Made Windu

Antara Kesiman

Jean-Christophe Burie
email: jcburie@univ-lr.fr

Jean-Marc Ogier
email: jean-marc.ogier@univ-lr.fr

Gusti Ngurah Made

Agus Wibawantara
email: agus.wibawantara@undiksha.ac.id

I Made

Gede Sunarya
email: sunarya@undiksha.ac.id

The First Handwritten Balinese Palm Leaf Manuscripts Dataset

Keywords: Balinese script, palm leaf manuscript, ground truth, image, dataset I

We present the AMADI_LontarSet, the first handwritten Balinese palm leaf manuscript dataset. It includes three components of dataset as follows: binarized images ground truth dataset, word annotated images dataset, and isolated character annotated images dataset. The dataset was constructed from a hundred pages of randomly selected collections of palm leaf manuscripts from Bali, Indonesia. The dataset is publicly available for scientific use.

INTRODUCTION

Ancient manuscripts record many important knowledges about world civilization histories. These manuscripts are a very valuable cultural heritage which contains a wide variety of social cultural life aspects. In Southeast Asia, most of the ancient manuscripts are discovered in the form of palm leaf manuscripts. They are written on a dried palm leaf by using a sharp pen (which looks like a small knife) and colored with natural dyes. The existence of palm leaf manuscripts in Southeast Asia is also very important both in term of quantity and variety of historical contents. It attracts the historians, philologists, and archeologists to discover more about the ancient ways of life. But unfortunately, there is only a limited access to the content of the manuscripts, because of the linguistic difficulties and the fragility of the document.

Therefore, the digitization and indexing projects for palm leaf manuscripts were proposed [START_REF] Kesiman | An Initial Study On The Construction Of Ground Truth Binarized Images Of Ancient Palm Leaf Manuscripts[END_REF][START_REF] Kesiman | An Analysis of Ground Truth Binarized Image Variability of Palm Leaf Manuscripts[END_REF]. They work not only to digitize the palm leaf manuscripts, but also to develop an automatic analysis, transcription and indexing system for the manuscripts. The main objectives are to preserve the cultural heritages, and to open a wider access to the content of manuscripts for all scholars in the world. To achieve those objectives, ancient palm leaf manuscripts finally received great attention from researchers in the field of document image analysis [START_REF] Kesiman | An Initial Study On The Construction Of Ground Truth Binarized Images Of Ancient Palm Leaf Manuscripts[END_REF][START_REF] Kesiman | An Analysis of Ground Truth Binarized Image Variability of Palm Leaf Manuscripts[END_REF][START_REF] Chamchong | Character segmentation from ancient palm leaf manuscripts in Thailand[END_REF][START_REF] Chamchong | Comparing Binarisation Techniques for the Processing of Ancient Manuscripts[END_REF]. Nowadays, the development of document analysis methods for palm leaf manuscripts is considered as a major challenge for handwritten document analysis. The challenges range wide from binarization process, character and text recognition tasks, to the word spotting methods.

In order to develop and to evaluate the performance of the document analysis methods, the dataset and the corresponding ground truth data are required. Based on our knowledge, there is no existing public dataset and ground truth image for palm leaf manuscripts. Therefore, creating a new dataset and ground truth image for palm leaf manuscripts was a necessary step for the research community. Under the scheme of the AMADI (Ancient Manuscripts Digitization and Indexation) Project, in this paper, we present the AMADI_LontarSet, the first handwritten Balinese palm leaf manuscript dataset. It includes three components of dataset as follows: binarized images ground truth dataset, word annotated images dataset, and isolated character annotated images dataset. The dataset is constructed from a hundred pages of randomly selected collections of palm leaf manuscripts from Bali, Indonesia.

This paper is organized as follow: Section II gives a brief description about Balinese script on the collection of palm leaf manuscripts and the challenges for document analysis. Section III presents a brief description about the corpus of palm leaf manuscripts and the digitization process. The ground truth construction for the AMADI_LontarSet is described in Section IV. Conclusions with some prospects for the future works are given in Section V.

