A Unified Methodology for the Generalisation of the Geometry of Features

Round 1

Reviewer 1 Report

The authors do respond to some of the comments, but not to the complete extend. Especially, comment 3 is overlooked and has not responded properly. I believe, this comment is the main part of improvement. Addressing this point increase 'Significance of Content', 'Scientific Soundness' and Interest to the readers'. At this point, I do not see much improvement at the contextual level. 

Author Response

Dear Sir, Madam,

Thank you for any comments and remarks. They allowed us to look at our considerations from a different point of view and to improve them.

Details of the answers are provided in the attachment.

Kind regards,

Joanna Bac-Bronowicz

Author Response File: Author Response.pdf

Reviewer 2 Report

Modern topic, well-structured paper, clear definition of the problems and their solutions.

Keywords are used for indexing the paper. They are the label of the manuscript. My recommendation is to avoid words with a broad meaning and words already included in the title. Only abbreviations firmly established in the field are eligible (e.g., GIS, GPS), avoiding those which are not broadly used (e.g., MRDB).

Some formatting and stylistic mistakes should be avoiding – lines 60, 61, 171, and many others.

Author Response

Dear Sir, Madam,

Thank you for any comments and remarks. They allowed us to look at our considerations from a different point of view and to improve them.

Details of the answers are provided in the attachment.

Kind regards,

Joanna Bac-Bronowicz

Author Response File: Author Response.doc

Reviewer 3 Report

Τhe manuscript is the result of a cooperative effort of scientists from various Polish institutions. It addresses an important issue in cartographic research and production that of line and area features generalization. It is noted that this is an improved version of the manuscript submitted for review earlier this year. The improvements of the new submission refer to:

1. A more analytical description of the proposed methodology and
2. The application of the proposed generalization procedure (scales s < 1) to a segment of the Vistula river and the analysis of the steps required for the implementation of the methodology in an algorithmic way.

The proposed procedure for generalization is based on well documented mathematical foundation and the analysis of the methodology helps a reader -with adequate mathematic and cartographic background- to assimilate the approach.

The authors adopt the term "contractive mapping" that is commonly used in mathematics but is not that familiar to cartographers and although it reflects the logic of the methodology presented, it is questionable whether it will be comprehensive by the average cartographer or GIS user. Authors may consider an alternative term (i.e unified, integrated ?....) for the title and use the term "contractive mapping” wherever it applies within the manuscript to establish the method. This way they will attract the interested readers/users community. 

The review of the manuscript has been rather adventurous due to fact that it is wordy and hard to read. I understand what they mean but the language used is not appropriate. There are a number of grammatical, syntactical and terminology errors that undermine the value of the paper and the importance of the work done. It is therefore indispensable for the manuscript to be edited by a professional editor.

In order to give an example of the extent of the revision required I edited the title and the abstract.

• It is suggested that the title be modified from “The application of the contractive self-mapping in the generalisation of the digital geometry of objects” to read “The application of contractive self-mapping in the generalization of the geometry of features”. In case that the authors decide not to use the term “contractive self-mapping” in the title, it could read “A unified methodology for the generalization of the geometry of features”. The alternative titles proposed are straight forward and communicate the message.

• The modified version of the abstract could be:

Development of generalization (simplification) methods for the geometry of features in digital cartography in prevailing cases consist of the improvement of existing algorithms without their
validation with respect to the similarity of feature geometry before and after the process, assessment of independence of result from the user of the algorithm, i.e. characteristics that are indispensable for automatic generalization. For preparation of a fully automatic generalization for spatial data, certain standard, unique and verifiable algorithms for particular groups of features are required. They will allow cartographers to draw features from these databases to be used directly on the maps. As a result, once collected data and their generalized unique counterparts at various scales, should constitute standardized sets together with their updating procedures. In this paper a solution is proposed, which consists of contractive self-mapping (contractor for scale s = 1) fulfilling assumptions of the Banach fixed-point theorem. The method of generalization of feature geometry using the contractive self-mapping approach is well justified  because a single update of source data can be applied to all scales simultaneously, feature data at every scale s < 1 are generalized using contractive mapping, which leads to a unique solution. Further generalization of the feature is carried out on larger scale spatial data (not necessarily source data), that reduces the time and cost of new elaboration. The main part of the article is the theoretical presentation of  objectifying the complex process of generalization of the geometry of a feature. The use of the inherent characteristics of metric spaces, narrowing mappings, Lipschitz and Cauchy conditions and Saliszczew measures as well as Banach theorems ensure the uniqueness of the generalization process. Their application to generalization makes this process objective, as it ensures that there is a single solution for portrayal of the generalized features at each scale. The present study is dedicated to researchers dealing with the theory of cartography.

