generalizing the hough transform to detect arbitrary shapes abstract the hough transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve the initial work showed how to detect both analytic curves 1 2 and non analytic curves 3 but these methods were restricted to binary edge images this work was generalized to the detection of some analytic curves in grey level images specifically lines 4 circles 5 and parabolas 6 the line detection case is the best known of these and has been ingeniously exploited in several applications 7 8 9 we show how the boundaries of an arbitrary non analytic shape can be used to construct a mapping between image space and hough transform space such a mapping can be exploited to detect instances of that particular shape in an image furthermore variations in the shape such as rotations scale changes or figure ground reversals correspond to straightforward transformations of this mapping however the most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler component shapes this makes the generalized hough transform a kind of universal transform which can be used to find arbitrarily complex shapes

algebraic foundations for qualitative calculi and networks abstract binary constraint problems have traditionally been considered as network satisfaction problems over some relation algebra a constraint network is satisfiable if its nodes can be mapped into some representation of the relation algebra in such a way that the constraints are preserved a qualitative representation is like an ordinary representation but instead of requiring that a b is the composition a b of the relations a and b as we do for ordinary representations we only require that c a b c a b for each c in the algebra a constraint network is qualitatively satisfiable if its nodes can be mapped to elements of a qualitative representation preserving the constraints if a constraint network is satisfiable then it is clearly qualitatively satisfiable but the converse can fail as we show however for a wide range of relation algebras including the point algebra the allen interval algebra rcc8 and many others a network is satisfiable if and only if it is qualitatively satisfiable unlike ordinary composition the weak composition arising from qualitative representations need not be associative so we can generalise by considering network satisfaction problems over non associative algebras we prove that computationally qualitative representations have many advantages over ordinary representations whereas many finite relation algebras have only infinite representations every finite qualitatively representable algebra has a finite qualitative representation the representability problem for the atom structures of finite non associative algebras is np complete the network satisfaction problem over a finite qualitatively representable algebra is always in np the validity of equations over qualitative representations is co np complete on the other hand we prove that there is no finite axiomatisation of the class of qualitatively representable algebras

qualitative representation of positional information abstract a framework for the qualitative representation of positional information in a two dimensional space is presented qualitative representations use discrete quantity spaces where a particular distinction is introduced only if it is relevant to the context being modeled this allows us to build a flexible framework that accommodates various levels of granularity and scales of reasoning knowledge about position in large scale space is commonly represented by a combination of orientation and distance relations which we express in a particular frame of reference between a primary object and a reference object while the representation of orientation comes out to be more straightforward the model for distances requires that qualitative distance symbols be mapped to geometric intervals in order to be compared this is done by defining structure relations that are able to handle among others order of magnitude relations the frame of reference with its three components distance system scale and type captures the inherent context dependency of qualitative distances the principal aim of the qualitative representation is to perform spatial reasoning as a basic inference technique algorithms for the composition of positional relations are developed with respect to same and different frames of reference the model presented in this paper has potential applications in areas as diverse as geographical information systems gis computer aided design cad and document recognition

on the consistency of cardinal direction constraints we present a formal model for qualitative spatial reasoning with cardinal directions utilizing a co ordinate system then we study the problem of checking the consistency of a set of cardinal direction constraints we introduce the first algorithm for this problem prove its correctness and analyze its computational complexity utilizing the above algorithm we prove that the consistency checking of a set of basic i e non disjunctive cardinal direction constraints can be performed in o n 5 time we also show that the consistency checking of a set of unrestricted i e disjunctive and non disjunctive cardinal direction constraints is np complete finally we briefly discuss an extension to the basic model and outline an algorithm for the consistency checking problem of this extension

boundary regularity for a family of overdetermined problems for the helmholtz equation if a nonconstant solution u of the helmholtz equation exists on a bounded domain with u satisfying overdetermined boundary conditions u and its normal derivative both required to be constant on the boundary then under certain assumptions the boundary of the domain is proved to be real analytic under weaker assumptions if a real analytic portion of the boundary has a real analytic extension then that extension must also be part of the boundary also an explicit formula for u is given and a condition which does not involve u is given for a bounded domain to have such a solution u defined on it both of these last results involve acoustic single and double layer potentials