II. PALM LEAF MANUSCRIPTS

A. The Collection of Palm Leaf Manuscripts from Bali, Indonesia

Bali has a great social and cultural history dating back several hundred years ago. Many literary texts of the Balinese were written on dried and treated palm leaves, called Lontar. The palm leaves are held and linked together by a string that passes through the central holes and knotted at the outer ends. Lontars store various forms of knowledge and historical record of the social life of Balinese cultures long ago. The content varies from ordinary texts to the most sacred writings. With a great influence from Indian culture, the Balinese manuscripts content were mostly based on the famous Indian epics of Ramayana and Mahabharata. Many Lontars contain information on important issues such as medicines and village regulations that are used as daily guidance, including texts on religion, holy formulae, rituals, family genealogies, law codes, treaties on medicine, arts and architecture, calendars, prose, poems and even magics. But unfortunately, many Lontars discovered are the collection of the museum and private family that has been in a state of disrepair due to age and due to inadequate storage conditions.

B. The Writing in Balinese Script

To create a Lontar, the texts were inscribed with a small knife-like pen (a special tool called Pengerupak). It is made of iron, with its tip sharpened in a triangular shape so it can make both thick and thin inscriptions. The manuscripts were then scrubbed by a natural dyes to leave a black color on the scratched part as text. The Balinese palm leaf manuscripts were written in Balinese script in Balinese language. Writing in Balinese script, there is no space between words in a text line. Some characters are written on upper baseline or under the baseline of text line (Fig. 1). Lontars were written in the ancient literary texts composed in the old Javanese language of Kawi and Sanskrit. Balinese script is considered to be one of the complex scripts from Southeast Asia. The alphabet and numeral of Balinese script is composed of ±100 character classes including consonants, vowels, diacritics, and some other special compound characters. In reality, the majority of Balinese have never read any Lontar because of language obstacles as well as tradition which perceived them as sacrilege.

C. The Challenges of Document Analysis for Palm Leaf Manuscript Images

Due to its specific characteristics, palm leaf manuscripts are providing new challenges in document analysis. Usually, palm leaf manuscripts are of poor quality since the documents have degraded over time due to storage conditions (Fig. 2). Natural materials from palm leaves certainly cannot fight against time, and therefore the process of digitizing and indexing Lontars are very important. The palm leaf manuscripts contain discolored parts and artefacts due to aging and low intensity variations or poor contrast, random noises, and fading [START_REF] Kesiman | An Initial Study On The Construction Of Ground Truth Binarized Images Of Ancient Palm Leaf Manuscripts[END_REF]. Several deformations in the character shapes are visible due to the merges and fractures of the use of nonstandard fonts, varying space between letters, and varying space between lines. It is known that the similarities of distinct character shapes, the overlaps, and interconnection of the neighboring characters further complicate the problem of OCR system [START_REF] Arica | Optical character recognition for cursive handwriting[END_REF]. One of the main problem faced when dealing with segmented handwritten character recognition is the ambiguity and illegibility of the characters [START_REF] Blumenstein | A novel feature extraction technique for the recognition of segmented handwritten characters[END_REF]. This characteristics provide a suitable challenge for testing and evaluation of robustness for feature extraction methods which were already proposed for character recognition. Balinese scripts on palm leaf manuscripts offer a real new challenge in document analysis system development.

III. CORPUS AND DIGITIZATION PROCESS

A. Location and Source of Collection

Our first corpus of palm leaf manuscript images are the sample images of the palm leaf manuscripts from Bali, Indonesia. It is hard to estimate the number of the whole collection of palm leaf manuscript in Bali because most of the palm leaf manuscript collections are kept by the private family as a private collection. For this research, in order to obtain the variety of the manuscript images, the sample images were collected from 23 different collections (contents), which come from 5 different locations (regions): 2 museums and 3 private families. It consists of randomly selected 10 collections from Museum Gedong Kertya, City of Singaraja, Regency of Buleleng, North Bali, Indonesia, 4 collections from manuscript collections of Museum Bali, City of Denpasar, South Bali, 7 collections from the private family collection from Village of Jagaraga, Regency of Buleleng, and 2 others collections from private family collections from Village of Susut, Regency of Bangli and from Village of Rendang, Regency of Karangasem. From those 23 collections, we captured 393 pages of palm leaf manuscript. A summary of the collection is listed in Table I.

