A comparison of loop closing techniques in monocular SLAM Loop closure detection systems for monocular SLAM come in three broad categories: (i) map-to-map, (ii) image-to-image and (iii) image-to-map. In this paper, we have chosen an implementation of each and performed experiments allowing the three approaches to be compared. The sequences used include both indoor and outdoor environments and single and multiple loop trajectories. Loop closure detection is an important problem for any SLAM system and, since cameras have become a common sensor in robotics applications, more people are turning towards vision based methods to achieve it. In this paper, we compare three quite different approaches to loop closure detection for a monocular SLAM system. The approaches essentially differ in where the data association for detecting the loop closure is done -in the metric map space or in the image space. The three approaches are as follows:. • Map-to-map -Correspondences are sought between features in two submaps taking into account both their appearance and their relative positions. In this paper we look at the method of Clemente et al. [1] , who applied the variable scale geometric compatibility branch and bound (GCBB) algorithm to loop closing in monocular SLAM. The method looks for the largest compatible set of features common to both maps, taking into account both the appearance of the features and their relative geometric location.. • Image-to-image -Correspondences are sought between the latest image from the camera and the previously seen images. Here, we discuss the method of Cummins et al. [2, 4] . Their method uses the occurrences of image features from a standard vocabulary to detect that two images are of the same part of the world. Careful consideration is given to the distinctiveness of the features -identical but indistinctive observations receive a low probability of having come from the same place. This is done to minimise false loop closures. B when the feature is initialised, but is warped to correspond with the current camera pose estimate. To speed up the observation of features, the image is only searched in an ellipse given by the uncertainty in the camera and feature estimate in a process called active search. By gating the search in this way the chances of incorrect data association are reduced. This is further helped by the use of the joint compatibility branch and bound algorithm (JCBB) [9] which detects observations which are incompatible with the others and rejects them. Despite the improvement given by active search and JCBB, there is still a chance of incorrect data association, particularly near loop closures when the system can believe that distant features are again visible and attempt to measure them. If the system is allowed to observe these features as usual, it will likely make incorrect data association due to the large uncertainty in the camera pose relative to these features. Our approach is to prevent the system from making these observations and delay the loop closure until a separate loop close module has detected it (Section 3). To determine which observations to attempt, we make use of the covisibility data from all the features in the map. We have tested three quite different approaches to detecting loop closure for monocular SLAM systems. Experiments were performed in both indoor and outdoor environments using the Hierarchcal SLAM technique to build a sequence of submaps (Table 1) .. We found the map-to-map matching technique to be unsuitable for monocular SLAM because the sparse maps contain too little information to reliably detect true correspondences while ruling out false ones.. The image-to-image method was shown to work well. However, to use this method for correcting a metric map, the relative pose and scale between corresponding images would need to be determined. The method would benefit from making some use of the relative positions of the detected visual words to remove some obvious false positives.. The image-to-map method works well and returned the highest number of true positives with no false positives. This is achieved by taking as much information as possible into account when detecting the loop closures. Unfortunately, this method does not scale well to larger environments like the image-to-image method. The results of our quantitative testing of the three methods using the second lap of the Pembroke College sequence are shown in Fig. 10 . The salient points that should be taken from this are:. • To create the curve for the image-to-map method, we varied the threshold on the fraction of successful landmark observations after a potential relocalisation. All other parameters were left at their default values. In practice, we require 50% of observations to succeed giving the 20% recall at 100% precision quoted in this paper.. • The curve for the image-to-image method is more complete since a single threshold (the match probability) can be varied to achieve a larger range of recall. The performance is similar to the image-to-map method with only a few extra false positives detected with high probability.. • The curve for the map-to-map method has fewer points. The threshold varied here is the number of landmarks in the compatible set. The twelve submaps built in the second lap were matched to the twelve from the first lap. In this run, a single true positive was found with a seven common features. For all lower thresholds many false positives were also found leading to a steep drop in precision.. We would not want the reader to infer too much from these numerical results. The actual numbers found would depend on the precise sequence used and the characteristics of the environment, but the general trends in the graph are representative of our overall findings. Of most importance are the relative performance, benefits, and failure modes of each algorithm. These aspects are now discussed more qualitatively.. We found the map-to-map matching technique of Clemente et al. is successful when a sufficient number of common features exists between two submaps. For instance, it reliably detect the overlap between consecutive submaps where common features are intentionally added to determine the relative scale. However, in general it is unsuitable for the sparse maps created by the monocular SLAM system. These maps are designed to be good enough to track the camera but otherwise as sparse as possible to allow faster updates. Perhaps a map-to-map based method would be more suitable if the maps contained higher level information or there were more consistency on which potential features are added to the map.. The image-to-image matching technique of Cummins et al. works well since it can be tuned to remove all false positive while still detecting 8% of true positives for the Pembroke College sequence. As the probability threshold is lowered, the first few false positives could easily be removed with a simple essential (a) Image-to-image matching: Loop closure detected using the method of Cummins et al. [2] in the Pembroke College sequence. The system detects visual words in each image and the co-occurrence of these words is used to calculate the probability of loop closure. The system finds a high probability that the most recent image matches one seen earlier in the sequence. Visual words detected in the two images are indicated in light (green) if they match in the other image and dark (red) if they do not. Note that interest point geometry is not considered.. (b) Image-to-image reliability: A second lap of the Pembroke College sequence was used to test the reliability of the image-to-image method. Correspondences were found between every frame in a second lap and every 40th frame in the first lap. With a threshold chosen to remove all false positives the system was successful in 8% of attempts. Gaps are in regions of the world with lots of foliage (where the image-to-map method also struggles). matrix test for geometric compatibility. This can be seen for the false match with highest probability in Fig. 11(b) . With this test, the performance of the image-to-image method would be equivalent to the image-to-map method. The fact that the image-to-image method does not rely on a good metric map existing can also be an advantage. This makes the system more flexible and allows it to work in a greater variety of applications. Finally, the method scales well to very large environments and has been shown to work on datasets of several kilometers [18] .. The best performance here was found using the image-to-map matching technique of Williams et al. with a true positive rate of 20% for the Pembroke College sequence. The image-to-map method is able to prune more false positives than the image-toimage method by making use of the geometry information of the features detected in the image since these features have already been mapped by the SLAM system. It is fast enough to detect loop closure while tracking but it requires a large amount of memory for the randomised fern classifier (1.25 MB per map feature). Offline learning of good vocabulary required.. Does not require metric map. Does not make use of geometric information. Scales well to large environments.. Does not give metric transformation directly.. Image-to-Map Detects true loop closures throughout the environment when tuned for 100% precision.. Requires good metric map.. Online training for map feature appearance. Very memory intensive. Relative transformation between submaps with scale is computed from trajectory.. (a) Image-to-map matching: Loop closure detected using the method of Williams et al. [3] . While tracking in the last submap, the system finds a camera pose consistent with the features in the first submap. The common trajectory is used to determine the relative rotation translation and scale needed to align the submaps. This limits its use to environments not much larger than those considered here. It is this classifier though that the system relies on for fast training and recognition of the map features in each image.. Perhaps even better performance could be achieved through a hybrid system combining the benefits of the image-to-image and the image-to-map methods. The loop closure detection system developed by Eade and Drummond [19] does just this. They first use a bag of visual words approach to establish which submap is in view. This stage is similar to the image-to-image method tested in this paper. Then, local landmarks are identified in the image and the camera pose relative to the landmarks is determined in a similar way to the image-to-map method. This global to local approach harnesses the strengths of each method. The loop closure detection techniques were tested on three different image sequences. One of these sequences was then chosen for more extensive quantitative testing of each algorithm using a second lap of the same loop. First we will discuss the general performance of the algorithms in the three sequences before presenting the quantitative results with more discussion on the process of detecting loop closure with each algorithm.