constants and finite unary relations in qualitative constraint reasoning extending qualitative csps with the ability of restricting selected variables to finite sets of possible values has been proposed as an interesting research direction with important applications c

a relation algebraic approach to the region connection calculus abstract we explore the relation algebraic aspects of the region connection calculus rcc of randell et al proceedings of the cade vol 11 pp 786 790 springer berlin 1992a in particular we present a refinement of the rcc8 table which shows that the axioms provide for more relations than are listed in the present table we also show that each rcc model leads to a boolean algebra finally we prove that a refined version of the rcc5 table has as models all atomless boolean algebras b with the natural ordering as the part of relation and that the table is closed under first order definable relations iff b is homogeneous

the complexity of constraint satisfaction problems for small relation algebras andreka and maddux notre dame j formal logic 35 4 1994 classified the small relation algebras those with at most 8 elements or in other terms at most 3 atomic relations they showed that there are eighteen isomorphism types of small relation algebras all representable for each simple small relation algebra they computed the spectrum of the algebra namely the set of cardinalities of square representations of that relation algebra in this paper we analyze the computational complexity of the problem of deciding the satisfiability of a finite set of constraints built on any small relation algebra we give a complete classification of the complexities of the general constraint satisfaction problem for small relation algebras for three of the small relation algebras the constraint satisfaction problem is np complete for the other fifteen small relation algebras the constraint satisfaction problem has cubic or lower complexity we also classify the complexity of the constraint satisfaction problem over fixed finite representations of any relation algebra if the representation has size two or less then the complexity is cubic or lower but if the representation is square finite and bigger than two then the complexity is np complete

reasoning about cardinal directions between extended objects the np hardness result the cardinal direction calculus cdc proposed by goyal and egenhofer is a very expressive qualitative calculus for directional information of extended objects early work has shown that consistency checking of complete networks of basic cdc constraints is tractable while reasoning with the cdc in general is np hard this paper shows however that if some constraints are unspecified then consistency checking of incomplete networks of basic cdc constraints is already intractable this draws a sharp boundary between the tractable and intractable subclasses of the cdc the result is achieved by a reduction from the well known 3 sat problem

querying temporal and spatial constraint networks in ptime we start with the assumption that temporal and spatial knowledge usually captured by constraint networks can be represented and queried more effectively by using the scheme of indefinite constraint databases because query evaluation in this scheme is in general a hard computational problem we seek tractable instances of query evaluation we assume that we have a class of constraints c with some reasonable computational and closure properties the computational properties of interest are that the satisfiability problem and an appropriate version of the variable elimination problem for c should be solvable in ptime under this assumption we exhibit general classes of indefinite constraint databases and first order modal queries for which query evaluation can be done with ptime data complexity we then search for tractable instances of c among the subclasses of horn disjunctive linear constraints over the rationals from previous research we know that the satisfiability problem for horn disjunctive linear constraints is solvable in ptime but not the variable elimination problem thus we try to discover subclasses of horn disjunctive linear constraints with tractable variable elimination problems the class of utvpi constraints is the largest class that we show to have this property finally we restate our general tractability results with c ranging over the newly discovered tractable classes interesting tractable query answering problems for indefinite temporal and spatial constraint databases are identified in this way we close our complexity analysis by precisely outlining the frontier between tractable and possibly intractable query answering problems

modification of hough transform for circles and ellipses detection using a 2 dimensional array abstract the hough transform is a robust technique which is useful in detecting straight lines in an edge enhanced picture however the extension of the conventional hough transform to recover circles and ellipses has been limited by slow speed and excessive memory this paper presents techniques aimed at improving the efficiency and reducing the memory size of the accumulator array based on these techniques only a 2 dimensional array is needed for the detection of circles and ellipses the approach centres on the use of parallel edge points and a method on reducing the dimension of the accumulator array

