Point cloud segmentation for planar surface detection is a valid problem of automatic laser scans... more Point cloud segmentation for planar surface detection is a valid problem of automatic laser scans analysis. It is widely exploited for many industrial remote sensing tasks, such as LIDAR city scanning, creating inventories of buildings, or object reconstruction. Many current methods rely on robustly calculated covariance and centroid for plane model estimation or global energy optimization. This is coupled with point cloud division strategies, based on uniform or regular space subdivision. These approaches result in many redundant divisions, plane maladjustments caused by outliers, and excessive number of processing iterations. In this paper, a new robust method of point clouds segmentation, based on histogram-driven hierarchical space division, inspired by kd-tree is presented. The proposed partition method produces results with a smaller oversegmentation rate. Moreover, state-of-the-art partitions often lead to nodes of low cardinality, which results in the rejection of many points. In the proposed method, the point rejection rate was reduced. Point cloud subdivision is followed by resilient plane estimation, using Mahalanobis distance with respect to seven cardinal points. These points were established based on eigenvectors of the covariance matrix of the considered point cluster. The proposed method shows high robustness and yields good quality metrics, much faster than a FAST-MCD approach. The overall results indicate improvements in terms of plane precision, plane recall, under-, and the over-segmentation rate with respect to the reference benchmark methods. Plane precision for the S3DIS dataset increased on average by 2.6pp and plane recall-by 3pp. Both over-and under-segmentation rates fell by 3.2pp and 4.3pp.
Politechnika Łódzka. Skrypt dla szkół wyższychNa rynku podręczników znajduje się wiele tekstów do... more Politechnika Łódzka. Skrypt dla szkół wyższychNa rynku podręczników znajduje się wiele tekstów dotyczących algebry liniowej i geometrii, jednak z uwagi na nowe standardy odnoszące się do algebry liniowej na kierunkach Informatyka i fizyka warto dostosować treści i sposób wykładu do tych kierunków studiów. Z tego powodu postanowiliśmy napisać jeden podręcznik do algebry i geometrii. W I części znajdują się podstawowe zagadnienia geometrii analitycznej w przestrzeniach jedno-, dwu- i trójwymiarowej. W II części zawarliśmy podstawowe zagadnienia z algebry, nie tylko liniowej, gdyż niektóre hasła ze standardów nauczania występują zwykle w rozdziałach algebry abstrakcyjnej.[...
The present paper concerns some generalized differential equations of second order for mappings f... more The present paper concerns some generalized differential equations of second order for mappings from a subset of Banach space into a Banach space. The subject matter refers to studies of generalized differential equations of the first order submitted in [4]. Let X, Y be Banach spaces over the field R and let U, V be open subsets of X and Y, respectively. Let h\, h,2 be mappings from U into X. In this paper we study the Cauchy problem D 2 f(x)(h 2 (x), h!(x)) = F(x, Df(x)(hi(x))), xeU for mappings from a subset of a Banach space into a Banach space, which are defined in C 2 class, at a neighbourhood of nonsingular point (that is, at a neighbourhood of such point xo for which hi(xo) ^ 0 and h 2 (xo) ^ 0).
In th is p a p e r we stu d y th e problem of ex istence an d un iqu eness o f holom o rphic solu... more In th is p a p e r we stu d y th e problem of ex istence an d un iqu eness o f holom o rphic solution of th e eq uation D f (z) (h (z)) = F (z , f (z)) for 2 6 B " t *ie cond iti°n /(0) = 0 and the a ssum p tio n th a t 0 is a sing u lar p o in t (i.e. /*(0) = 0).
In 2000 J. Borsík, J. Doboš, and M. Repický characterized sums of quasi-continuous functions with... more In 2000 J. Borsík, J. Doboš, and M. Repický characterized sums of quasi-continuous functions with closed graphs. More precisely, they showed that such a sum must be Baire one star, and proved that each Baire one star function defined on a separable metric space which is Baire in the strong sense is the sum of three quasi-continuous functions with closed graphs. They showed also that not every Baire one star function defined on R is the sum of two quasi-continuous functions with closed graphs, and asked for characterization of such sums. The goal of this article is to present the required characterization.