O O O B I O O B I 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 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 B I 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 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 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 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


Asymptotic synchronization of the Colpitts oscillator In this paper we deal with the observer-based asymptotic synchronization problem for a class of chaotic oscillators. Some results based on a differential algebraic approach are used in order to determine the algebraic observability of unknown variables. The strategy consists of proposing a slave system (observer) which tends to follow asymptotically the master system. The methodology is tested in the real-time asymptotic synchronization of the Colpitts oscillator by means of a proportional reduced order observer (PROO) of freemodel type. In this paper we study the asymptotic synchronization problem in chaotic systems based on the observer theory. We also show the real-time synchronization in the Colpitts oscillator by using a reduced order observer of free-model type, which has asymptotic convergence. Some experimental results show the effectiveness of the proposed methodology.

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Multiply Balanced Edge Colorings of Multigraphs In this paper, a theorem is proved that generalizes several existing amalgamation results in various ways. The main aim is to disentangle a given edge-colored amalgamated graph so that the result is a graph in which the edges are shared out among the vertices in ways that are fair with respect to several notions of balance (such as between pairs of vertices, degrees of vertices in the both graph and in each color class, etc). The connectivity of color classes is also addressed. Most results in the literature on amalgamations focus on the disentangling of amalgamated complete graphs and complete multipartite graphs. Many such results follow as immediate corollaries to the main result in this paper, which addresses amalgamations of graphs in general, allowing for example the final graph to have multiple edges. A new corollary of the main theorem is the settling of the existence of Hamilton decompositions of the family of graphs K(a 1 , . . . , a p ; λ 1 , λ 2 ); such graphs arose naturally in statistical settings. Throughout this paper, all graphs are finite and undirected (possibly with loops and multiple edges). The letters G and H denote graphs. Sets may contain repeated elements (so are really multisets). Each edge is represented by a 2-element multisubset of the vertex set; in particular {u, u} represents a loop on the vertex u. A k-edge-coloring of G is a mapping K : E(G) → C, where C is a set of k colors (often we use C = {1, . . . , k}), and the edges of one color form a color class.. Informally speaking, amalgamating a finite graph G can be thought of as taking G, partitioning its vertices, then for each element of the partition squashing the vertices to form a single vertex in the amalgamated graph H. Any edge incident with an original vertex in G is then incident with the corresponding new vertex in H, and any edge joining two vertices that are squashed together in G becomes a loop on the new vertex in H.. More precisely, H is an amalgamation of G if there exists a function φ called an amalgamation function from V (G) onto V (H) and a bijection φ : E(G) → E(H) such that e joining u and v is in E(G) if and only if φ (e) joining φ(u) and φ(v) is in E(H); We write φ(G) = H. In particular, this requires that e be a loop in H if and only if, in G, it either is a loop or joins distinct vertices u, v, such that φ(u) = φ(v). (Note that φ is completely determined by φ.) Associated with φ is the number function η : V (H) → N defined by η(v) = |φ −1 (v)|, for each v ∈ V (H). We also shall say that G is a detachment of H in which each vertex v of H splits (with respect to φ) into the vertices in φ −1 ({v}). A detachment of H is, intuitively speaking, a graph obtained from H by splitting some or all of its vertices into more than one vertex. If η is a function from V (H) into N, then an η-detachment of H is a detachment of H in which each vertex u of H splits into η(u) vertices. In other words, G is an η-detachment of H if there exists an amalgamation function φ of G of Nash-Williams [27, 28] .. The main theorem of this paper, Theorem 3.1, not only generalizes several well-known graph amalgamation results, (for example, in [14, 16, 20, 22, 30] ,Theorem 1, Theorem 1, Theorem 3.1, Theorem 2.1 and Theorem 2.1 respectively all follow as immediate corollaries)), but also provides the right tool to find necessary and sufficient conditions for K(a 1 , . . . , a p ; λ 1 , λ 2 ) to be Hamiltonian decomposable, as shown in Theorem 4.3. The latter graph, K(a 1 , . . . , a p ; λ 1 , λ 2 ), is of particular interest to statisticians, who consider group divisible designs with two associate classes, beginning over 50 years ago with the work of Bose and Shimamoto [3] . Recently, partitions of the edges of K(a 1 , . . . , a p ; λ 1 , λ 2 ) into sets, each of which induces a cycle of length m, have been extensively studied for small values of m [10, 11, 12] . Theorem 4.3 provides a companion to this work, settling the problem completely for longest (i.e. Hamiltonian) cycles with a really neat proof. When a 1 = . . . = a p = a, we denote K(a 1 , . . . , a p ; λ 1 , λ 2 ) by K(a (p) ; λ 1 , λ 2 ). It is expected that Theorem 3.1 can be used to provide conditions under which one can embed an edge-colored K(a (p) ; λ 1 , λ 2 ) into an edge-colored K(a (p+r) ; λ 1 , λ 2 ) such that every color class of K(a (p+r) ; λ 1 , λ 2 ) induces a Hamiltonian cycle. However obtaining such results will be much more complicated than for companion results for simple graphs, with a complete solution unlikely to be found in the near future.. We describe terminology and notation in Section 2. Then we prove the main result in Section 3. In Section 4, we give necessary and sufficient conditions for the graph K(a 1 , . . . , a p ; λ 1 , λ 2 ) to be Hamiltonian decomposable as a corollary of the main theorem.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O 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 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 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