B. Camera and Digitization Support

To capture the manuscript images, we used a Canon EOS 5D Mark III camera. The camera settings are as follows [START_REF] Kesiman | An Analysis of Ground Truth Binarized Image Variability of Palm Leaf Manuscripts[END_REF]: F-stop: f/22 (diafragma), exposure time: 1/50 sec, ISO speed: ISO-6400, focal length: 70 mm, flash: On -1/64, distance to object: 76 cm, focus: Quick mode -Auto selection 'On'. We also designed a black box camera support by wood to avoid the irregular lighting/luminance condition and to fits our semi outdoor capturing location (Fig. 3). This camera support was optimally designed to be used under some restricted conditions given by the museum or the owner of the manuscripts. Two additional light are added inside the black box support with White Neon 50 cm 20 watt.

Thumbnail samples of the captured images are showed in Fig. 4. To digitize large collections of palm leaf manuscript and to place them online, the philologists consider the quality of these images are good enough.

IV. GROUND TRUTH CONSTRUCTION

A. Binarized Images Ground Truth Dataset

Binarization process is one of the early and important stage in document analysis pipeline, is also a real challenge for palm leaf manuscripts. Some document analysis methods still require a good binarized image as a preliminary condition. In order to evaluate and to select an optimal binarization method, the ground truth binarized image is needed. Therefore, creating the binarized images ground truth dataset for palm leaf manuscripts is a necessary step in our research.

In our previous work [START_REF] Kesiman | An Initial Study On The Construction Of Ground Truth Binarized Images Of Ancient Palm Leaf Manuscripts[END_REF], we proposed a specific semilocal binarization scheme to overcome the ground truth creation difficulty on degraded and low quality palm leaf manuscript images (Fig. 5). This scheme will help as the initial binarization process for the semi-automatics framework for construction of ground truth binarized image (Fig. 6). This framework is based on the one used to build the database in DIBCO competition series [START_REF] Ntirogiannis | Performance Evaluation Methodology for Historical Document Image Binarization[END_REF]. The idea of our 'semi-local' concept is to apply a powerful global binarization method on only precise local character area. The first initial binarization process is needed to optimally separate text from the background, and it provides a first binary image for the skeletonizing process of the characters on manuscript. Figure 6. Ground truth construction procedure used for DIBCO series [START_REF] Ntirogiannis | Performance Evaluation Methodology for Historical Document Image Binarization[END_REF] In this framework, human intervention plays a very important task by performing the manual correction of the character skeletons based on character edges (detected using Canny algorithm [START_REF] Canny | A Computational Approach to Edge Detection[END_REF]). In order to purely measure the variability of human subjectivity in our ground truth creation, for some images, we did not apply any initial binarization and skeletonization methods. The skeletonization process is completely performed by human. More than 70 students from the Department of Informatics Education, Ganesha University of Education, Singaraja Bali, were asked to trace manually the skeleton of the Balinese character found in palm leaf manuscript image with PixLabeler tool [START_REF] Saund | PixLabeler: User Interface for Pixel-Level Labeling of Elements in Document Images[END_REF]. One student worked with two different images, and one image was ground truthed by two different students. These two manually skeletonized image will be reskeletonized with Matlab function bwmorph 1 to make sure that the skeleton is only one pixel wide.

The final estimated ground truth binarized image is then automatically constructed by dilating the skeleton image, constrained by the character edges. The skeleton is dilated until Canny edges intersect each binarized component of the dilated skeleton in a ratio of 0.1. This value of minimal ratio between number of pixels in intersection of Canny edge and number of pixels of the dilated skeleton is found based on our empirical experiment and observation on the thickness of the character stroke in our manuscripts [START_REF] Kesiman | An Analysis of Ground Truth Binarized Image Variability of Palm Leaf Manuscripts[END_REF]. Table II shows the summary of binarized images ground truth dataset for the AMADI_LontarSet. For the training-based binarization method, we divide our dataset into two subset: 50 images for training and 50 images for testing. Fig. 7 shows some samples of binarized images ground truth from our dataset. For more detail about the analysis of ground truth binarized image variability of palm leaf manuscripts, please refer to our previous work in [START_REF] Kesiman | An Analysis of Ground Truth Binarized Image Variability of Palm Leaf Manuscripts[END_REF].

B. Word Annotated Images Dataset

To create the word annotated ground truth dataset of the manuscript, we asked a collaborative work between the Balinese script philologists, students from the Department of Informatics, and students from the Department of Balinese Literature. The philologists read the manuscripts and create the Latin transcription. Based on this Latin transcription, a pair of students (one student in Informatics and one student in Balinese Literature) works together to segment and to annotate each word in manuscripts. The validation and correction of word annotation are done based on the expertise of the philologists. Any further discussion remains open between the philologists and the ground truthers to correct and to validate the transcription while the annotation process.

