilizer states that cannot be distilled to a single-qubit nonstabilizer state? We have given some candidate states, one of which might have sufficient structure for an analysis. In particular, it is interesting to specialize this question to those two-qubit states arising from the Jamiolkowski isomorphism.. Research conducted while the author was at the University of California, Berkeley, supported in part by NSF ITR Grant CCR-0121555, and ARO Grant DAAD 19-03-1-0082.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Adaptive 4-8 Texture Hierarchies Figure 1: Two screen shots of an overflight of Fort Hunter Liggett, CA that illustrate the use of 4-8 texture hierarchies. On the left is the seamless textured image produced by the system, while the right shows the outline of the texture tiles used in producing the image.We address the texture level-of-detail problem for extremely large surfaces such as terrain during realtime, view-dependent rendering. A novel texture hierarchy is introduced based on 4-8 refinement of raster tiles, in which the texture grids in effect rotate 45 degrees for each level of refinement. This hierarchy provides twice as many levels of detail as conventional quadtree-style refinement schemes such as mipmaps, and thus provides per-pixel view-dependent filtering that is twice as close to the ideal cutoff frequency for an average pixel. Because of this more gradual change in low-pass filtering, and due to the more precise emulation of the ideal cutoff frequency, we find in practice that the transitions between texture levels of detail are not perceptible. This allows rendering systems to avoid the complexity and performance costs of per-pixel blending between texture levels of detail.The 4-8 texturing scheme is integrated into a variant of the Realtime Optimally Adapting Meshes (ROAM) algorithm for viewdependent multiresolution mesh generation. Improvements to ROAM included here are: the diamond data structure as a streamlined replacement for the triangle bintree elements, the use of lowpass-filtered geometry patches in place of individual triangles, integration of 4-8 textures, and a simple out-of-core data access mechanism for texture and geometry tiles. Graphics hardware has become orders of magnitude faster and cheaper in recent years, yet there remains a strong need to render textured geometry from databases containing far more detail than can be displayed in realtime. A classic motivating example is terrain visualization, in which photo-imagery and elevation data are available on planetary scales, resolving to ten meters or better on average, with meter or sub-meter data available in some regions (such as the one-meter database of Fort Hunter Liggett, CA, shown in Figure 1 ). With new data collection instruments and data handling capabilities, this wealth of information is likely to grow rapidly. The NASA MOLA data, for example, covers Mars at a resolution of 128 elevation bins per degree, totaling around one billion elevations [1] . Publicly available data from the USGS covers the state of Washington at 10 meter horizontal and 10cm vertical spacing, totaling 1.4 billion elevation values [19] . Dynamic, viewdependent adaptations of geometric meshes and texture tile hierarchies are required to provide fast and accurate renderings of these large-scale terrain databases.. Since hardware rendering rates have grown to exceed 200 million triangles per second, this means that choosing triangle adaptations for uniform screen size will result in roughly one-pixel triangles for full-screen display at 100 frames-per-second rendering rates. At this point it is no longer desirable to make triangles nonuniform in screen space due to variations in surface roughness, since this will only lead to sub-pixel triangles and artifacts. This situation for geometry is now in a similar regime to that of texture level-of-detail adaptation, which seeks to make each texel project to roughly one pixel in screen space. Overall then our goal is to low-pass filter the geometry and textures so that triangles and texels project to about a pixel.. While many geometric hierarchies have been devised for largedata view-dependent adaptation, the above analysis suggests that uniform aspect-ratio triangles are more desirable for attaining better control of geometric antialiasing. Also, better low-pass filtering methods are known for regular grids. Texture hierarchies are more constrained than geometry, since graphics hardware works most effectively with raster tiles of modest, power-of-two sizes. For efficiency of texture loading and packing, we avoid consideration of texture atlas schemes in which a power-of-two tile is filled with ir- regular sub-regions that are used independently. This leads us to use regular grids for efficiency and uniformity of treatment. In theory, there are only two regular tilings of the plane that allow conformant adaptive meshes to be formed without special fix-ups at level of detail transitions: the 4-8 meshes and the 4-6-12 meshes [7, 8] . We chose the 4-8 meshes, shown in Figure 2 , since these match the constraints of texture hardware and have many known desirable properties [12, 6, 13] . While several data structures have been devised to support 4-8 refinement, we found that additional streamlining and unification was possible. This paper introduces a diamond data structure, in which each diamond element simultaneously has unique associations with a vertex (its center), an edge (its distinguished diagonal), and a quadrilateral face of a 4-8 refinement mesh. A diamond represents the pairing of two right isosceles triangles at the same level of detail in the 4-8 mesh that share a base edge. Since basic operations on the 4-8 mesh must treat these diamonds as a unit, it is logical and efficient to use the diamond as the backbone data structure rather than bintree triangles. Section 3 provides details on the diamond structure and its use in 4-8 incremental mesh adaptation.. Both geometry and textures are treated as small regular grids, called tiles, defined for each diamond in the hierarchy. Tiles at a level of resolution matching the input data are either copied or resampled. Coarser tiles are computed using low-pass filtering in an out-of-core traversal. Finer tiles can be obtained using 4-8 subdivision [23] with the optional addition of procedural detail. For efficient input and output, files and disk blocks are laid out using a diamond indexing scheme based on the Sierpinski space-filling curve. Tiles are described in Section 4. Sierpinski indexing, and out-of-core preprocessing are described in Section 5.. For geometric rendering, patches of 256 or 1024 triangles are stored as indexed vertex arrays in Sierpinski order for highly efficient rendering on graphics hardware. Using uniform refinement, any power of four increase in triangle count will result in conformant meshes [18, 11] . We are able to achieve triangle throughput close to the practical limits on recent PC video cards. Section 6 outlines how patches are laid out and updated.. The adaptive 4-8 textures, defined in detail in Section 7, fill each diamond area with a regular-grid image raster, rendered using bilinear interpolation. Neighboring tiles share boundary samples on their mutual edges, and the 4-8 mesh refinement naturally defines a parent-child grid-structure relationship suitable for various filtering operations. We allow each ROAM leaf triangle patch to independently choose which texture level-of-detail to map to, based on its estimated pixel area for the current view transform. A mapping from the triangle patches' parameterization to the texture diamond's parameter space is computed as needed when this level-of-detail selection changes. This change requires an update of the vertex array texture coordinate data stored in special graphics hardware memory (e.g. AGP memory), which is an expensive operation that can require synchronization with previously launched asynchronous rendering activity. Therefore the triangle-patch texture level-of-detail updates are budgeted per frame based on similar dual-queue operations used by the ROAM algorithm.. Overall this approach to forming tile hierarchies and accessing them during frame-to-frame incremental updates results in a visually seamless, high quality display of arbitrarily large terrain and imagery databases. Some implementation details and numerical results are presented in Section 8, but the ultimate proof is to see the system in action on a huge data set. The visual appearance is in our experience consistently very high. Indeed, we were pleasantly surprised that no per-pixel blending of texture level-of-detail seems to be needed; we believe this is due to the gradual factor-of-two changes in information content between levels. We have presented a solution to the texture level-of-detail problem for real-time view-dependent rendering of extremely large terrain meshes. We introduce a new texture hierarchy based upon a 4-8 mesh, which, when coupled with a similar adaptive geometry scheme, provides a mechanism for real-time display of the terrain. The 4-8 hierarchy provides twice as many levels of detail as conventional quadtree-style refinement schemes such as mipmaps. Because of this more gradual change, we find in practice that the transitions between texture levels of detail are less perceptible. The 4-8 scheme is integrated into a variant of the ROAM algorithm, and together with a simple out-of-core data access mechanism based upon Sierpinski curves allows out-of-core access for the display of very large textured meshes.. Future work based on this terrain system can be expanded to include dual queues at all levels of cache, for both geometry and texture, replacing the reactive least-recently-used strategy with prefetching and optimized priority modeling. Anisotropic filtering could help with highly warped terrain data, such as near cliffs, and with the horizon aliasing for near-planar regions. Further experimentation with different types of texture maps, such as normal maps for lighting calculations, may enhance the visual quality of a scene and allow dynamic