Quasi-static assignment of voltages and optional cycles for maximizing rewards in real-time systems with energy c-onstraints There exist real-time systems for which it is possible to trade off precision for timeliness. In these cases, a function assigns reward to the application depending on the amount of computation allotted to it. At the same time, many such applications run on battery-powered devices with stringent energy constraints. This paper addresses the problem of maximizing rewards subject to time and energy constraints. We propose a quasi-static approach where the problem is solved in two steps: first, at design-time, a number of solutions are computed and stored (off-line phase); second, one of the precomputed solutions is selected at run-time based on actual values of time and energy (on-line phase). Thus our approach is able to exploit, with low on-line overhead, the dynamic slack caused by tasks executing less number of cycles than in the worst case. We conduct numerous experiments in order to show the advantages of our approach. The trade-off between energy consumption and performance has extensively been studied under the framework of Dynamic Voltage Scaling (DVS) [8] , [5] .. There exist real-time applications, such as image processing and multimedia, in which approximate but timely results are acceptable. Fuzzy images in time are often preferable to perfect images too late. Thus it is possible to trade off precision for timeliness. Such systems have been studied under the Imprecise Computation (IC) model [4] , where tasks are composed of mandatory and optional parts: both parts must be finished by the deadline but the optional part can be left incomplete at the expense of the quality of results. A function associated with each task assigns reward as a function of the amount of computation allotted to it: the more the optional part executes, the more reward it produces.. While DVS techniques have mostly been studied in the context of hard real-time systems, IC approaches have until now disregarded the power/energy aspects. Rusu et al. [9] proposed recently the first approach in which energy, reward, and deadlines are considered under a unified framework. Their goal is to maximize the total reward without exceeding deadlines or the available energy. This approach solves the optimization problem statically, at compile-time, and therefore considers only worst cases. Such an approach can only exploit the static slack, which is due to the fact that at nominal voltage the processor runs faster than needed.. Dynamic approaches have been used for hard real-time systems in order to exploit the dynamic slack, which is caused by tasks executing less cycles than in the worst case. In this paper we consider tasks composed of mandatory and optional parts and we aim at finding a Voltage/Optional-cycles (V/O) assignment (actually a set of assignments as explained later), such that the total reward is maximal while guaranteeing the deadlines and the energy budget. We exploit the dynamic time and energy slack caused by variations in the actual number of execution cycles. Furthermore, we consider the time and energy overhead incurred during voltage transitions.. Static V/O assignment refers to finding at design-time one assignment of voltages and optional cycles that makes the reward maximal while guaranteeing the time and the energy constraints (this is the problem addressed by [9] ). Dynamic V/O assignment refers to finding at run-time, every time a task completes, a new V/O assignment for tasks not yet started, but considering the actual execution times and energy values. Static V/O assignment causes no on-line overhead, but it is pessimistic because actual execution times are typically far off from worst-case values. Dynamic V/O assignment exploits information known only after tasks complete and accordingly computes new assignments aiming at improving the reward, but the energy and time overhead for on-line computations is high, even if polynomial-time algorithms can be used. We propose a Quasi-Static (QS) approach that is able to exploit, with low on-line overhead, the dynamic slack: first, at design-time, a set of V/O assignments are computed and stored (off-line phase); second, the selection among the precomputed assignments is left for run-time, based on actual completion times and consumed energy (on-line phase).. QS scheduling for maximizing utility in hard/soft real-time systems was recently discussed [1] , but without any energy consideration. To our knowledge, this is the first work that considers reward, energy, and deadlines in a QS framework. We addressed the problem of maximizing rewards for realtime systems with energy constraints, in the frame of the Imprecise Computation model. We proposed a quasi-static approach, whose chief merit is the ability to exploit the dynamic slack at very low on-line overhead. This is possible because, in our QS approach, a set of solutions are prepared and stored at design-time, leaving for run-time only the selection of one of them.. We considered that the voltage can continuously be varied. If only discrete voltages are supported, the approach can easily be adapted by using well-known techniques for obtaining the voltage levels that replace the calculated ideal one [8] .. We evaluated our approach through numerous synthetic benchmarks and a realistic application. We found that significant gains in terms of reward can be obtained by the QS approach. We showed also that, due to its large on-line overheads, a dynamic approach performs poorly. Thus, the dynamic slack can efficiently be exploited only if high overheads are avoided, as done by our QS approach.

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 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 B I 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 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 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