hybrid image segmentation using watersheds and fast region merging a hybrid multidimensional image segmentation algorithm is proposed which combines edge and region based techniques through the morphological algorithm of watersheds an edge preserving statistical noise reduction approach is used as a preprocessing stage in order to compute an accurate estimate of the image gradient then an initial partitioning of the image into primitive regions is produced by applying the watershed transform on the image gradient magnitude this initial segmentation is the input to a computationally efficient hierarchical bottom up region merging process that produces the final segmentation the latter process uses the region adjacency graph rag representation of the image regions at each step the most similar pair of regions is determined minimum cost rag edge the regions are merged and the rag is updated traditionally the above is implemented by storing all rag edges in a priority queue we propose a significantly faster algorithm which additionally maintains the so called nearest neighbor graph due to which the priority queue size and processing time are drastically reduced the final segmentation provides due to the rag one pixel wide closed and accurately localized contours surfaces experimental results obtained with two dimensional three dimensional 2 d 3 d magnetic resonance images are presented

a model for describing and composing direction relations between overlapping and contained regions current models of direction relations are not designed to describe direction information inside the minimum bounding rectangle mbr of a reference region thus the direction relations between overlapping and contained regions cannot be effectively described and derived to resolve this problem a new model of direction relations namely interior boundary direction relations is proposed in this study to describe direction concepts relative to the interior or boundary of a region such as east part of a region west border of a region a line goes through east part of a region and etc by combining the interior and exterior direction relations three types of compositions of direction relations are investigated 1 composing two interior direction relations which can be used to derive the interior or exterior direction relations between two regions with the same parent region 2 composing an interior direction relation with an exterior direction relation and 3 composing an interior with an exterior direction relation the results indicate that the new interior boundary direction relations and its compositions with exterior direction relations are powerful in describing and deriving direction relations between overlapped and contained regions

region connection calculus its models and composition table originating in allen s analysis of temporal relations the notion of composition table has become a key technique in providing an efficient inference mechanism for a wide class of theories in the field artificial intelligence this paper is mainly about the consistency based composition table rcc8 ct of the region connection calculus rcc raised by randell cui and cohn first we show each rcc model is a consistent model of the rcc8 ct then after an exhaustive analysis we show that no rcc model can be interpreted extensionally anyway and hence give a negative answer to a conjecture raised by bennett all these results are given in an extensional rcc8 composition table where we attach to each cell entry in the rcc8 ct a superscript to indicate in what circumstances an extensional interpretation is possible

new results on the pompeiu problem let pn w enko a w w e c n e n be a polynomial with complex coefficients in this paper we prove that if dc c2 is a simplyconnected bounded open set whose boundary is a closed simple curve parametrized by x s xl s ix2 s pn els s e xt 7t then d has the pompeiu property unless n 1 and p1 w a1w a2 in which case d is a disk this result supports the conjecture that modulo sets of zero twodimensional lebesgue measure the disk is the only simply connected bounded open set which fails to have the pompeiu property

generalized hough transform using regions with homogeneous color a novel generalized hough transform algorithm which makes use of the color similarity between homogeneous segments as the voting criterion is proposed in this paper the input of the algorithm is some regions with homogeneous color these regions are obtained by first pre segmenting the image using the morphological watershed algorithm and then refining the resultant outputs by a region merging algorithm region pairs belonging to the object are selected to generate entries of the reference table for the hough transform every r table entry stores a relative color between the selected region pairs this is done in order to compute the color similarity and in turn generate votes during the voting process and some relevant information to recover the transformation parameters of the object based on the experimental results our algorithm is robust to change of illumination occlusion and distortion of the segmentation output it recognizes objects which were translated rotated scaled and even located in a complex environment

adaptive split and merge segmentation based on piecewise least square approximation the performance of the classic split and merge segmentation algorithm is severely hampered by its rigid split and merge processes which are insensitive to the image semantics the author proposes efficient algorithms and data structures to optimize the split and merge processes by piecewise least square approximation of image intensity functions this optimization aims at the unification of segment finding and edge detection the optimized split and merge algorithm is shown to be adaptive to the image semantics and hence improves the segmentation validity of the previous algorithms this algorithm also appears to work well on noisy sources since the optimization is done within the split and merge framework the better segmentation performance is achieved at the same order of time complexity as the previous algorithms