Obviously this cannot be done by the reviewer for the full extent of the manuscript.

The main shortcomings of the manuscript are:

1. Evaluation of the results of the method as applied to segments of the Vistula river at various scales, with respect to line (shape) similarity and positional displacement using conventional measures (i.e. Turning Function,……, Modified Hausdorff distance, etc.) and the associated metrics. Given the conditions involved in the proposed procedure I do not expect negative results but it is necessary to evaluate the results as a proof of concept. It is pointed out that the requirement for shape similarity of the resulting line is acknowledged and emphasized by the authors in the abstract.
2. Time is a critical factor in cartographic processing/production and an assessment of the time required to implement the method on databases of varying geographical extent/size will be an additional element of the efficiency of the proposed procedure.
3. Blocks of conclusions relevant to the methodology proposed, appear in three different sections of the manuscript. More specifically they start in the following lines: line 325, line 371 and line 449. It is strongly recommended that these conclusions be included in one block and placed in the end of the manuscript.

Some additional comments

• The sentence in lines 52-54 is repeated in lines 55-57
• Line 60: rephrase to read “cartographic portrayal of……..”
• In a number of cases the verb “conserve” is used for conditions that is not right. Replace it with “hold” or other appropriate synonym (A requirement necessary for a given statement or theorem to hold)
• Line 297: replace “extremum” with “extreme”
• Line 309: replace “modernization” with “improvement” or some appropriate term
• Line 493: replace “automatization” with “automation”

Author Response

Dear Sir, Madam,

Thank you for any comments and remarks. They allowed us to look at our considerations from a different point of view and to improve them.

Details of the answers are provided in the attachment.

Kind regards,

Joanna Bac-Bronowicz

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Authors are encouraged to develop  a full fledged  application on cartographic feature generalization implementing their method. This will enable them to generalize features of different shape characteristics, derive conclusions on the efficiency of the method and finally develop databases at different scales.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

The manuscript addresses an important issue in cartographic research and production, that of line and area features generalization. 

The proposed procedure for generalization is based on documented mathematical foundation and the analysis of the methodology helps a reader -with sufficient mathematical background- to assimilate the approach.

The term "contractive mapping" that is commonly used in mathematics is not that familiar to cartographers and although it reflects the logic of the methodology presented, it is questionable whether it will be comprehensive by the average cartographer or GIS user. Authors may consider an alternative term (i.e unified?....) to establish the method and attract the interested reader community. 

The main weaknesses of the manuscript are:

1. Application of the method to a real world dataset and evaluation of the results at various scales with respect to line (shape) similarity and positional displacement using conventional measures (i.e. Turning Function,……, Modified Hausdorff distance, etc.) and the associated metrics. Given the conditions  involved in the proposed procedure I do not expect negative results but it will be good to evaluate the results as a proof of concept.
2. Time is a critical factor in cartographic processing/production and an assessment of the time required to implement the method on databases of varying extent will be an additional element of the efficiency of the proposed procedure.
3. There is a number of grammatical, syntactical and terminology errors that undermine  the value of the paper i.e.
• use of preposition “in” instead of “at” when reference is made to scale
• use of the term “surface” features instead of “area or polygon” features
• Use of the term “broken line” instead of “segmented line”
• etc…………

Conluding, editing of the manuscript by an expert editor is required.

Author Response

Dear Sir or Madam,

we kindly thank you for all comments and remarks. They allowed us to look at our considerations from a different point of view and to improve them. We have tried to take into account the comments of Reviewers.

Our article has undergone a detailed linguistic proofreading by a native speaker. All his corrections were made. We left the term "broken line" in the text as used, appearing in mathematical dictionaries and accepted by the translator as correct.

The presentation of our research results has also been modified. We gave the Table A1 more transparent form.

We decided to stick to the term "contraction" - "narrowing mapping", because it is a well-established mathematical term and because it is the essence of the proposed solution - its replacement with a more colloquial term could distract readers from the essence of the algorithm.