Global delay optimization using structural choices This paper presents a fast global method for delay optimization after technology mapping. Timing analysis is used to identify timing-critical areas in the mapped network where new structures are synthesized to favor late-arriving signals. Unlike previous methods that make incremental local changes to the mapped network, the proposed method records many alternative structures and defers the final decision to the technology mapper. Experimental results for networks mapped into 6-input look-up tables (6-LUTs) show that the delay is, on average, improved 14% using a realistic delay library for LUTs with variable-pin delays and wire-delay estimation. The area penalty after the delay optimization is about 2% and can be eliminated by area-oriented resynthesis. When the algorithm is compared with DAOmap, the experimental results show 27% logic level reduction while the area is increased by only 1%. The algorithm is also fast and applicable to very large networks. The runtime of the proposed algorithm is 16x and 3x faster than DAOmap for large industrial and academic designs, respectively. Technology mapping converts a logic network, called the subject graph, into a network of logic nodes, which correspond to primitives in a particular technology. For example, technology mapping for FPGAs [4] [6] [7] transforms the network into K-input lookup tables (K-LUTs) that can implement any Boolean function of K or less variables. The subject graph is often an And-Inverter Graph (AIG), composed of two-input ANDs and inverters.. Logic restructuring with the goal of reducing delay of a mapped network has long been an important part of both technology independent [17] [2] [12] [16] and technology dependent synthesis [10] [13] [9] [5] . However, existing methods for delay-oriented logic restructuring have the following drawbacks:. • Numerous local changes to the network may be applied, but with no guarantee that the delay is globally improved or that area has been effectively spent for delay improvements.. • Algorithms of high computational complexity are often used, leading to excessive runtime. Much effort is spent on deciding where to make the changes.. • Structural flexibilities that may be available during mapping are typically not used during post-mapping resynthesis. The proposed method mitigates these limitations. Unlike the previous methods, it does not perform a sequence of local changes, each one updating the mapped network and then running incremental timing analysis after each change. It need not analyze cuts of a set of critical paths nor distribute slacks on off-critical paths. Instead, it computes timing information only once. This is analyzed and a set of new candidate structures, a subset of which may lead to reducing delay after the next iteration of mapping, are recorded in the subject graph using choice nodes [10] [3] .. Decisions about which subset of structures to use are deferred to the technology mapper. The motivation is that the mapper has a global picture of both delay and area, as well as a good view of structural flexibilities presented during mapping, and thus can better decide what structures to use.. The new logic structures are created by cofactoring logic cones, in timing critical regions, with respect to timing-critical variables. The cofactors are combined using multiplexers controlled by the critical variables and then decomposed and simplified as an AIG, resulting in a logic structure that favors the late-arriving variables. A similar method was discussed in [2] and called the generalized select transform (GST) [12] [16] . This was used recently for timing optimization of sequential circuits [18] . The proposed algorithm can be extended to work for the sequential case as well.. The rest of this paper is organized as follows. Section 2 describes the background. Section 3 describes the algorithm. Section 4 reports experimental results. Section 5 concludes the paper and outlines future work. This paper proposes a simple and efficient algorithm for improving delay after technology mapping. The algorithm creates alternative structures for speeding up a circuit. The location of these structures is not as critical as in classical methods because their possible use is postponed until the next round of mapping. By iterating the speedup and technology mapping several times, subsequent delay improvements can be obtained. The algorithm is efficient because only one delay analysis is done during each speedup synthesis phase, while other methods iterate delay analysis during each new structure found.. Future work should include: (a) quantifying the improvements in delay after place-and-route, (b) extending the algorithm to work for sequential circuits as suggested in [18] , (c) applying similar optimizations for cost functions other than delay. Also, the algorithm should be equally applicable to mapping for standard cells as well as FPGAs, and this should be developed. A Boolean network is a directed acyclic graph (DAG) with nodes corresponding to logic gates and directed edges corresponding to wires connecting the gates. The terms Boolean network, netlist, and circuit are used interchangeably in this paper. If the network is sequential, the memory elements are assumed to be D-flip-flops with initial states.. A node n has zero or more fanins, i.e. nodes that are driving n, and zero or more fanouts, i.e. nodes driven by n. The primary inputs (PIs) are nodes without fanins in the current network. The primary outputs (POs) are a subset of nodes of the network. A fanin (fanout) cone of node n is a subset of all nodes of the network, reachable through the fanin (fanout) edges of the node.. A node is a logic component having a propagation delay. An edge, also called wire, is the pin-to-pin connection between two adjacent nodes. The delay of a path includes logic delays and wire delays. The logic delay occurs in a logic component, such as a LUT. The wire delay occurs on the edges. In modern FPGAs, the delay for each pin in a LUT is different, so a variable-pin-delay Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. model is used in this paper. Wire delays are usually not known until placement and routing. To approximate wire delays, a fixed delay is added to the delay of all pins of the LUTs in the library. A self-explanatory pseudo-code is given in Figure 3 .1. The algorithm takes the mapped netlist and the subject graph used for mapping. The netlist is analyzed to detect timing-critical areas for logic restructuring while the subject graph is used to accumulate the alternative logic structures for the next round of mapping. Several parameters are used in the computation: the timing window (w) determines the range of slacks of the near-timingcritical nodes to be restructured; the logic depth (l) of cones selected for delay-oriented restructuring; and the limit (p) on the number of timing-critical edges of the cone to consider. mapped netlist performSpeedup ( subject graph S, // S is an And-Inverter Graph mapped netlist M, // M was previously derived by tech-mapping of S timing window w, // w is used to detect the critical path logic depth l, // l is used to detect a logic cone rooted at a node edge count p // p limits the number critical edges of the cone { perform timing analysis of M with unit-delay or LUT-library model; detect the critical section of M as nodes n such that 0 ≤ slack(n) ≤ w; detect timing-critical edges connecting these nodes; for each timing critical node n { find cone C of M that extends l levels down from n; detect the set of timing-critical edges V feeding into C; if the number of edges in V exceeds p continue; find logic cone C' in S corresponding to C in M; find variables V' in S corresponding to V in M; derive cofactors of the function of C' w.r.t. variables in V'; build multiplexer tree C'' of the cofactors using variables in V'; add structural choice C'= C'' to the subject graph S; } derive netlist M' by mapping subject graph S with added choices; return M'; } The following subsections provide the details on timing analysis and identification of timing-critical edges (Section 3.1), logic restructuring for delay (Section 3.2), and using structural choices in technology mapping (Section 3.3).