We used ALETHEIA2 , an advanced document layout and text ground-truthing system [START_REF] Clausner | Aletheia -An Advanced Document Layout and Text Ground-Truthing System for Production Environments[END_REF], to segment and to annotate the words (Fig. 8). After the segmentation and the annotation process, the manuscript images are then cropped based on word polygon coordinates in the XML file produced by ALETHEIA (Fig. 9). For all word annotated images in this dataset, we use the filename format as follows:

where word indicates the word string of this word segment, filename indicates the original manuscript image of this word segment, idword indicates the id of this word segment (used only for Aletheia software), cTL indicates column coordinates of top left point for this word segment, rTL indicates row coordinates of top left point for this word segment, cBR indicates column coordinates of bottom right point for this word segment, rBR indicates row coordinates of bottom right point for this word segment. The image coordinates for column=1 and row=1 are considered as the pixel on the top left corner of the image. Table III shows the summary of word annotated images dataset for the AMADI_LontarSet.

C. Isolated Character Annotated Images Dataset

By using the collection of word annotated images which were produced in our previous ground truthing process, we collected our isolated handwritten Balinese character dataset. First, we applied Otsu [START_REF] Pratikakis | ICDAR 2013 Document Image Binarization Contest (DIBCO 2013)[END_REF][START_REF] Messaoud | A design of a preprocessing framework for large database of historical documents[END_REF] binarization method to all word patch images. We automatically extracted all connected component found on the binarized word patch images. Our Balinese philologists then annotated manually all connected components that represent a correct character in Balinese script. To facilitate the work of the philologists, we developed a simple web based user interface for this character annotation process (Fig. 10). This interface shows all character segments which are automatically segmented from each word annotated image based on character component extraction. With this web-based interface, more than one philologist can work together to verify, to correct and to validate the annotation of the characters. All annotated characters are also displayed in group based on their given class. A hyperlink from each annotated character to their corresponding word annotated images is provided to allow the philologists to verify and to correct the annotation (Fig. 11). All patch images that have been segmented and annotated at character level will serve as our isolated character dataset. Table IV shows the summary of isolated character annotated images dataset for the AMADI_LontarSet. The number of sample images for each classes is different. Some classes are frequently found in our collection of palm leaf manuscripts, but some others are rarely used. Thumbnail samples of these character annotated images are showed in Fig. 12. Fig. 13 shows the overall scheme of ground truth construction for all dataset of palm leaf manuscript images.

V. CONCLUSIONS AND FUTURE WORKS

The development of document analysis methods for palm leaf manuscripts is considered as a major challenge for handwritten document analysis. In order to develop and to evaluate the performance of the document analysis methods, the dataset and the corresponding ground truth data for palm leaf manuscripts is necessary. We present the AMADI_LontarSet, the first handwritten Balinese palm leaf manuscript dataset. It includes three components of dataset as follows: binarized images ground truth dataset, word annotated images dataset, and isolated character annotated images dataset. The whole dataset will be publicly available for scientific use after the ICFHR 2016 conference on http://amadi.univ-lr.fr/ICFHR2016_Contest/. For the future works, we will develop the dataset in term of data quantity and variety to be able to provide sufficiently a larger train data set for document analysis methods.

Figure 1 .

 1 Figure 1. Balinese script on palm leaf manuscripts

Figure 2 .

 2 Figure2. The degradations on palm leaf manuscripts[START_REF] Kesiman | An Initial Study On The Construction Of Ground Truth Binarized Images Of Ancient Palm Leaf Manuscripts[END_REF]

Figure 3 .Figure 4 .

 34 Figure 3. Camera support for digitizing process of palm leaf manuscripts

Figure 5 .

 5 Figure5. Semi-local binarization scheme[START_REF] Kesiman | An Initial Study On The Construction Of Ground Truth Binarized Images Of Ancient Palm Leaf Manuscripts[END_REF]

Figure 8 .Figure 9 .

 89 Figure 8. Word annotation with ALETHEIA

Figure 10 .Figure 11 .