The main part of the article is the theoretical presentation of the possibility of objectifying the complex process of generalizing the geometry of an object. The existing methods based on graph and fractal theories or on the use of artificial intelligence do not guarantee the uniqueness of this process (the sole solution). The use of the features of metric spaces, narrowing mappings, Lipschitz and Cauchy conditions and Salishchev measures as well as Banach theorems ensure the uniqueness of the generalization process. Their application to generalization makes this process objective, as it ensures that there is a sole solution at each scale of the generalization of the object geometry. The justification for this fact, included in the presented study, is dedicated to researchers dealing with the theory of cartography and no doubt will be understandable to them.

The positive result of the test studies with the use of the proposed algorithm became a premise for starting work on the construction of an IT tool for objective generalization of the object geometry. In our opinion, its completion will be extremely valuable for practical cartography. It will also take into account the requirements for generalization defined by the INSPIRE Directive. The requirements of the Data Harmonization and Interoperability Directive are included in the timetable for further work on objectifying the generalization process. Their results, aimed primarily at the needs of practical cartography, will be successively published.

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper requires a very thorough rewrite. In its current condition, it is too hard to understand - and one cannot reproduce the work if they choose to. Authors should upload their code or software so that others can use it! 

Author Response

Dear Sir or Madam,

we kindly thank you for all comments and remarks. They allowed us to look at our considerations from a different point of view and to improve them. We have tried to take into account the comments of Reviewers.

Our article has undergone a detailed linguistic proofreading by a native speaker. All his corrections were made.

The presentation of our research results has also been modified. We gave the Table A1 more transparent form.

The main part of the article is the theoretical presentation of the possibility of objectifying the complex process of generalizing the geometry of an object. The existing methods based on graph and fractal theories or on the use of artificial intelligence do not guarantee the uniqueness of this process (the sole solution). The use of the features of metric spaces, narrowing mappings, Lipschitz and Cauchy conditions and Salishchev measures as well as Banach theorems ensure the uniqueness of the generalization process. Their application to generalization makes this process objective, as it ensures that there is a sole solution at each scale of the generalization of the object geometry. The justification for this fact, included in the presented study, is dedicated to researchers dealing with the theory of cartography and no doubt will be understandable to them.

Thus, the article describes the concept of solving the generalization problem with test results. It is our intention to present the concept in the scientific community in order to engage in a wider discussion among cartographers. The algorithm's software is under development. To emphasize that we do not consider the topic to be finished, we added point 6 to the final conclusions, citing the latest articles on the topic.

The positive result of the test studies with the use of the proposed algorithm became a premise for starting work on the construction of an IT tool for objective generalization of the object geometry. In our opinion, its completion will be extremely valuable for practical cartography. It will also take into account the requirements for generalization defined by the INSPIRE Directive. The requirements of the Data Harmonization and Interoperability Directive are included in the timetable for further work on objectifying the generalization process. Their results, aimed primarily at the needs of practical cartography, will be successively published.

Reviewer 3 Report

This paper proposes a rather adequate approach of using so-called ‘Contractive self-mapping’ and propose it as a standard in digital generalization. This is an interesting topic and can potentially fit the purposes of the submitted journal.

However, the manuscript can (should) be further improved. In general, the authors should probably

1). Improve the Introduction part; 2). Enhance the Related Work part; 3). Complement and elaborate the Methodology part; 4). Revise and better describe the Experiments and Analysis part to make it more convincing; 5). Separate (add a section) Discussion part. Furthermore, the manuscript needs to be polished by writing with academic language.

Detailed comments:

1. The research gap and its urgency is not completely opened up and clarified in the introduction part. That would be great to see a more thorough research analysis on the topic to bring the topic to its real significance.
2. Connected with the previous point, in line 54, the authors propose a solution to, however, the justification and appraisal of the proposed methods by the research have not been clarified enough. That would be good to delineate other research on the usage of ‘contractive self-mapping’ if available. Otherwise, the first-time application of the approach should be emphasized.
3. As a whole, the method clearly does simplification of features (lines, polygons, etc.), which highly overlaps (in principle) with the line simplification algorithm of Douglas and Peucker,1973 (also called as ‘Point Remove’) and Wang et al, 1998 (also called as ‘Bend Simplify’). Consequently, that would be great to know the advantages of the proposed method over the existing simplification techniques. Even the experimentational comparison of the methods would boost the scientific value and merit of the paper.
4. The minimum dimensions used by the approach (Saliszczew minimum 75 dimensions), which is ok. However, as the English version of the literature does not exist in the provided literature, it is better to list the dimensions, maybe as a table, for the sake of convenience to the reader. Or the authors could reformulate the experiments using internationally used dimensions (just advice).
5.   The is an error in line 118.
6. The quality of the figure can (should) surely be improved. Especially, Figures 2, 3, 4.