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Statistical Multi-Object Shape Models Abstract. The shape of a population of geometric entities is characterized by both the common geometry of the population and the variability among instances. In the deformable model approach, it is described by a probabilistic model on the deformations that transform a common template into various instances. To capture shape features at various scale levels, we have been developing an object-based multi-scale framework, in which a geometric entity is represented by a series of deformations with different locations and degrees of locality. Each deformation describes a residue from the information provided by previous steps. In this paper, we present how to build statistical shape models of multi-object complexes with such properties based on medial representations and explain how this may lead to more effective shape descriptions as well as more efficient statistical training procedures. We illustrate these ideas with a statistical shape model for a pair of pubic bones and show some preliminary results on using it as a prior in medical image segmentation. In many shape analysis areas, including deformable models (Grenander, 1995; Kass et al., 1987) , it is desirable to consider shape as a property of a population of geometric entities, such as object sections (e.g., the left lobe of livers), objects (e.g., livers), or groups of objects (e.g., liver-kidney complexes). As such, it describes both the common geometric features and the geometric variability among instances of the population. With the deformable model approach, a representative instance S 0 , usually referred to as the model or template, is chosen for a given shape, say S. The geometry of S 0 is essentially specified by transformations on certain canonical geometric primitives, for instance, the positions of boundary/surface points or positions and boundary normal directions of medial structures. The overall transformation is a "summary" of the shape geometry and captures the typical geometric conformation of S at various levels of detail, including the geometry of objects, parts, sections, and their relative configurations. Any instance of S, say S, is then defined via a further geometric deformation F applied to S 0 , i.e. S = F(S 0 ). The map. establishes a correspondence between the space of all such geometric transformations, F, and the set of all geometric entities, G. We can regard an instance of the shape S as a random sample from an underlying probability measure ν on G. Intuitively, ν puts soft constraints on "what an instance of the shape S should look like". Because of the correspondence ψ, the geometric variability among shape instances, which is captured by ν, can be effectively described via variability in geometric transformations applied to the template. One way to define ν, then, is to introduce a probability measure μ on F and to let ν be the probability measure induced by the mapping ψ. This is the approach we will adopt in this paper. The measure μ can be effectively used as shape priors to make statistical inferences on what one observes (Grenander et al., 1991; Zhu, 1999; Pizer et al., 2003a; Gerig et al., 2001) . Existing geometric representations include representation by dense sample points, landmarks, diffeomorphisms on displacement velocity fields (Joshi, 1997) , distance functions or their level sets , skeletons (Siddiqi et al., 2002) , shocks (Kimia et al., 1995) , multigrid and scale-space based methods (Lu et al., 2002) , etc. To develop statistical models, the geometric representation also needs a notion of correspondence among different shape instances. For example, if we use boundary points to describe the contour of a hand, then the thumbs in different hands should be described by the same set of points. Without such a correspondence the statistical model would not be robust. Examples of statistical shape models are deformable templates (Grenander et al., 1991) , point distribution models (Cootes et al., 1998 (Cootes et al., , 1995 , spherical harmonic descriptors (Kelemen et al., 1999) for 3D objects, to name a few. Most of these methods do not respect object-based scale levels, so they lack the ability to explicitly describe important geometric information such as locality, inter-object relations, etc. The statistical models typically face the high-dimensionlow-sample-size (HDLSS) problem: on the one hand, the number of parameters needed to accurately describe the geometry is usually very large; on the other hand, the available training samples are often limited, as is the case in many medical imaging applications.. Many working with geometric probabilities in medical image analysis have dealt with multi-object shape statistics by concatenating the descriptors for all the objects and doing global statistics on the resulting tuple. Examples are Cootes et al. (1999) and . These do not have the locality of the object or smaller. A few investigators have produced statistics that are hierarchical by scale and include a scale describing the individual objects making up the complex but not having the smaller scale descriptions be residues from other scales (Vaillant and Davatizikos, 1999; Kapur et al., 1998) , but Davatzikos et al. (2003) has taken this approach using residues. However, objects change not only on their own but due to their neighbors, and yet when describing an object statistically, few have attempted to describe the inter-relationships between objects statistically. have attempted to describe inter-relationships. They represent these via the distance function to objects' boundaries, to which, they agree, linear statistical methods are not well-suited. Moreover, they have not described inter-relationships in a hierarchical fashion, or they have used hierarchy but no statistical inter-relationships . The approach we attempt is simultaneously hierarchical by scale using inter-scale residues and describes objects not only by themselves but also in terms of their inter-relationships with other objects.. In order to efficiently characterize a population of geometric entities, it is important to realize that geometric deformations have various localities and we believe they should be incorporated in shape description (Yushkevich et al., 2001 ). In our study of geometric entities such as objects and boundaries, locality is relative to object scale level and must be taken with respect to the components of which an entity is formed. For example, at the object complex level, a global deformation is one that applies to all objects in it, while a local deformation applies only to some of the objects (but as a whole); at the individual object level, being a local deformation means it applies only to certain natural sections making up the object. The geometric features described by the deformations at each object scale level thus have certain sizes and distances that are relevant to that level. The differences in description between scale levels reflect different levels of detail. Moreover, the relevant distance within a scale level induces a notion of neighbors, i.e., nearby geometric entities at that scale: nearby objects, nearby object sections, etc. This neighbor relation, together with the spatial extent of features and levels of detail in description, realize the notion of locality and form the basis of our representation. In the context of describing a population of entities, locality reflects the spatial correlation between various geometric components of different scales among the population.. This notion of locality suggests we use object-based scale levels and describe residues within and between scales similar to the wavelet approaches (Mallat, 1989; Unser, 1996) . We argue that it is more advantageous not to describe a geometric entity S by a single transformation F, bur rather represent it in a coarse to fine manner by decomposing F into a series of, say K , deformations, i.e., (Pizer et al., 2005) . In this way geometric features at various object scale levels can be explicitly described by the corresponding transformations at that level.. is the representation of S at step k, and the deformation F k describes a residual transformation relative to S k−1 , measured in terms of both across-scale and within-scale primitive relationships. In other words, the smaller scale features are described as residues of larger scale features. At any particular object scale level, we will assume that each residual feature tends to be more correlated with those that are close by, compared to those that are further away. Any strong correlation between entities that are not close to each other is a global feature and is supposed to have already been accounted for by the deformation at the (previous) larger scale level. This is an important assumption that we make in developing statistical shape models, an assumption based on measurements we have made in certain sample populations. Consider, for example, the shape of a pair of pubic bones (see Fig. 1(b) ). In this case F 1 may be a single global level deformation that is applied to the both bones simultaneously, F 2 may represent a further deformation of the left bone, F 3 may represent a collection of even further local deformations of the left bone, each applied to a very small part of it, and so on.. In addition to providing more intuitive and accurate geometric descriptions, the above multi-step approach also has the potential of leading to more efficient probabilistic models. We believe that by taking advantage of locality one can effectively characterize each deformation by a much smaller number of parameters. Because the process of estimating these parameters suffers a lot less from the HDLSS problem, it might be possible to obtain more reliable and stable estimations of statistical shape models from limited training samples.. A valid statistical shape model needs to have certain generative and predictive power. It should be able to capture most of the variations in a object population and produce instances that are similar to training samples and are geometrically proper (Pizer et al., 2005) , meaning that these instances preserve topology, do not have geometric singularities and have no or very little inter-penetration among objects.. We have been developing a methodology for describing 3D entities using medial representations combined with voxel scale displacements of the object interior and boundary, which together form a representation called m-reps (Pizer et al., 2003a; Joshi et al., 2002) . In this framework, a geometric entity is represented at discrete scales and locations. At each scale it is described by a set of geometric primitives and their relative transformations. For a population of geometric entities, we establish correspondence among instances by fixing the topology of our representation. As a result, what differs among members of the population is the quantitative, geometric parameters and not qualitative properties of structure or topology. One method for determining the fixed topology from a population is described in Styner and Gerig (2001) .. We describe shapes at multiple object scale levels to provide locality and efficiency in statistical analysis. The relationships between adjacent scale levels and among intra-scale neighbors make Markov models the natural choice. In this framework, we learn a series of probability models, each of which can be effectively characterized by a reasonably small number of parameters and thus can be estimated with limited number of training cases.. In what follows, we briefly describe m-reps in Section 2. Details of the multi-object m-rep models are presented in Sections 3-5. Section 6 shows an example of using statistical shape models to segment pubic bones. We finish with some discussion in Section 7. The entire estimation process is summarized in the Algorithm 5. We illustrated a new method of describing shapes that consist of multiple geometric objects. Based on our mreps representation, the geometric features of various scales and inter-object relationships are characterized by a multi-scale probabilistic model, which is in turn characterized by a series of probability distributions on residues. This method has the advantage of being able to provide accurate, intuitive geometric information and efficiency in statistical training. The shape model can be effectively used in a variety of image analysis applications, such as segmentation, shape discrimination, and atlas building.. As we have mentioned, the method described in the previous sections depends on the order we choose to traverse the multi-object complex. Now we briefly describe an alternative that does not specifically requires a predetermined order.. To explain, let us consider how we might use the probability model for segmentation. The idea is to maximize the joint posterior distribution of all objects, Pr(O 1 , O 2 , . . . , O M |I ). In the method described earlier, we break this distribution into a product of distributions (see Eq. (4)). An alternative approach is to use the iterative conditional mode (ICM) method (Besag, 1986) , where one iteratively maximizes the conditional distributions Pr(O i |{O j =i }). It has been shown that under suitable conditions, the solution to this approach provides a good approximation to the maximizer of the original joint distribution. A method based on such iteration and methods of augmentation and prediction is described in Jeong et al. (2006) . Therefore, we can focus on learning the conditional distributions Pr(O i |{O j =i }), which can be described by the difference between the actual deformation of object i and the predicted deformation of it based on those of its neighbors. Clearly, this approach does not depend on the order in which we choose to traverse the objects.. The basic assumptions in our methodology are that geometric entities can be described by a series of successive residual deformations from a common template and that these residual deformations can be treated as conditionally independent. Ultimately, the questions of in which order we describe objects and how many PGA modes to use at each step come down to whether our choices make those assumptions valid. Depending on the situation, it may make sense to have schemes that have only global deformations or only local deformations, or have schemes going back and forth between scale levels.. The ideas of residual deformation and prediction can also be applied to objects made up of multiple m-reps figures, in which case the hinge atoms on the subfigures are the natural choices for augmenting atoms. For details refer to Han et al. (2004) .. The methods described in this paper are applicable to any shape representation of objects (Pizer et al., 2005) . In particular, boundary-based representations and atlas diffeomorphism representations can be used. However, the primitives of these representations typically directly describe position or displacements only, and thus interscale residues describe displacements only. Probability distributions on the primitives or their residues can access local orientational and size relations indirectly but not directly. It remains to be determined if the benefits of m-reps that they do access such relations directly provide more stable estimation of the probability distributions described in this paper, given the limited number of training samples that are frequently available.. Our tests have suggested that the statistical shape models learned from training sets produce visually valid samples. However, we need more rigorous ways of evaluating these probability models and comparing them with other shape models. This is still work in progress. Other questions that require further investigation include the following: method for determining augmenting atoms, prediction algorithms, and object-based image match models.