 1011 Figure 10. Screenshot of web based user interface for the character annotation process

Figure 12 .Figure 13 .

 1213 Figure 12. Samples of character-level annotated patch images of Balinese script on palm leaf manuscripts

TABLE I .

 I COLLECTION OF PALM LEAF MANUSCRIPTS FROM BALI, INDONESIA

				Nb of
	Location	Collection Code	Content	captured
				pages
		IIA-10-1534	Awig-awig Desa Tunju	8
		IIA-5-789	Sima Desa Tejakula	8
		IIB-2-180	Dewa Sasana	8
			Panugrahan
		IIIB-12-306	Bhatara Ring	8
	Museum Gedong		Pura Pulaki
	Kertya, Singaraja	IIIB-42-1526	Buwana	8
	(10 collections)	IIIB-45-2296	Pambadah	8
		IIIC-19-1293	Krakah Sang Graha	8
		IIIC-20-1397	Taru Pramana	8
		IIIC-23-1506	Siwa Kreket	8
			Tikas
		IIIC-24-1641	Patanganan	8
			Weda
		MB-AdiParwa(Purana)-5338.2-IV.a	Adi Parwa (Purana)	40
	Museum Bali, Denpasar	MB-AjiGriguh-5783-107.2	Aji Griguh	20
	(4 collections)	MB-	Arjuna Wiwaha-
		ArjunaWiwaha-	Grantang Basa	30
		GrantangBasaII	II
		MB-TaruPramana	Taru Pramana	40
		JG-01	Unknown	16
		JG-02	Unknown	10
	Village of Jagaraga,	JG-03	Unknown	16
	Buleleng	JG-04	Unknown	12
	(7 collections)	JG-05	Unknown	8
		JG-06	Unknown	5
		JG-07	Unknown	10
	Village of Susut,
	Bangli	Bangli	Sabung Ayam	82
	(1 collection)
	Village of Rendang, Karangasem (1 collection)	WN	Surat Jual Beli Tanah	24
		TOTAL		393

TABLE II

 II

		.	SUMMARY OF BINARIZED IMAGES GROUND TRUTH
			DATASET FOR THE AMADI_LONTARSET
	No.		Data		Format	Qty.
	1.	Original Manuscript	Images	of	RGB Color image -JPG	100 images
	2.	Binarized Ground Truth Image (1 st ground truther)	Binary image -BMP	100 images
	3.	Binarized Ground Truth Image (2 nd ground truther)	Binary image -BMP	100 images

1 http://fr.mathworks.com/help/images/ref/bwmorph.html Figure 7. Samples of binarized images ground truth dataset

TABLE III .

 III SUMMARY OF WORD ANNOTATED IMAGES DATASET FOR THE AMADI_LONTARSET

	No.	Data	Format	Qty.
	1.	Training Set: Original Images of Manuscript	RGB Color image -JPG	130 images
	2.	Training Set: Transcription of manuscript of No 1	TXT	130 filetexts
	3.	Training annotated images of No 1 Set: Word	RGB Color image -JPG	15,022 images
	4.	Testing Images of Manuscript Set: Original	RGB Color image -JPG	100 images
	5.	Testing Set: Transcription of manuscript of No 4	TXT	100 filetexts
	6.	Testing annotated images of No 4 Set: Word	RGB Color image -JPG	10,475 images
	7.	Testing Set: Selected word annotated images as query-by-example	RGB Color image -JPG	36 images
	8.	Testing Set: Ground truth images for all query images of No 7	RGB Color image -JPG	257 images

TABLE IV

 IV

		.	SUMMARY OF BINARIZED IMAGES GROUND TRUTH
			DATASET FOR THE AMADI_LONTARSET
	No.		Data	Format	Qty.
	1.	Training Set: Character annotated images	RGB Color image -JPG	133 classes 11,710 images
	2.	Testing Set: Character annotated images	RGB Color image -JPG	133 classes 7,673 images

http://www.primaresearch.org/tools/Aletheia

ACKNOWLEDGMENT

The authors would like to thank Museum Gedong Kertya, Museum Bali, and all families in Bali, Indonesia, for providing us the samples of palm leaf manuscripts, and the students from the Department of Informatics Education and the Department of Balinese Literature, Ganesha University of Education for helping us in ground truthing process for this research project. This work is also supported by the DIKTI BPPLN Indonesian Scholarship Program and the STIC Asia Program implemented by the French Ministry of Foreign Affairs and International Development (MAEDI).