symmetry theorems for the overdetermined eigenvalue problems abstract the well known schiffer conjecture saying that for a smooth bounded domain r n if there exists a positive neumann eigenvalue such that the corresponding neumann eigenfunction u is constant on the boundary of then is a ball in this paper we shall prove that the schiffer conjecture holds if and only if the third order interior normal derivative of the corresponding neumann eigenfunction is constant on the boundary we also prove a similar result to the berenstein conjecture for the overdetermined dirichlet eigenvalue problem

the maximal subgroups of the baby monster i abstract in this paper we describe the completion of the determination of the maximal subgroups of the baby monster simple group our results are proved using computer calculations with matrix generators for the group the full details of the calculations will appear elsewhere

a new result on the pompeiu problem a nonernpty bounded open set q c r n 2 is said to have the pompeiu property if and only if the only continuous function f on rn for which the integral of f over oa is zero for all rigid motions a of rn is f 0 o we consider a nonempty bounded open set q c r t n 2 with lipschitz boundary and we assume that the complement of q is connected we show that the failure of the pomnpeiu property for q implies some geometric conditions using these conditions we prove that a special kind of solid tori in r n 3 has the pompeiu property so far the result was proved only for solid tori in jr we also examine the case of planar domains finally we extend the example of solid tori to domains in rn bounded by hypersurfaces of revolution

some results on the schiffer conjecture in r 2 abstract let be an open bounded domain in r 2 with connected and c boundary and a solution of 0 1 0 2 n 0 0 3 const 0 for some 0 denoting by 0 1 2 the set of all neumann eigenvalues for the laplacian on we show that 1 if 8 or 2 if is strictly convex and centrally symmetric 13 then must be a disk

rcc8 binary constraint network can be consistently extended the rcc8 constraint language developed by randell et al has been popularly adopted by the qualitative spatial reasoning and gis communities the recent observation that rcc8 composition table describes only weak composition instead of composition raises questions about renz and nebel s maximality results about the computational complexity of reasoning with rcc8 this paper shows that any consistent rcc8 binary constraint network rcc8 network for short can be consistently extended given an rcc8 network and z a fresh variable suppose xty and t is contained in the weak composition of r and s this means that we can add two new constraints xrz and zsy to without changing the consistency of the network the result guarantees the applicability to rcc8 of one key technique theorem 5 of j renz b nebel on the complexity of qualitative spatial reasoning a maximal tractable fragment of the region connection calculus artificial intelligence 108 1999 69 123 which allows the transfer of tractability of a set of rcc8 relations to its closure under composition intersection and converse

reasoning about temporal relations the tractable subalgebras of allen s interval algebra allen s interval algebra is one of the best established formalisms for temporal reasoning this article provides the final step in the classification of complexity for satisfiability problems over constraints expressed in this algebra when the constraints are chosen from the full allen s algebra this form of satisfiability problem is known to be np complete however eighteen tractable subalgebras have previously been identified we show here that these subalgebras include all possible tractable subsets of allen s algebra in other words we show that this algebra contains exactly eighteen maximal tractable subalgebras and reasoning in any fragment not entirely contained in one of these subalgebras is np complete we obtain this dichotomy result by giving a new uniform description of the known maximal tractable subalgebras and then systematically using a general algebraic technique for identifying maximal subalgebras with a given property

combining topological and size information for spatial reasoning information about the size of spatial regions is often easily accessible and when combined with other types of spatial information it can be practically very useful in this paper we introduce four classes of qualitative and metric size constraints and we study their integration with the region connection calculus rcc 8 a well known approach to qualitative spatial reasoning with topological relations we propose a new path consistency algorithm for combining rcc 8 relations and qualitative size relations the algorithm is complete for deciding satisfiability of an input set of topological constraints over one of the three maximal tractable subclasses of rcc 8 containing all the basic relations moreover its time complexity is cubic and is the same as the complexity of the best known method for deciding satisfiability when only these topological relations are considered we also provide results on finding a consistent scenario in cubic time for these combined classes regarding metric size constraints we first study their combination with rcc 8 and we show that deciding satisfiability for the combined sets of constraints is np hard even when only the rcc 8 basic relations are used then we introduce rcc 7 a subalgebra of rcc 8 that can be used for applications where spatial regions cannot partially overlap we show that reasoning with the seven rcc 7 basic relations and the universal relation is intractable but that reasoning with the rcc 7 basic relations combined with metric size information is tractable finally we give a polynomial algorithm for the latter case and a backtracking algorithm for the general case