lighting. As memory bandwidth increases, it may also be possible to play animated textures of certain areas in a scene to demonstrate time varying properties like plant life or erosion. The development of realtime, high quality procedural detail is also of interest. Our performance results were measured using a 3Ghz Xeon processor with 1GB of RAM and a GeForce FX 5900 Ultra. We ran the tests at a resolution of 640 × 480 utilizing the NVidia vertex array range specification combined with chunked triangle patches to exploit the graphics-card capabilities. These results are based on a flight path through the 10-meter data of Washington state [19] with around 1.4 billion elevation and texel values at the finest resolution. The source elevation data totals 2.7 gigabytes on disk before preprocessing. Textures were procedurally generated and colored from the original geometry and stored in RGB-565 format.. The out-of-core preprocessing step for this particular data set took approximately 53 minutes including the calculation of the shaded texture map from the geometry. Without the shading step, preprocessing texture and geometry data into tiles took 33 minutes.. In the rendering application, approximately 53% of the time for a given frame is spent preparing the vertex array data. During this time, vertex pointers are set up and triangle patches that need to be updated either due to geometry updates or texture coordinate updates are transferred to AGP memory to be pulled by the GPU. Around 45% is spent managing vertex and texture coordinate cache allocation and traversing the hierarchy to evaluate when triangle patches or texture coordinate updates are necessary. The time taken by the split/merge optimization loop is a user defined parameter, but in this test less than two percent time was spent on this. Less than one percent each was spent on fetching geometry and texture from disk, priority updates, coordinate mapping calculations, triangle patch building, frustrum culling, and new texture loading. In our implementation, priority queues also allowed a user-defined number of fixed textures to be sent to graphics-card texture memory per frame. Our results show that the main bottleneck lies in the graphics-card upload bandwidth and the loop for determining appropriate triangle patch updates to geometry and texture.. Performance statistics for our implementation are shown in Figure 12 , taken during a flyover of Mount Rainier (shown in the accompanying video). In the lower-right graph, the rendering preparation line refers to the updating of AGP memory and set up of vertex pointers. Traversal and allocation involves walking through the diamond hierarchy and managing system memory. The geometry optimization line represents the split/merge time taken per frame. The remaining calculations, generally taking less than two percent of the frame time, are labeled "other". Snapshots from the flyover are highlighted in Figure 13 . A great variety of geometric level-of-detail algorithms have been devised for realtime rendering of massive terrains and other data sets. An overview of many historical methods can be found in [16] . The most common means of organizing geometry are Triangulated Irregular Networks (TINs) [20, 9] , and Hierarchies of Right Triangles (HRTs) [15, 7] . Generally the HRT methods can be implemented to have greater performance and lower memory use per triangle, but require a modest increase in triangle budget to achieve the same accuracy [7] . For the reasons outlined earlier, we focus on regular-grid representations and HRT view-dependent adaptations, and review the relevant papers here.. First it is important to note that HRTs are equivalent to adaptive 4-8 meshes. An early paper using HRTs for view-dependent dynamic meshing was Lindstrom et al. [12] . They utilize an elegant block-adaptive refinement using frame-to-frame coherence, followed by a fine-grained bottom-up vertex-reduction method to reduce the size of the mesh for display purposes. Duchaineau et al. [6] introduce a dual-queue algorithm (ROAM) to incrementally split and merge HRT elements while maximizing the use of frame-to-frame coherence for frustum culling, priority computations, mesh updates and triangle stripping. Lindstrom and Pascucci [13] simplify the overall HRT processing to a minimal triangle bintree recursion per frame that requires no special effort to maintain crack-free meshes, produces a single generalized triangle strip as output, and uses a novel vertex indexing scheme to automatically make out-of-core access efficient using an existing operating-system virtual memory system. They extend this [14] to allow smoother view-dependent meshes through interpolation, and test additional space-fill indexing strategies. Gerstner uses Sierpinski indexing for triangles, and identifies the resulting duplicate indices using a simple state machine. The method is intended for use during recursive traversal of the triangle bintrees, and requires explicit links in the vertex database to avoid gaps in the disk or memory layout. Pajarola [17] utilizes a restricted quadtree triangulation, similar to an adaptive 4-8 mesh, for terrain visualization. Pomeranz [18] demonstrates how the ROAM algorithm can be extended to utilize pre-computed HRT patches in place of individual triangles to better exploit modern graphics hardware while maintaining crackfree triangulations. Levenberg [11] extends this further by allowing HRT patches to be computed dynamically during interaction.. Large texture processing has been attempted by several researchers. Williams [24] introduces the mipmap method of prefiltering texture levels of detail, which are images of increasingly reduced resolution arranged as a pyramid. Starting with the finest level, each coarser level represents the image using one quarter the number of texels (half the number of texels in each dimension). Per-pixel rendering with a mipmap is accomplished by projecting the pixels into mipmap space using texture coordinates and camera transformations. Typically a rendered pixel is colored using a variant of trilinear interpolation of eight texels taken from two adjacent levels of the mipmap hierarchy.. Tanner et al. [21] introduce clipmaps, an extension of mipmaps, that also utilizes a factor-of-four texture pyramid, but allows arbitrarily large out-of-core textures to be paged into the in-memory pyramid. This algorithm utilizes the fact that a complete mipmap pyramid is rarely used during the rendering of a single image (particularly in terrain rendering), and much of the pyramid can be clipped away, allowing much larger textures to be used.. Ulrich [22] combines a quadtree of mipmap and geometry tiles, called chunks, to handle out-of-core view-dependent meshing and texturing of huge terrains. The texture and geometry chunks are produced in a preprocessing step and are static during runtime interaction. Geometry chunks are based on adaptive 4-8 refinement, with special "flanges" to hide the tiny cracks that occur at chunk boundaries. Each chunk is stored in special graphics memory and can be rendered with a single draw call. The chunks are refined based on the viewpoint to meet the desired visual fidelity, and are paged from disk. Similarly, mipmap tiles are loaded and accessed from the geometry chunks based on calculations of maximum pixel size in the mipmap. This determines the finest level of detail that will be used in a mipmap, and by refining the mipmap tiles accordingly, the mipmap per-pixel blending will automatically generate seamless texture imagery across tile boundaries.. Further research by Döllner et al. integrates clipmap-like behavior with terrain rendering by using memory-mapped texture files [5] . Their method utilizes a multiresolution texture system that works in conjunction with a multiresolution model for the terrain geometry. They build a tree of texture patches that is closely associated with the hierarchical model of the terrain geometry. The rendering algorithm simultaneously traverses the multiresolution model for terrain geometry and texture trees, selecting geometry patches and texture patches according to a user-defined visual error threshold. However, their method utilizes in-core quadtrees for texture storage, resulting in a power-of-four texture hierarchy.. Cignoni et al. [2, 3, 4] have demonstrated the ability to display both adaptive geometry and texture of large terrain data sets in real-time. They utilize a quadtree texture hierarchy and a bintree of triangle patches (TINs) for the geometry. The triangle patches are constructed off-line with high-quality simplification and triangle stripping algorithms, and are selectively refined from scratch each frame. Textures are managed as square tiles, organized as a quadtree. The rendering system traverses the texture quadtree until acceptable error conditions are met, and then traverses the corresponding patches in the geometry bintree system until a space error tolerance is reached.. In contrast to this previous work, we seek to maximally exploit frame-to-frame coherence with view-dependent refinement, similar to the ROAM algorithm, but with chunked/patch geometry and texture tiles paging in from disk. High-quality low-pass filtering is applied to geometry tiles in addition to textures so as to minimize geometric aliasing artifacts and to reduce average geometric error. A new Sierpinski disk layout improves coherence of tile access and caching, while the 4-8 textures minimize visible seams at patch boundaries. Like ROAM, our algorithm can maintain nearconstant frame rates by optimizing to a triangle budget in addition to selecting a desired screen error tolerance.