Jean-Christophe Burie
email: jean-christophe.burie@univ-lr.fr

Mickael Coustaty
email: mickael.coustaty@univ-lr.fr

Setiawan Hadi

Made Windu

Antara Kesiman

Jean-Marc Ogier
email: jean-marc.ogier@univ-lr.fr

Erick Paulus

Kimheng Sok

I Made

Gede Sunarya

Dona Valy

ICFHR 2016 Competition on the Analysis of Handwritten Text in Images of Balinese Palm Leaf Manuscripts

Keywords: Balinese script, palm leaf manuscript, binarization, query-by-example word spotting, isolated character recognition, performance evaluation

This paper presents the results of the Competition on the Analysis of Handwritten Text in Images of Balinese Palm Leaf Manuscripts that was organized in the context of the 15 th International Conference on Frontiers in Handwriting Recognition (ICFHR-2016). This competition provides a suitable challenge for testing and evaluation of robustness for some methods, image features and descriptors which were already proposed for handwritten text analysis of document image. In this competition, three different challenges in document analysis of palm leaf manuscript images are proposed: Challenge 1: Binarization of Palm Leaf Manuscript Images, Challenge 2: Query-by-Example Word Spotting on Palm Leaf Manuscript Images, and Challenge 3: Isolated Character Recognition of Balinese Script in Palm Leaf Manuscript Images. The first handwritten Balinese palm leaf manuscript dataset, the AMADI_LontarSet, is used for performance evaluation. This paper describes the competition details including the dataset creation and the ground truth construction, the evaluation measures used, a short description of each participant as well as the performance of the all submitted methods.

INTRODUCTION

Palm leaf manuscripts offer a new challenge in document image analysis system due to the physical characteristics and conditions of the manuscripts. The palm leaf manuscripts contain discolored parts and artefacts due to aging and low intensity variations or poor contrast, random noises, and fading. Several deformations in the character shapes are visible due to the merges and fractures of the use of nonstandard fonts, varying space between letters, and varying space between lines [START_REF] Kesiman | An Analysis of Ground Truth Binarized Image Variability of Palm Leaf Manuscripts[END_REF][START_REF] Kesiman | An Initial Study On The Construction Of Ground Truth Binarized Images Of Ancient Palm Leaf Manuscripts[END_REF].

This competition tries to bring added value to digitized palm leaf manuscripts by developing methods to analyze and access quickly and efficiently to the content of manuscript and to make palm leaf manuscript more accessible, readable and understandable to a wider audience. In this competition, three different challenges in document analysis of palm leaf manuscript images are proposed: Challenge 1: Binarization of Palm Leaf Manuscript Images, Challenge 2: Query-by-Example Word Spotting on Palm Leaf Manuscript Images, and Challenge 3: Isolated Character Recognition of Balinese Script in Palm Leaf Manuscript Images.

The three challenges on this competition represent three problems which are still challenging and are still an open question on handwritten text analysis of document image especially for palm leaf manuscript images. The Balinese palm leaf manuscripts were written in Balinese script in Balinese language. In the scope of this competition, we will focus on scripts written on palm leaf whose characters are even more elaborate in ancient written form. The manuscript datasets used in this competition, the AMADI_LontarSet, are the sample images of the palm leaf manuscripts from Bali, Indonesia. In order to obtain the variety of the manuscript images, the sample images were collected from 23 different collections (contents), which come from five different locations (regions): two museums and three private families. It consists of randomly selected ten collections from Museum Gedong Kertya, City of Singaraja, Regency of Buleleng, North Bali, Indonesia, four collections from Museum Bali, City of Denpasar, South Bali, seven collections from a private family collection from Village of Jagaraga, Regency of Buleleng, and two others collections from a private family collections from Village of Susut, Regency of Bangli and from Village of Rendang, Regency of Karangasem. From those 23 collections, we captured 393 pages of palm leaf manuscript. The description of dataset for each challenge is presented in each section of the challenge. This competition provides a suitable challenge for testing and evaluation of robustness for some methods, image features and descriptors which were already proposed for handwritten text analysis of document image. All researchers were invited to participate in one or more challenges. This paper is organized as follow: Section II gives a brief description about the participants. Section III-V present the detail description of each challenge. Finally, some conclusions are given in Section VI.