We prove that the set of all complex series which are nonabsolutely convergent is c-algebrable. W... more We prove that the set of all complex series which are nonabsolutely convergent is c-algebrable. We establish a similar result for the set of all divergent complex series with bounded partial sums.
In this paper we consider the problem of the existenoe of the holomorphic solutions of the differ... more In this paper we consider the problem of the existenoe of the holomorphic solutions of the differential equation i)f(z)h(z) = Dh(0)f(z) for z e B n and the problem of the uniqueness of the solutions for this equation with the initial conditions f(0) =0 and Df(0} = I.
In the paper there is disscussed a notion of a density point of a Borel subset of a metric space ... more In the paper there is disscussed a notion of a density point of a Borel subset of a metric space with respect to a Borel measure fi. There are considered densities with respect to equivalent measures and density with respect to the limit of a sequence of equivalent measures. Let us start from the classical definition of a density of a measurable subset of the real line at a point XQ € R with respect to Lebesgue measure A. A number d € [0,1] is called the density of a measurable set E C R at a point xo if d= lim-. /i-o+ 2 h If d = 1 we say that XQ is a density point of a set E. We shall assume that X is a metric space, // is a Borel measure on X and XQ e X belongs to the support of fi i.e. for any ball B r with the center xo and arbitrary radius r, we have fi(B r) > 0. Moreover, let fi be finite on some ball B ro. The simple generalization of a notion of the density with respect to Lebesgue measure leads us to the following DEFINITION 1. A number d € [0,1] is called density of a Borel set A at a point XQ with respect to the measure n if "= um»< A "f>. r-»0+ ll\B r) If d = 1 we say that x$ is a fi-density point of a set A. Recall that a measure u is absolutely continuous with respect to the measure /z (i/ fx), defined on the same cr-algebra T, if from the fact n(A) = 0 it follows that v(A) = 0. We say that measures /i and is are equivalent if fi v and v fj,. It is well known, that if /x and u are cr-finite measures on
Wykonano w ramach RPBP III.30.V.0The present paper is the outcome of investigations and theoretic... more Wykonano w ramach RPBP III.30.V.0The present paper is the outcome of investigations and theoretical analysts carried out for several years, aiming at an answer to the following questions: - what should the fund of the mathematics teacher's knowledge look like, within what scope and in what way should we convey this knowledge to him? In the commencing part of the paper, we analyze critically the existing system of educating teachers of mathematics; later, we present a proposal of a structure of five-year master's studies preparing the graduates for work in the profession of a mathematics teacher. Basing ourselves on the evolved criteria of choice of mathematical contents which should be considered indispensable in educating the teachers, we present a project of the minimum of knowledge of the fundamental subjects: mathematical analysis, algebra, geometry, probability and elements of statistics, theoretical arithmetic, logic and set theory, complex analysis, topology, differen...
In the family of all measures equivalent to the Borel measure µ defined in a metric space X, we l... more In the family of all measures equivalent to the Borel measure µ defined in a metric space X, we look for measures generating the same density points (preserving µ-density at fixed point x 0 ∈ X).
In this paper we consider univalent holomorphic maps of the unit polydisk P^n into C^n. We find a... more In this paper we consider univalent holomorphic maps of the unit polydisk P^n into C^n. We find a necessary and sufficient condition for this function to be starlike. Further, we show that the class of normalized and starlike maps of the unit polydisk P^n into C^n is compact and connected.W pracy tej rozważana jest pewna podklasa klasy odwzorowań jednokrotnych holomorficznych policylindra jednostkowego w C^n. Na początku przedstawiony został pewien warunek konieczny i dostateczny na to, aby odwzorowanie było gwiaździste. Podstawowy rezultat tej pracy to wykazanie, że unormowana klasa odwzorowań gwiaździstych jest zwarta i spójna.Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukę
Gender recognition, across different races and regardless of age, is becoming an increasingly imp... more Gender recognition, across different races and regardless of age, is becoming an increasingly important technology in the domains of marketing, human-computer interaction and security. Most state-of-the-art systems consider either highly constrained conditions or relatively large databases. In either case, often not enough attention is paid to cross-racial age-invariant applications. This paper proposes a~method of hybrid classification, which performs well even with a small training set. The design of the classifier enables the construction of reliable decision boundaries insensitive to an aging model as well as to race variation. For a training set consisting of one hundred images, the proposed method reached an accuracy level of 90%, whereas the best method known from the literature, tested under the restrictions imposed on the database, achieved only 78% accuracy.