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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Single view reflectance capture using multiplexed scattering and time-of-flight imaging This paper introduces the concept of time-of-flight reflectance estimation, and demonstrates a new technique that allows a camera to rapidly acquire reflectance properties of objects from a single viewpoint, over relatively long distances and without encircling equipment. We measure material properties by indirectly illuminating an object by a laser source, and observing its reflected light indirectly using a time-of-flight camera. The configuration collectively acquires dense angular, but low spatial sampling, within a limited solid angle range -all from a single viewpoint. Our ultra-fast imaging approach captures space-time "streak images" that can separate out different bounces of light based on path length. Entanglements arise in the streak images mixing signals from multiple paths if they have the same total path length. We show how reflectances can be recovered by solving for a linear system of equations and assuming parametric material models; fitting to lower dimensional reflectance models enables us to disentangle measurements.We demonstrate proof-of-concept results of parametric reflectance models for homogeneous and discretized heterogeneous patches, both using simulation and experimental hardware. As compared to lengthy or highly calibrated BRDF acquisition techniques, we demonstrate a device that can rapidly, on the order of seconds, capture meaningful reflectance information. We expect hardware advances to improve the portability and speed of this device. Acquiring material properties of real-world materials has a long and rich history in computer graphics; existing techniques directly image the sample being measured to acquire different properties including tabulated reflectance functions, spatially varying reflectances, and parametric models (see [Weyrich et al. 2009 ] for a survey of state-of-the-art techniques.). These reflectance functions, are necessary for relighting, material editing, and rendering, as well as for matching and material identification.. In this paper, we present a new acquisition approach to reflectance measurement. Our approach is unique in two ways: we exploit ultra-fast time-of-flight (ToF) imaging to achieve rapid acquisition of materials; and we use indirect observation to acquire many samples simultaneously, and in fact, even permit around-the-corner measurement of reflectance properties. The key insight of this research is to exploit ultra-fast imaging to measure individual light transport paths, based on the distance traveled at the speed of light. This capability uniquely lets us separately measure the direct (0-bounce), 1-bounce, 2-bounce, and more, light paths; in comparison, traditional approaches use controlled laboratory settings to minimize the impact of multi-bounce light transport, or must explicitly separate direct and indirect lighting from all bounces.. We make the following contributions:. a) We present a new technique for reflectance acquisition by separating light multiplexed along different transport paths. Our approach uses indirect viewing with 3-bounce scattering coupled with time-of-flight imaging to capture reflectances. Our proof-ofconcept system demonstrates first steps towards rapid material acquisition. b) We exploit space-time images captured by a time-of-flight camera, that image different light transport paths over time. The inherent challenge is to decode material measurements in the presence of mixing over angular and spatial dimensions (we call this "entanglement"), where light arrives along multiple paths at the same point at the same time.. c) When there is no entanglement, it is possible to directly pick out the specular peak from streak images, enabling easy measurement of a material's gloss parameters. In the presence of entanglement, we show how fitting parametric models to our data successfully disentangles measurements.. d) Using time-of-flight (ToF) principles and indirect measurement, ours is the first solution to rapidly and remotely recover reflectance, even when the surface is not directly visible (around-the-corner). To the best of our knowledge this is the first approach to use light transport measurements in this manner. Our approach allows for remote reflectance capture without having to be close, or in contact, with the target material. No special instrumentation of the target material or scene is required.. There are several limitations to the current work. The acquisition is limited to a subset of the 4D space of a reflectance function expressed via lower-order parametric fits. The signal to noise ratio is not very high because the energy received after three bounces can be low. There are limits to the spatial and temporal resolution of the device, thus limiting the size of patches and the maximum sharpness of the reflectance function. For simplicity, we have assumed that the source and receiver surfaces (left and right walls) have a known diffuse reflectance; though this is not a fundamental limitation. Currently we use only a single wavelength laser, due to cost reasons, but getting lasers with different wavelength would permit spectral measurements.. Acquiring material properties enables a range of applications including image relighting, material editing, and material classification. We expect that improvements in laser technologies and timeresolved imaging will