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


Integrated Handwriting Recognition And Interpretation Using Finite-State Models The interpretation of handwritten sentences is carried out using a holistic approach in which both text image recognition and the interpretation itself are tightly integrated. Conventional approaches follow a serial, first-recognition then-interpretation scheme which cannot adequately use semantic-pragmatic knowledge to recover from recognition errors. Stochastic finite-sate transducers are shown to be suitable models for this integration, permitting a full exploitation of the final interpretation constraints. Continuousdensity hidden Markov models are embedded in the edges of the transducer to account for lexical and morphological constraints. Robustness with respect to stroke vertical variability is achieved by integrating tangent vectors into the emission densities of these models. Experimental results are reported on a syntax-constrained interpretation task which show the effectiveness of the proposed approaches. These results are also shown to be comparatively better than those achieved with other conventional, N-gram-based techniques which do not take advantage of full integration. The recognition of a handwritten sentence, i.e. decoding its symbolic representation in terms of characters, digits and/or words, is not the ultimate purpose in many tasks involving handwritten input. On the contrary, in these tasks, the handwritten text is often used just as an intermediate means to express some semantic message. The goal of an ideal automatic system in these cases is to obtain an adequate interpretation of the handwritten message, rather than achieving a good recognition of the individual text constituents of this message. This is clearly illustrated in two prominent tasks: postal address processing and bank check reading.. A system for postal address processing uses knowledge about postal domains and tries to guess the correct destination even if only incomplete or contradictory information appears or can be recognized in the postal address. Here recognition would consist in getting adequate hypotheses about the words and numbers written in the envelope; interpretation, in contrast, should yield a unique entry to the postal database containing the right addresses. Similarly, a bank check reading system has to interpret the legal amount (written in letters) to determine the real numeric sum (and to optionally verify whether this sum matches the courtesy amount -written in digits). Here recognition would consist in getting adequate hypotheses about the written words, while the goal of interpretation is to come out with a numeric expression which, overall, reflects what was written in letters as accurately as possible. It is not of great importance whether all the words comprising the legal amount were correctly written or whether they can be exactly recognized or not; only the reliability of the interpreted numeric result really matters.. From this point of view, the role of an interpretation system is to map input images into adequate target meanings and the written words or numbers should be considered just as intermediate results or hidden variables.. Under this paradigm, accurate handwriting interpretation requires a tight cooperation of lexical, syntactic and semantic/pragmatic knowledge. Each source of knowledge adds valuable, possibly redundant information which is best exploited in conjunction with that obtained from the other sources. This is just the very same situation that appears in the field of continuous speech recognition. 16 In this field, knowledge integration benefits are attained by following three basic principles: (i) adopt simple, homogeneous and easily understandable models for all the knowledge sources; (ii) formulate the problem as one of searching for an optimal path through an adequate structure based on these models; and (iii) use appropriate techniques to learn the different models from training data. These principles are actually the basis of those systems developed using finite-state devices such as hidden Markov models and stochastic finite-state grammars. Integrated recognition and interpretation of handwriting text via finite-state models has been proposed. We advocate the use of HMMs with tangent vectors for increased robustness with respect to vertical shift and stochastic finite-state transducers for their adequacy to globally model all the relevant constraints. A syntax-constrained interpretation task resembling legal amount interpretation for bank checks has been adopted as an illustrative example. Experimental results have been reported showing the effectiveness of the proposed approach. They constitute a significant improvement over previous (preliminary) results obtained in the same task. 4 Apart from the impact of integrated processing, this improvement is due to the inclusion of elaborated preprocessing and feature extraction techniques. The proposed approach was empirically evaluated on the Spanish numbers task described in Sec. 3.4. It was also compared with a more conventional approach based on a serial combination of word recognition using N -gram syntactic modeling, followed by text-to-number translation based on a perfect text-to-number transducer. To acquire a database of handwritten sentences of Spanish numbers, two independent lists of numbers were randomly generated: one of 10,000 items (L1) and other of 300 items (L2), and 29 writers were asked to write numbers from these lists. Each writer was given a blank sheet of paper and a pencil, and asked to write numbers in well-separated lines to facilitate their segmentation. Filled sheets were scanned at 300 dpi in 8-bit grayscale. After segmentation of the scanned sheets, 485 images of handwritten numbers were collected, from which 298 were transcribed from list L1 by 18 writers and 187 from list L2 by the remaining 11 writers.. c Some examples are shown in Fig. 7 . For the experiments reported hereafter, the 298 sentence images were employed as a training set and the 187 sentence images as a test set. Details about this database and the partitions used in the experiments are shown in Table 1 . In addition, the text-only sentences of L1 were used to train N -gram language models in some of the comparative experiments described in Sec. 4.2. Two measures are used to assess the empirical results: Word Error Rate (WER) and Digit Error Rate (DER). Both measure the percentage of tokens that have to be substituted, inserted or deleted in the system hypotheses in order to match the corresponding reference sequences. Tokens are words for WER and decimal digits for DER. WER and DER measure recognition and interpretation errors, respectively. It should be noted that, for practical application to the proposed task, WER values are of little interest. In practice, the output of a legal amount reading system generally needs to be compared with the result of a digit recognizer, which provides a complementary hypothesis of the check sum, based on the courtesy amount. The automatic (or manual) work needed to compare and eventually correct the results, is directly related with the number of digit errors. Therefore, since this is a digit-by-digit comparison, it is the DER measure what actually matters. In principle, WER and DER are not directly comparable measures. For the Spanish numbers, for instance, the average number of words in a text sentence of our database is 5.6, while the average number of digits in the corresponding decimal representation is 8.3. So, at first sight, DER might be expected to be lower than WER. However, many typical single-word errors correspond to two or more digit errors. For instance, mistaking "diez " for "dos" (a typical error in our system) in a sentence like "mil dos" corresponds to changing "1002 " into "1010 ", which entail two digit errors. And mistaking the word "noventa" for "millones" in a sentence such as "mil millones" corresponds to changing "1000000000 " into "1090 "; i.e. seven digit errors! On the average, for a good system, DER is expected to be somewhat lower than WER (for Spanish number sentences), the difference approaching to zero with increasing system accuracy.