Politechnika Łódzka. Skrypt dla szkół wyższychNa rynku podręczników znajduje się wiele tekstów do... more Politechnika Łódzka. Skrypt dla szkół wyższychNa rynku podręczników znajduje się wiele tekstów dotyczących algebry liniowej i geometrii, jednak z uwagi na nowe standardy odnoszące się do algebry liniowej na kierunkach Informatyka i fizyka warto dostosować treści i sposób wykładu do tych kierunków studiów. Z tego powodu postanowiliśmy napisać jeden podręcznik do algebry i geometrii. W I części znajdują się podstawowe zagadnienia geometrii analitycznej w przestrzeniach jedno-, dwu- i trójwymiarowej. W II części zawarliśmy podstawowe zagadnienia z algebry, nie tylko liniowej, gdyż niektóre hasła ze standardów nauczania występują zwykle w rozdziałach algebry abstrakcyjnej.[...
In th i s paper we give the parametric representation of a s t a r l i k e map of the unit b a l ... more In th i s paper we give the parametric representation of a s t a r l i k e map of the unit b a l l Bn into C n . Bes ides , we prove the existence and the uniqueness of the solut ion of the equation Df(z)h(z) = f ( z ) (see [6] , Th.1) , where h e M, among loca l ly biholomorpnic maps s a t i s f y i n g the conditions Γ(0) = 0, Df(0) = I . The f i n a l part of the paper includes an estimation of the norm of the s t a r l i k e map. Let Cn stand for the space of r complex var iab les ζ = ( z ^ , z 2 , . . . , z n ) , ζ j e C , j = 1 , 2 , . . . T h e sca l a r product and the norm wil l be denoted by = > ; z.Wj and IIζII = J J = \A, re spect ive ly . The open ba l l {z j l lz-a II < r } i s denoted by B n ( a ; r ) , the unit ba l l Β η ( ϋ ; 1 ) , for short , by B n . The l e t t e r I wi l l always represent the identi ty map on C n . The c l a s s of holomorphic maps
Point cloud segmentation for planar surface detection is a valid problem of automatic laser scans... more Point cloud segmentation for planar surface detection is a valid problem of automatic laser scans analysis. It is widely exploited for many industrial remote sensing tasks, such as LIDAR city scanning, creating inventories of buildings, or object reconstruction. Many current methods rely on robustly calculated covariance and centroid for plane model estimation or global energy optimization. This is coupled with point cloud division strategies, based on uniform or regular space subdivision. These approaches result in many redundant divisions, plane maladjustments caused by outliers, and excessive number of processing iterations. In this paper, a new robust method of point clouds segmentation, based on histogram-driven hierarchical space division, inspired by kd-tree is presented. The proposed partition method produces results with a smaller oversegmentation rate. Moreover, state-of-the-art partitions often lead to nodes of low cardinality, which results in the rejection of many points. In the proposed method, the point rejection rate was reduced. Point cloud subdivision is followed by resilient plane estimation, using Mahalanobis distance with respect to seven cardinal points. These points were established based on eigenvectors of the covariance matrix of the considered point cluster. The proposed method shows high robustness and yields good quality metrics, much faster than a FAST-MCD approach. The overall results indicate improvements in terms of plane precision, plane recall, under-, and the over-segmentation rate with respect to the reference benchmark methods. Plane precision for the S3DIS dataset increased on average by 2.6pp and plane recall-by 3pp. Both over-and under-segmentation rates fell by 3.2pp and 4.3pp.
Politechnika Łódzka. Skrypt dla szkół wyższychNa rynku podręczników znajduje się wiele tekstów do... more Politechnika Łódzka. Skrypt dla szkół wyższychNa rynku podręczników znajduje się wiele tekstów dotyczących algebry liniowej i geometrii, jednak z uwagi na nowe standardy odnoszące się do algebry liniowej na kierunkach Informatyka i fizyka warto dostosować treści i sposób wykładu do tych kierunków studiów. Z tego powodu postanowiliśmy napisać jeden podręcznik do algebry i geometrii. W I części znajdują się podstawowe zagadnienia geometrii analitycznej w przestrzeniach jedno-, dwu- i trójwymiarowej. W II części zawarliśmy podstawowe zagadnienia z algebry, nie tylko liniowej, gdyż niektóre hasła ze standardów nauczania występują zwykle w rozdziałach algebry abstrakcyjnej.[...