improve the stability, efficiency, and portability of this approach. We believe this design could in the future enable rapid, "in-the-wild" measurement of real-world scenes, without instrumentation. Nicodemus et al. [1977] introduced the Bidirectional Reflectance Distribution Function (BRDF), which characterizes light reflection from surfaces. BRDF acquisition has received much attention with efforts to acquire isotropic and anisotropic BRDFs, and spatially varying BRDFs and BTFs (bidirectional texture functions) [Ward 1992; Marschner et al. 1999; Dana et al. 1999; Lensch et al. 2001; Lensch et al. 2003; Matusik et al. 2003; Ngan et al. 2005; Lawrence et al. 2006; Ghosh et al. 2009; Ghosh et al. 2010a; Dong et al. 2010; Wang et al. 2009 ]. These acquisition processes are often lengthy, requiring extensive laboratory settings with calibration, and hours or even days of acquisition. Weyrich et al. [2009] present a detailed survey of the state of the art, and introduce a taxonomy of six major designs for material acquisition. In this work, we have demonstrated a high speed photography device to acquire segmented scene reflectances using indirect reflections. We have identified the underlying constraints in using timeof-flight capture, including entanglement of light paths with the same path length. We demonstrate disentanglement for several patches, on the order of tens, by fitting to low dimensional parametric models.. While fast and smaller solid state lasers are coming, merging them with fast imaging devices is a clear logical step. We believe that this approach acquisition has potential to enable fast, portable, and remote BRDF capture devices. Without the need to instrument a scene, our work may spur applications like real-world material classification, real-time material editing, and relighting. Our approach can also be used when capturing complete BRDFs is not the ultimate goal but sampling a part of it for material detection and classification can suffice. In addition, around the corner recovery of material properties can enable radical applications, e.g., recovering malignant growth in endoscopy beyond the reach of a camera. Our approach also fits in the general spririt of computational photography to allow one to capture meaningful properties from a single camera viewpoint and then allow powerful post-capture operations, in this case to relight or edit materials. Our single-view point approach exploits the temporal dimension, but it introduces traditional problems of time-of-flight cameras in space-time resolution, signal to noise ratio and dynamic range.. Limited angular sampling: In a closed room, one can theoretically sample all the pairs of incoming and outgoing directions from an object point. In practice, we can sample only a subset of all half angles as the coverage is dependent on the field of view of the camera. Despite these limited angles, a 3-parameter BRDF model can be estimated. We also rely on the friendly reflectances of the sources and receivers, though this is not a fundamental limitation.. Space-time resolution: Our at-a-distance capture mechanism means that we cannot resolve small features with varying BRDF or surface normals. So our approach is suitable for coarsely segmented reflectance patches. Surfaces with rich surface details can be acquired accurately to the limit of the spatio-temporal resolution of the ToF device.. Time resolution limits our ability to perform linear inversion. Currently our camera only captures one spatial dimension, however, we can scan the laser in two dimensions over the scene to increase the sampling range of angles, and further sweep the camera.. Color: Since the laser operates at a single wavelength our images are monochrome and taken in the near infrared. Colored images could be taken with a white light supercontinuum source, a set of 3 lasers at different colors, or a tunable optical parametric oscillator.. Signal to noise ratio and capture time: The theoretical signal to noise ratio (SNR) of the combined streak camera system is about 1000:1. A common way to improve the SNR by several orders of magnitude is to bundle the same laser power into fewer pulses at a lower repetition rate but with the same pulse length.. Our acquisition time of 10-15 seconds per streak camera image is a result of our current hardware, which averages over a large number of frames to improve SNR. A commercially available laser with pulse energy of about 1 mJ could reduce the acquisition time to nanoseconds, while offering better SNR as well.. Dynamic range: Capturing specular peaks and weak diffuse reflections in a single photo is limited due to the camera dynamic range. We partially overcome this by using two different exposure photos.. Acquisition in the presence of ambient light: The time-of-flight cameras are well suited for "in-the-wild" acquisition in the presence of ambient light. Most ambient light is never detected by the sensor because of the short capture window. Even highly sensitive photon counting systems use these techniques to operate in daylight and