a new approach to cyclic ordering of 2d orientations using ternary relation algebras abstract in tarski s formalisation the universe of a relation algebra ra consists of a set of binary relations a first contribution of this work is the introduction of ras whose universe is a set of ternary relations these support rotation as an operation in addition to those present in tarski s formalisation then we propose two particular ras a binary ra cyc b whose universe is a set of binary relations on 2d orientations and a ternary ra cyc t whose universe is a set of ternary relations on 2d orientations the ra cyc t more expressive than cyc b constitutes a new approach to cyclic ordering of 2d orientations an atom of cyc t expresses for triples of orientations whether each of the three orientations is equal to to the left of opposite to or to the right of each of the other two orientations cyc t has 24 atoms and the elements of its universe consist of all possible 2 24 subsets of the set of all atoms amongst other results 1 we provide for cyc t a constraint propagation procedure computing the closure of a problem under the different operations and show that the procedure is polynomial and complete for a subset including all atoms 2 we prove that another subset expressing only information on parallel orientations is np complete 3 we show that provided that a subset s of cyc t includes two specific elements deciding consistency for a problem expressed in the closure of s can be polynomially reduced to deciding consistency for a problem expressed in s and 4 we derive from the previous result that for both ras we jump from tractability to intractability if we add the universal relation to the set of all atoms a comparison to the most closely related work in the literature indicates that the approach is promising

on the complexity of qualitative spatial reasoning a maximal tractable fragment of the region connection calculus the computational properties of qualitative spatial reasoning have been investigated to some degree however the question for the boundary between polynomial and np hard reasoning problems has not been addressed yet in this paper we explore this boundary in the region connection calculus rcc 8 we extend bennett s encoding of rcc 8 in modal logic based on this encoding we prove that reasoning is np complete in general and identify a maximal tractable subset of the relations in rcc 8 that contains all base relations further we show that for this subset path consistency is sufficient for deciding consistency

a representation theorem for boolean contact algebras we prove a representation theorem for boolean contact algebras which implies that the axioms for the region connection calculus rcc d a randell a g cohn z cui computing transitivity tables a challenge for automated theorem provers in d kapur ed proceedings of the 11th international conference on automated deduction cade 11 lecture notes in artificial intelligence vol 607 springer saratoga springs ny 1992 pp 786 790 are complete for the class of subalgebras of the algebras of regular closed sets of weakly regular connected t1 spaces

composing cardinal direction relations we study the recent proposal of goyal and egenhofer who presented a model for qualitative spatial reasoning about cardinal directions our approach is formal and complements the presentation of goyal and egerdaofer we focus our efforts on the composition operator for two cardinal direction relations we consider two interpretations of the composition operator consistency based and existential composition we point out that the only published method to compute the consistency based composition does not always work correctly then we consider progressively more expressive classes of cardinal direction relations and give consistency based composition algorithms for these classes our theoretical framework allows us to prove formally that our algorithms are correct when we consider existential composition we demonstrate that the binary relation resulting from the composition of two cardinal direction relations cannot be expressed using the relations defined by goyal and egenhofer finally we discuss some extensions to the basic model and consider the composition problem for these extensions

on binary constraint problems the concepts of binary constraint satisfaction problems can be naturally generalized to the relation algebras of tarski the concept of path consistency plays a central role algorithms for path consistency can be implemented on matrices of relations and on matrices of elements from a relation algebra we give an example of a 4 by 4 matrix of infinite relations on which on iterative local path consistency algorithm terminates we give a class of examples over a fixed finite algebra on which all iterative local algorithms whether parallel or sequential must take quadratic time specific relation algebras arising from interval constraint problems are also studied the interval algebra the point algebra and the containment algebra