The present paper concerns some generalized differential equations of second order for mappings f... more The present paper concerns some generalized differential equations of second order for mappings from a subset of Banach space into a Banach space. The subject matter refers to studies of generalized differential equations of the first order submitted in [4]. Let X, Y be Banach spaces over the field R and let U, V be open subsets of X and Y, respectively. Let h\, h,2 be mappings from U into X. In this paper we study the Cauchy problem D 2 f(x)(h 2 (x), h!(x)) = F(x, Df(x)(hi(x))), xeU for mappings from a subset of a Banach space into a Banach space, which are defined in C 2 class, at a neighbourhood of nonsingular point (that is, at a neighbourhood of such point xo for which hi(xo) ^ 0 and h 2 (xo) ^ 0).
In th is p a p e r we stu d y th e problem of ex istence an d un iqu eness o f holom o rphic solu... more In th is p a p e r we stu d y th e problem of ex istence an d un iqu eness o f holom o rphic solution of th e eq uation D f (z) (h (z)) = F (z , f (z)) for 2 6 B " t *ie cond iti°n /(0) = 0 and the a ssum p tio n th a t 0 is a sing u lar p o in t (i.e. /*(0) = 0).
In 2000 J. Borsík, J. Doboš, and M. Repický characterized sums of quasi-continuous functions with... more In 2000 J. Borsík, J. Doboš, and M. Repický characterized sums of quasi-continuous functions with closed graphs. More precisely, they showed that such a sum must be Baire one star, and proved that each Baire one star function defined on a separable metric space which is Baire in the strong sense is the sum of three quasi-continuous functions with closed graphs. They showed also that not every Baire one star function defined on R is the sum of two quasi-continuous functions with closed graphs, and asked for characterization of such sums. The goal of this article is to present the required characterization.
We prove that the set of all complex series which are nonabsolutely convergent is c-algebrable. W... more We prove that the set of all complex series which are nonabsolutely convergent is c-algebrable. We establish a similar result for the set of all divergent complex series with bounded partial sums.
In this paper we consider the problem of the existenoe of the holomorphic solutions of the differ... more In this paper we consider the problem of the existenoe of the holomorphic solutions of the differential equation i)f(z)h(z) = Dh(0)f(z) for z e B n and the problem of the uniqueness of the solutions for this equation with the initial conditions f(0) =0 and Df(0} = I.
In the paper there is disscussed a notion of a density point of a Borel subset of a metric space ... more In the paper there is disscussed a notion of a density point of a Borel subset of a metric space with respect to a Borel measure fi. There are considered densities with respect to equivalent measures and density with respect to the limit of a sequence of equivalent measures. Let us start from the classical definition of a density of a measurable subset of the real line at a point XQ € R with respect to Lebesgue measure A. A number d € [0,1] is called the density of a measurable set E C R at a point xo if d= lim-. /i-o+ 2 h If d = 1 we say that XQ is a density point of a set E. We shall assume that X is a metric space, // is a Borel measure on X and XQ e X belongs to the support of fi i.e. for any ball B r with the center xo and arbitrary radius r, we have fi(B r) > 0. Moreover, let fi be finite on some ball B ro. The simple generalization of a notion of the density with respect to Lebesgue measure leads us to the following DEFINITION 1. A number d € [0,1] is called density of a Borel set A at a point XQ with respect to the measure n if "= um»< A "f>. r-»0+ ll\B r) If d = 1 we say that x$ is a fi-density point of a set A. Recall that a measure u is absolutely continuous with respect to the measure /z (i/ fx), defined on the same cr-algebra T, if from the fact n(A) = 0 it follows that v(A) = 0. We say that measures /i and is are equivalent if fi v and v fj,. It is well known, that if /x and u are cr-finite measures on
Wykonano w ramach RPBP III.30.V.0The present paper is the outcome of investigations and theoretic... more Wykonano w ramach RPBP III.30.V.0The present paper is the outcome of investigations and theoretical analysts carried out for several years, aiming at an answer to the following questions: - what should the fund of the mathematics teacher's knowledge look like, within what scope and in what way should we convey this knowledge to him? In the commencing part of the paper, we analyze critically the existing system of educating teachers of mathematics; later, we present a proposal of a structure of five-year master's studies preparing the graduates for work in the profession of a mathematics teacher. Basing ourselves on the evolved criteria of choice of mathematical contents which should be considered indispensable in educating the teachers, we present a project of the minimum of knowledge of the fundamental subjects: mathematical analysis, algebra, geometry, probability and elements of statistics, theoretical arithmetic, logic and set theory, complex analysis, topology, differen...