over hundreds of thousands of kilometers; for example, laser links from Earth to the Moon and Mars, and commercial airborne LIDAR systems [Degnan 2002; Warburton et al. 2007] .. Portability: While ultra-fast lasers have not yet reached a state of maturity to make them portable, this approach shows promise in creating portable and compact devices in the future. Our system can be extended for usage in unstructured environments with arbitrary geometry and lighting. Moreover, our algorithm in itself is not limited to a particular geometric configuration.. Laser speckle: Imaging devices using coherent light often suffer from laser specle noise. The laser coherence is, however, not maintained in multiple diffuse bounces. When the laser light returns to the camera after two or three bounces, it is no longer coherent and laser speckle is not observed.. Our work uniquely combines cutting edge research in ultra-fast optics with emerging topics in computer graphics. Our computational approach has been validated, but our physical prototype is a modification of electro-optic hardware which is expensive, currently nonportable, and may take years to become practical. But there are no specific fundamental challenges to improve these systems. We now present the results of our time-of-flight reflectance measurement system. We first evaluate our results using a simulation of the device, to focus on demonstrating its capabilities with a good hardware implementation, and to validate against ground truth values. Finally we demonstrate acquisition using our hardware setup.. We simulate two scenarios using this setup: single patch and multiple patch. We choose nine materials from the database by Ngan et al [2005] to represent a wide variety of reflectances. We simulate the three different channels separately using the corresponding parameters. The first scenario contains a single unit-area (1cm. 2 ) patch placed on P. The second scenario simulates a twodimensional grid of nine patches arranged in a 3 × 3 configuration. Capturing BRDFs requires measuring a large number of lightingviewing combinations for the material. To decrease acquisition costs, many techniques focus on matching to parametric models (e.g., [Sato et al. 1997; Yu et al. 1999; Lensch et al. 2001; McAllister 2002; Gardner et al. 2003; Lensch et al. 2003; Goldman et al. 2010] ). Various approaches decrease acquisition costs and increase coverage by exploiting properties of BRDFs including reciprocity, separability, spatial smoothness, and compressibility [Zickler et al. 2005; Sen et al. 2005; Garg et al. 2006; Wang et al. 2008; Dong et al. 2010] . Lighting configurations and variations have been considered including polarization and structured illumination [Wenger et al. 2005; Sen et al. 2005; Ma et al. 2007; Ghosh et al. 2010b ].. Most BRDF techniques directly, or indirectly through a mirror surface [Weyrich et al. 2009 ], view and image the material sample with some notable exceptions [Han and Perlin 2003; Hawkins et al. 2005; Kuthirummal and Nayar 2006] . Hawkins et al. [2005] developed the dual light stage, and imaged a diffuse environment to increase angular measurements.. There has been a long line of research in computer vision in modeling interreflections to accurately model shape and reflectance [Forsyth and Zisserman 1990; Nayar et al. 1991] . Recently there has been interest in recovering scene properties such as geometry and albedo from multiple bounces of light Seitz et al. 2005; Sen et al. 2005; Kirmani et al. 2009; Liu et al. 2010; Bai et al. 2010] , and also on recovering shape and material simultaneously [Holroyd et al. 2008] .. In contrast to prior techniques we do not directly image the surface sample, but rather, indirectly image a diffuse surface and use timeof-flight principles to detect and measure all the bounces of light arriving at the diffuse surface, after interacting with the samples we want to measure. This approach enables rapid (on the order of seconds) acquisition of reflectances of multiple patches (tens of materials) simultaneously, over a range of angular measurements. Modifying existing time-of-flight (ToF) cameras to report a full time profile with sufficient SNR for our purpose is quite challenging. Our emphasis in this paper is on the computational and al- Figure 6 : The time-of-flight camera setup involves a laser projector via a Ti:Sapphire laser with steering mirrors and a pico-second accurate camera. This setup corresponds to Figure 2-(b) . Reflectance of the "object" is recovered by aiming the camera and the laser projector at the diffuse wall.. gorithmic aspects. Following experimental setup was used for our proof-of-concept implementation.. Our light source is a mode-locked 795 nm Ti:Sapphire laser. The camera is a Hamamatsu C5680 streak camera that captures a series of 512 one-dimensional images, i.e., lines of 672 pixels in the scene, with a time resolution of about 2 picoseconds. Figure 6 shows our setup in the configuration corresponding to Figure 2 -(b).

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O