a unifying approach to temporal constraint reasoning abstract we present a formalism disjunctive linear relations dlrs for reasoning about temporal constraints dlrs subsume most of the formalisms for temporal constraint reasoning proposed in the literature and is therefore computationally expensive we also present a restricted type of dlrs horn dlrs which have a polynomial time satisfiability problem we prove that most approaches to tractable temporal constraint reasoning can be encoded as horn dlrs including the ord horn algebra by nebel and burckert and the simple temporal constraints by dechter et al thus dlrs is a suitable unifying formalism for reasoning about temporal constraints

reasoning about qualitative temporal information abstract representing and reasoning about incomplete and indefinite qualitative temporal information is an essential part of many artificial intelligence tasks an interval based framework and a point based framework have been proposed for representing such temporal information in this paper we address two fundamental reasoning tasks that arise in applications of these frameworks given possibly indefinite and incomplete knowledge of the relationships between some intervals or points i find a scenario that is consistent with the information provided and ii find the feasible relations between all pairs of intervals or points for the point based framework and a restricted version of the interval based framework we give computationally efficient procedures for finding a consistent scenario and for finding the feasible relations our algorithms are marked improvements over the previously known algorithms in particular we develop an o n2 time algorithm for finding one consistent scenario that is an o n improvement over the previously known algorithm where n is the number of intervals or points and we develop an algorithm for finding all the feasible relations that is of far more practical use than the previously known algorithm for the unrestricted version of the interval based framework finding a consistent scenario and finding the feasible relations have been shown to be np complete we show how the results for the point algebra aid in the design of a backtracking algorithm for finding one consistent scenario that is shown to be useful in practice for planning problems

the complexity of query evaluation in indefinite temporal constraint databases abstract in previous work we have developed the scheme of indefinite l constraint databases where l the parameter is a first order constraint language this scheme extends the constraint database proposal of kanellakis et al 1990 1995 to include indefinite or uncertain information in the style of imielinski and lipski 1984 in this paper we study the complexity of query evaluation in an important instance of this abstract scheme indefinite temporal constraint databases our results indicate that the data combined complexity of query evaluation does not change when we move from queries in relational calculus over relational databases to queries in relational calculus with temporal constraints over temporal constraint databases this fact remains true even when we consider query evaluation in relational databases with indefinite information vs query evaluation in indefinite temporal constraint databases in the course of our work we provide precise bounds on the complexity of decision quantifier elimination for a subtheory of presburger arithmetic and a subtheory of real addition with order the bounds for the latter theory are original and of independent interest

on redundant topological constraints redundancy checking is an important task in the research of knowledge representation and reasoning in this paper we consider redundant qualitative constraints for a set of qualitative constraints we say a constraint x r y in is redundant if it is entailed by the rest of a prime subnetwork of is a subset of which contains no redundant constraints and has the same solution set as it is natural to ask how to compute such a prime subnetwork and when it is unique we show that this problem is in general intractable but becomes tractable if is over a tractable subalgebra s of a qualitative calculus furthermore if s is a subalgebra of the region connection calculus rcc8 in which weak composition distributes over nonempty intersections then has a unique prime subnetwork which can be obtained in cubic time by removing all redundant constraints simultaneously from as a by product we show that any path consistent network over such a distributive subalgebra is minimal and globally consistent in a qualitative sense a thorough empirical analysis of the prime subnetwork upon real geographical data sets demonstrates the approach is able to identify significantly more redundant constraints than previously proposed algorithms especially in constraint networks with larger proportions of partial overlap relations

qualitative constraint satisfaction problems an extended framework with landmarks dealing with spatial and temporal knowledge is an indispensable part of almost all aspects of human activity the qualitative approach to spatial and temporal reasoning known as qualitative spatial and temporal reasoning qstr typically represents spatial temporal knowledge in terms of qualitative relations e g to the east of after and reasons with spatial temporal knowledge by solving qualitative constraints when formulating qualitative constraint satisfaction problems csps it is usually assumed that each variable could be here there and everywhere practical applications such as urban planning however often require a variable to take its value from a certain finite domain i e it is required to be here or there but not everywhere entities in such a finite domain often act as reference objects and are called landmarks in this paper the paper extends the classical framework of qualitative csps by allowing variables to take values from finite domains the computational complexity of the consistency problem in this extended framework is examined for the five most important qualitative calculi viz point algebra interval algebra cardinal relation algebra rcc5 and rcc8 we show that all these consistency problems remain in np and provide under practical assumptions efficient algorithms for solving basic constraints involving landmarks for all these calculi