In the family of all measures equivalent to the Borel measure µ defined in a metric space X, we l... more In the family of all measures equivalent to the Borel measure µ defined in a metric space X, we look for measures generating the same density points (preserving µ-density at fixed point x 0 ∈ X).
In this paper we consider univalent holomorphic maps of the unit polydisk P^n into C^n. We find a... more In this paper we consider univalent holomorphic maps of the unit polydisk P^n into C^n. We find a necessary and sufficient condition for this function to be starlike. Further, we show that the class of normalized and starlike maps of the unit polydisk P^n into C^n is compact and connected.W pracy tej rozważana jest pewna podklasa klasy odwzorowań jednokrotnych holomorficznych policylindra jednostkowego w C^n. Na początku przedstawiony został pewien warunek konieczny i dostateczny na to, aby odwzorowanie było gwiaździste. Podstawowy rezultat tej pracy to wykazanie, że unormowana klasa odwzorowań gwiaździstych jest zwarta i spójna.Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukę
Gender recognition, across different races and regardless of age, is becoming an increasingly imp... more Gender recognition, across different races and regardless of age, is becoming an increasingly important technology in the domains of marketing, human-computer interaction and security. Most state-of-the-art systems consider either highly constrained conditions or relatively large databases. In either case, often not enough attention is paid to cross-racial age-invariant applications. This paper proposes a~method of hybrid classification, which performs well even with a small training set. The design of the classifier enables the construction of reliable decision boundaries insensitive to an aging model as well as to race variation. For a training set consisting of one hundred images, the proposed method reached an accuracy level of 90%, whereas the best method known from the literature, tested under the restrictions imposed on the database, achieved only 78% accuracy.
Politechnika Łódzka. Skrypt dla szkół wyższychNa rynku podręczników znajduje się wiele tekstów do... more Politechnika Łódzka. Skrypt dla szkół wyższychNa rynku podręczników znajduje się wiele tekstów dotyczących algebry liniowej i geometrii, jednak z uwagi na nowe standardy odnoszące się do algebry liniowej na kierunkach Informatyka i fizyka warto dostosować treści i sposób wykładu do tych kierunków studiów. Z tego powodu postanowiliśmy napisać jeden podręcznik do algebry i geometrii. W I części znajdują się podstawowe zagadnienia geometrii analitycznej w przestrzeniach jedno-, dwu- i trójwymiarowej. W II części zawarliśmy podstawowe zagadnienia z algebry, nie tylko liniowej, gdyż niektóre hasła ze standardów nauczania występują zwykle w rozdziałach algebry abstrakcyjnej.[...
In th i s paper we give the parametric representation of a s t a r l i k e map of the unit b a l ... more In th i s paper we give the parametric representation of a s t a r l i k e map of the unit b a l l Bn into C n . Bes ides , we prove the existence and the uniqueness of the solut ion of the equation Df(z)h(z) = f ( z ) (see [6] , Th.1) , where h e M, among loca l ly biholomorpnic maps s a t i s f y i n g the conditions Γ(0) = 0, Df(0) = I . The f i n a l part of the paper includes an estimation of the norm of the s t a r l i k e map. Let Cn stand for the space of r complex var iab les ζ = ( z ^ , z 2 , . . . , z n ) , ζ j e C , j = 1 , 2 , . . . T h e sca l a r product and the norm wil l be denoted by = > ; z.Wj and IIζII = J J = \A, re spect ive ly . The open ba l l {z j l lz-a II < r } i s denoted by B n ( a ; r ) , the unit ba l l Β η ( ϋ ; 1 ) , for short , by B n . The l e t t e r I wi l l always represent the identi ty map on C n . The c l a s s of holomorphic maps
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