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


Second order ambient intelligence Abstract. This text attempts to describe an imagined future of ambient intelligence. It assumes that one day most of the current issues within ambient intelligence will be solved and that a second order ambient intelligence will be formulated, one with new research agendas. It describes several topics and ideas that might be part of this agenda and surmises on the prerequisites for this change.Keywords: critique of ambient intelligence, temporal design, adaptive systems, long-term behavior, animal machine interaction, critical futurism, second order ambient intelligence Ambient intelligence (AmI) is still a comparatively new field of research. As in many new fields of inquiry, its current state is far from what AmI-researchers and professionals believe it capable of. Unfortunately, many AmI systems you can actually experience today leave you wondering what all the excitement is about. I recently visited a smart house that has wall to wall voice control to activate curtains and open windows. Speech recognition is notorious for its unreliability in noisy environments and unconstrained vocabularies. The proud home inhabitant, hired by a company to demonstratively live in this smart house, used a microphone headset in an attempt to keep the signal to noise ratio between his voice and the inevitable background noise at a level the voice recognition system could cope with. The system designers were well aware of the potential of miscommunication between speakers and voice activated control systems, and added an additional level of robustness in the usage scenario. Each voice command was preceded by a signature prompt that cued the listening system to the incoming command. The signature prompt was cast into a form of addressing people are fAmIliar with: a name. So the house had a name, a name that sounded spiffy and could be picked up easily by the AmI system, readying it for the actual command intended for execution.. The idea is compelling; a perfect solution, one that combines a state of the art technology with useful best-practices to increase robustness; one that includes integration into established social norms. The reality was different however. The presenter trained in using the system, found himself repeating commands various times during the demonstration. Each one was preceded by the house name as if he were calling a disobedient dog. Our loud and boisterous comments in the background only made the situation worse. The window shades opened and closed out of sync not unlike the gadgets in the Villa Arpel of Jacques Tati's Mon Oncle [17] .

B I I 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 B I I 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 B I I I B I B I B I B I I B I B I I 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


Building Mashups by example Creating a Mashup, a web application that integrates data from multiple web sources to provide a unique service, involves solving multiple problems, such as extracting data from multiple web sources, cleaning it, and combining it together. Existing work relies on a widget paradigm where users address those problems during a Mashup building process by selecting, customizing, and connecting widgets together. While these systems claim that their users do not have to write a single line of code, merely abstracting programming methods into widgets has several disadvantages. First, as the number of widgets increases to support more operations, locating the right widget for the task can be confusing and time consuming. Second, customizing and connecting these widgets usually requires users to understand programming concepts. In this paper, we present a Mashup building approach that (a) combines most problem areas in Mashup building into a unified interactive framework that requires no widgets, and (b) allows users with no programming background to easily create Mashups by example. Recently, average Internet users have evolved from content consumers to content providers. In the past, creating a simple web application was a complicated process. Today, we can create professional looking blogs or profile pages on a social network site without knowing HTML.. The latest generation of WWW tools and services enables web users to generate web applications that combine content from multiple sources, and provide them as unique services that suit their situational needs. This type of web applications is referred to as a Mashup. A Mashup can be created as easily as manually typing information into each map marker in GoogleMap. More interesting Mashups, such as Zillow (zillow.com) and SkiBonk (skibonk.com), are much more complex because they need to deal with five basic issues:. Data Retrieval involves extracting data from web pages into a structured data source (i.e., table or XML). In addition to figuring out the rules to extract particular data from HTML pages [8, 9] , the structure of data on a page or the location of data which can span multiple web pages can make the process more complicated.. Source Modeling is the process of assigning the attribute name for each data column so a relationship between a new data source and existing data sources can be deduced.. Data Cleaning is required to fix misspellings and transform extracted data into an appropriate format. For example, the extracted data "Jones, Norah" might need to be transformed to "Norah Jones" to conform to the format of existing data sources.. Data Integration specifies how to combine two or more data sources together. For example, building a Mashup that lists all the movies ever performed by this year's Oscar award winners will require us to merge (a) an Oscar winner list and (b) a movie database using a database join operation on the winner's names.. Data Visualization takes the final data generated by the user and displays it (i.e., a table, a map, or a graph). Customizing the display and specifying the interaction model for the GUI often requires programming.. Our goal is to create a Mashup building framework where an average Internet user with no programming experience can build Mashups easily. Currently, there exist various Mashup building tools, such as Microsoft's Popfly Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.. IUI'08, January [13] [14] [15] [16] 2008 , Maspalomas, Gran Canaria, Spain. Copyright 2008 ACM 978-1-59593-987-6/ 08/ 0001 $5.00 (www.popfly.ms), Dapper (www.dapper.net), and Yahoo's Pipes (pipes.yahoo.com) to name a few. These tools aim at allowing users to build Mashups without writing code. However, not having to write code to build a Mashup does not always mean building one is easy. Most existing solutions employ a widget approach, where users select, customize, and connect widgets to perform complex operations. Figure 1 shows some widgets in Yahoo's Pipes that provide support for: fetching a RSS Feed, looping, and replacing a string using a regular expression.. There are two problems with the widget approach. First, the numbers of widgets (i.e., 43 for Yahoo's Pipes, 300+ for Microsoft's Popfly) can increase as Mashup tools try to increase their functionality. As a result, locating a widget that will accomplish the task can be difficult and time consuming. Second, while no programming is required, users often need to understand programming concepts to fully utilize them. Furthermore, most systems focus on particular information integration issues while ignoring others. As a result, the process of building Mashups is still quite complicated and the range of Mashups that naïve users can build is still limited.. In this paper, we illustrate how to address the first four Mashup building issues, often solved separately or partially, into one seamless process using the programming by demonstration paradigm. Using our approach, users (a) do not have to program or understand programming concepts to build a Mashup, and (b) indirectly solve each issue during the Mashup building process by only providing examples.. The rest of the paper is organized as follow: we first describe our motivating example, which highlights our approach. Then, we outline our approach and the details of each component.. Next, we survey current Mashup solutions from both industry and the research world. Then, we provide the preliminary evaluation of our implementation against the current state-of-the-art offerings. Finally, we discuss our contributions and plans for future work. First we survey existing Mashup tools. Then, we review related fields of research. Designing the experiments that include qualitative and quantitative measurements between these systems is a challenge. First, Dapper and Pipes do not cover all the problem areas; Dapper's main focus is on data extraction from web sources and it outputs the result as an RSS feed. On the other hand, Pipes has widgets for cleaning and combining sources, but it cannot extract data from web sources that do not provide RSS feeds. Second, these systems have a high learning curve; users must read tutorials, try out examples, and understand programming concepts.. For our evaluation, we solve the first problem by combining Dapper and Pipes to finish our designed tasks; we use Dapper for data extraction and Pipes for the other data processing tasks. Note that the approach of combining tools to build a Mashup is not uncommon and is widely practiced by developers at MashupCamp (www.Mashupcamp.com), a biannual conference on cutting edge Mashup technology. For the second problem, we use an expert that knows every system used in the evaluation to do all the tasks. Then, the measurement is done as a unit of "steps." Each of the following actions constitutes one unit step: (a) typing values in a textbox, (b) clicking a button, (c) selecting options from a list, (d) dragging and dropping widgets from one area to another area, and (e) connecting one widget to another widget.. In our experiment, the expert will carry out three Mashup building tasks. Each task is designed to address some specific problem areas in the Mashup building process. Performance will be measured in the number of "steps" segmented by each problem area. Tasks 1. Extracting a list of female adult contemporary artists (i.e., album name, artist name, description) created by an Amazon.com user at http://www.tiny.cc/0ctOx Notice that cleaning is needed to correct some artist names ("Jones, Norah" to "Norah Jones"). This is a simple task of extracting a list of data that requires simple cleaning.. 2. Extract and combine cheapest gas prices from Los Angeles (www.losangelesgasprices.com), and Orange County (http://www.orangecountygasprices.com). These two data sources have identical structure and will require a database "union" to combine the two sources. There is no cleaning in this task.. 3. Extract and combine the best sushi restaurant data with LA health ratings. This task is the same as the motivating example and we will assume that LA health rating data has already been extracted. This task requires using a database "join" to combine the two sources. Table 2 shows the number of steps for each, task segmented by problem areas. K represents Karma, while DP represents Dapper/Pipes combination. Overall, Karma takes fewer steps in each area to complete the three tasks.