reasoning about cardinal directions between extended objects direction relations between extended spatial objects are important commonsense knowledge recently goyal and egenhofer proposed a relation model known as the cardinal direction calculus cdc for representing direction relations between connected plane regions the cdc is perhaps the most expressive qualitative calculus for directional information and has attracted increasing interest from areas such as artificial intelligence geographical information science and image retrieval given a network of cdc constraints the consistency problem is deciding if the network is realizable by connected regions in the real plane this paper provides a cubic algorithm for checking the consistency of complete networks of basic cdc constraints and proves that reasoning with the cdc is in general an np complete problem for a consistent complete network of basic cdc constraints our algorithm returns a canonical solution in cubic time this cubic algorithm is also adapted to check the consistency of complete networks of basic cardinal constraints between possibly disconnected regions

generalized region connection calculus the region connection calculus rcc is one of the most widely referenced system of high level qualitative spatial reasoning rcc assumes a continuous representation of space this contrasts sharply with the fact that spatial information obtained from physical recording devices is nowadays invariably digital in form and therefore implicitly uses a discrete representation of space recently galton developed a theory of discrete space that parallels rcc but question still lies in that can we have a theory of qualitative spatial reasoning admitting models of discrete spaces as well as continuous spaces in this paper we aim at establishing a formal theory which accommodates both discrete and continuous spatial information and a generalization of region connection calculus is introduced grcc the new theory takes two primitives the mereological notion of part and the topological notion of connection rcc and galton s theory for discrete space are both extensions of grcc the relation between continuous models and discrete ones is also clarified by introducing some operations on models of grcc in particular we propose a general approach for constructing countable rcc models as direct limits of collections of finite models compared with standard rcc models given rise from regular connected spaces these countable models have the nice property that each region can be constructed in finite steps from basic regions two interesting countable rcc models are also given one is a minimal rcc model the other is a countable sub model of the continuous space r 2

boolean connection algebras a new approach to the region connection calculus abstract the region connection calculus rcc is a well established formal system for qualitative spatial reasoning it provides an axiomatization of space which takes regions as primitive rather than as constructions from sets of points the paper introduces boolean connection algebras bcas and proves that these structures are equivalent to models of the rcc axioms bcas permit a wealth of results from the theory of lattices and boolean algebras to be applied to rcc this is demonstrated by two theorems which provide constructions for bcas from suitable distributive lattices it is already well known that regular connected topological spaces yield models of rcc but the theorems in this paper substantially generalize this result additionally the lattice theoretic techniques used provide the first proof of this result which does not depend on the existence of points in regions

reasoning about temporal relations a maximal tractable subclass of allen s interval algebra we introduce a new subclass of allen s interval algebra we call ord horn subclass which is a strict superset of the pointisable subclass we prove that reasoning in the ord horn subclass is a polynomial time problem and show that the path consistency method is sufficient for deciding satisfiability further using an extensive machine generated case analysis we show that the ord horn subclass is a maximal tractable subclass of the full algebra assuming p np in fact it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations

a fuzzy sets theoretic approach to approximate spatial reasoning relational composition based reasoning has become the most prevalent method for qualitative reasoning since allen s 1983 work on temporal intervals underlying this reasoning technique is the concept of a jointly exhaustive and pairwise disjoint set of relations systems of relations such as rcc5 and rcc8 were originally developed for ideal regions not subject to imperfections such as vagueness or fuzziness which are found in many applications in geographic analysis and image understanding this paper however presents a general method for classifying binary topological relations involving fuzzy regions using the rcc5 or the rcc8 theory our approach is based on fuzzy set theory and the theory of consonant random set some complete classifications of topological relations between fuzzy regions are also given furthermore two composition operators on spatial relations between fuzzy regions are introduced in this paper these composition operators provide reasonable relational composition based reasoning engine for spatial reasoning involving fuzzy regions