Author Response

Dear Sir or Madam,

we kindly thank you for all comments and remarks. They allowed us to look at our considerations from a different point of view and to improve them. We have tried to take into account the comments of Reviewers.

Our article has undergone a detailed linguistic proofreading by a native speaker. All his corrections were made.

Referring to the remark concerning the need to emphasize the urgency to fill the research gap, we would like to highlight: Generalisation of the object geometry using a fully automatic method is an urgent need in the process of spatial data handling according to the INSPIRE directive, in terms of their harmonisation and interoperability. The algorithms used so far in the process of data generalisation do not meet the condition of full automation, which affects the uniqueness of the result. The article presents a solution that in the process of generalising an object ensures its unambiguous (objective) result. This result was obtained using in the process:

- properties of metric space for data,

- tapering mapping using for the first time a binary tree diagram to create tapering triangles. The constricting triangles satisfy the Lipschitz condition, the Cauchy condition, the assumptions of the Banach theorem. Their sides are verified according to A. Salishchev's minimum measures, in the structure of mapping the source line segments into each other, rejected as a result of the generalization scale.

To the best of our knowledge, this is the first time this proposed approach is being used.

Advantages of the proposed method over the existing algorithms:

1. a) the generalization on each scale of the object has an unambiguous result,
2. b) the obtained result is verified by Cauchy's condition,
3. c) sides of triangles unrecognizable on a given scale are removed.

Reference [5] in English has been added, which contains the minimum dimensions used by the approach of Saliszczew.

The error on line 118 has been corrected.

The presentation of our research results has been modified. We gave them more clear form.

Summarising: The main part of the article is the theoretical presentation of the possibility of objectifying the complex process of generalizing the geometry of an object. The existing methods based on graph and fractal theories or on the use of artificial intelligence do not guarantee the uniqueness of this process (the sole solution). The use of the features of metric spaces, narrowing mappings, Lipschitz and Cauchy conditions and Salishchev measures as well as Banach theorems ensure the uniqueness of the generalization process. Their application to generalization makes this process objective, as it ensures that there is a sole solution at each scale of the generalization of the object geometry. The justification for this fact, included in the presented study, is dedicated to researchers dealing with the theory of cartography and no doubt will be understandable to them.

Thus, the article describes the concept of solving the generalization problem with test results. It is our intention to present the concept in the scientific community in order to engage in a wider discussion among cartographers. The algorithm's software is under development. To emphasize that we do not consider the topic to be finished, we added point 6 to the final conclusions, citing the latest articles on the topic.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

With respect to the authors’ response on the comments provided by the reviewer at the first round of the review process, I would like to point out the following:

The Peer-reviewer’s responsibilities toward readers amongst others are:

• To ensure that the methods are adequately detailed to allow the reader to judge the scientific merit of the studydesign and be able to replicate the study, if desired.
• To ensure that the terminology used commensurate with the internationally adopted one in the field of Cartography.

Based on the above:

• The term “broken line” for a cartographer or a GIS person means a “dashed line” and thus the term used in the manuscript does not serve the purpose.
• Likewise the term “contraction” while is a well established mathematical term I am afraid that it will not communicate the right message to the cartographic audience. Anyway I leave to the authors to decide which term they will use.

In the cover letter the authors admit that the main part of the article is a theoretical presentation. This statement must appear in both the abstract of the paper and its main body. Otherwise implementation in a software module and its results should have been provided ( see relevant comment from the 1^st round of the review).  In the concluding remarks of the paper reference should be made that the development of a software module implementing the method described is included in their plans for future work (as it is stated in the cover letter).

Last but not least the term “generalization” appears with a “z” in the title of the revised version of the paper but with an “s” in the rest of the document. 

Reviewer 3 Report

The authors agree with the comments made by the reviewers and they complemented small improvements. However, the comments made by the reviewer has not been completely covered except for some grammar correction and addition to the conclusion of the paper.

Although the authors provide responses to the review's comments in a separate form, I believe, substantial improvements are needed in the paper, especially to the previously made 'Detailed comments' 1. 2. and 3.

Thus, I cannot recommend the paper to acceptance, unless substantial improvements are made.