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ON THE USEFULNESS OF KNOWLEDGE OF ERROR VARIANCES IN THE CONSISTENT ESTIMATION OF AN UNREPLICATED ULTRASTRUCTURAL MODEL This article considers an unreplicated ultrastructural model and discusses the asymptotic properties of three consistent estimators of slope parameter arising from the knowledge of measurement error variances. Conditions are deduced when knowing the error variances associated with both the study and the explanatory variables is more=less beneficial than using a single error variance in the formulation of slope estimators. One of the important requirements for the application of least squares procedure to a linear regression model is that the explanatory variables are measured without any error. Such a requirement may not be accomplished in many practical situations, and the available observations on one or more explanatory variables are subjected to measurement errors. Consequently, the optimal properties of the least squares procedure are vitiated, so much so that the estimators of the regression coefficients are not only biased but inconsistent too.. The quest for consistent estimators of the regression coefficients in the presence of measurement errors has led to the strategy of adjusting the least squares estimators when some additional information about the model is available; see, e.g., Cheng and Van Ness (1999) and Fuller (1987) for a comprehensive exposition. Among the various formulations of the additional information about the model parameters, there are three interesting specifications. In the context of a bivariate regression model, these relate to the specification of the variance of measurement errors associated with the study variable, explanatory variable or both in the form of their ratio. As all the three kinds of prior information allow us to estimate the parameters consistently, it is probably pertinent to find out which type of prior information is more useful in the sense of providing less biased and=or more efficient estimators. This issue is just touched upon by Cheng and Van Ness (1994, p. 180 ). This problem is addressed in this article and situations are identified where the utilization of both the error variances in the formulation of a consistent estimator of the slope parameter is worthwhile in comparison to the use of merely one error variance.. The exact (analytic) finite sample properties of the estimators based on the knowledge of one of the two measurement error variances are difficult to obtain, see, e.g., Cheng and Van Ness (1999, p. 57) . In order to study the performance of these estimators, another alternative approach is to employ the large sample asymptotic approximation theory and base the inferences on these expressions. These expressions for efficiency properties involve some unknown population values and thus may leave the results unfit for practical applications. While dealing with measurement error models, it can be well appreciated that the reliability ratios associated with the study and explanatory variables are easily available or can be well estimated; see Gleser (1992; for more details on this aspect. So under the given circumstances, an attempt is made in this paper to express the large sample asymptotic approximations for the three popular estimators in terms of reliability ratios associated with study and explanatory variables.. Further, the dominance conditions for the superiority of one estimator over the other are obtained in terms of reliability ratios. Their advantage is that in practical situations, generally one has the idea of reliability ratios of the dependent and independent variables. Based on this knowledge, one can decide and choose the estimator which will behave more efficiently.. The literature dealing with measurement error models generally assumes the measurement errors to have a normal distribution. The distribution of measurement errors essentially depends on the nature of the experiment involved and may not always be necessarily normal. Thus the specification of normality may lead to some incorrect and invalid statistical inferences. To study the impact of not necessarily normally distributed measurement errors on the efficiency properties of consistent estimators, some investigations are reported in this article.. In order to study the finite sample properties of consistent estimators and to see how well the large sample asymptotic approximations hold for small samples, a Monte-Carlo experiment study is also reported.. The plan of the presentation is as follows. Section 2 describes the unreplicated ultrastructural model with not necessarily normally distributed errors and presents three estimators arising from the knowledge of measurement error variances. In Section 3, the asymptotic properties of these three estimators are analyzed and the implications of their properties are discussed for examining the question of whether knowledge of one variance over the other is more beneficial when the aim is to estimate the slope parameter consistently. The details of a Monte-Carlo experiment are reported in Section 4. Finally, some remarks are offered in Section 5. The derivation of results is presented in the Appendix.

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