II. THE PARTICIPANTS

III. CHALLENGE 1: BINARIZATION OF PALM LEAF MANUSCRIPT IMAGES

A. Description of the Challenge

This challenge is focused on the binarization method for palm leaf manuscript images. The binarization problem is still challenging and is still an open question especially for palm leaf manuscript images. Visually, several alternative well-known binarization algorithms do not provide a good binarized image for palm leaf manuscript images. They extract unrecognizable characters on palm leaf manuscripts with noise. Therefore, to separate text (and, if any, graphic) from the background of palm leaf manuscript images, a specific and adapted binarization technique is required. The input of this challenge is a set of original color images of palm leaf manuscript, and the output is the binarized image of the manuscript.

B. Dataset

To create the ground truth binarized image of palm leaf manuscript, we adopted a semi-automatics framework for construction of ground truth binarized image [START_REF] Kesiman | An Initial Study On The Construction Of Ground Truth Binarized Images Of Ancient Palm Leaf Manuscripts[END_REF]. For our manuscript collection, the skeletonization process is completely performed by human. The skeletons of the Balinese character (and, if any, graphic) in palm leaf manuscript image were traced and drawn manually with PixLabeler tool [START_REF] Saund | PixLabeler: User Interface for Pixel-Level Labeling of Elements in Document Images[END_REF]. The skeletons are then automatically processed to create the estimated ground truth binarized image of the manuscript. Human subjectivity has a great effect in producing a variability of ground truth binarized image. This phenomena becomes much more visible when we are working on ancient type manuscript which is still hard to be ground truthed even by human. Therefore, for our dataset, one manuscript was ground truthed by two different ground truthers. And for the binarization challenge in this competition, we will evaluate each binarized image with two different ground truth binary images. The dataset is partitioned into training and test subsets. For the training subset, we have provided 50 original images, 50 ground truth binary images Version 1 (from the 1 st ground truther) and 50 ground truth binary images Version 2 (from the 2 nd ground truther) (Fig. 1). For the testing subset, 50 original images (different from the training subset) have been provided. (2) TP, defined as true positive, occurs when the image pixel is labeled as foreground and the ground truth is also. FP, defined as false positive, occurs when the image pixel is labeled as foreground but the ground truth is labeled as background. FN, defined as false negative, occurs when the image pixel is labeled as background but the ground truth is labeled as foreground.

C MSE PSNR = ( 5
)
where C is defined as 1, the difference between foreground and background colors in the case of binary image. A higher PSNR indicates a better match.

Negative Rate Metric (NRM): NRM is defined from negative rate of false negative (NRFN) and negative rate of false positive (NRFP).

FN FN FN TP NR + = ( 6
)
FP FP FP TN NR + = (7)
TN, defined as true negative, occurs when both the image pixel and ground truth are labeled as background. The definitions of TP, FN, and FP are the same than the ones given for the F-Measure.

A lower NRM indicates a better match.

For each binarization metric evaluated on each ground truth binary images, we rank the participant's score. We then assign point, from 1 (best result) to N (worst result, N is the number of participants). All points from 3 binarization metrics evaluated on 2 different ground truth binarized images of each participant will be accumulated to decide the winner.

D. Participant Methods

Group 1: First, they use two neural network classifiers C1 and C2 to classify each pixel as background or not. Two binarized images B1 and B2 are got in this step. C1 is a rough classifier which tries to detect all the foreground pixels while probably making mistakes for some background pixel. C2 is an accurate classifier which should not classify the background pixel as foreground pixel while probably missing some foreground pixels. Second, they join this two binary images to get the final classification result. In this step, they use each foreground pixel in C2 as a seed and find all the foreground pixels in B1 and B2 which is connected with the seed pixel. All the foreground pixels in B1 which is not connected to any seed pixel in B2 are eliminated. The output image in this step is denoted as B3. Finally, the skeleton image of B3 is extracted and the dilated skeleton image is the final binary image of the input image. In the training stage, they set the structure of C1 and C2 as 124x100x100x1 and 221x100x100x1, respectively. All the transfer functions were set as the sigmoid function. In C1, the input feature fi of each pixel Pi is the combination of the RGB values of Pi and the subtractions between the gray value of Pi and the neighborhoods Pj, j=1,...,121. Neighborhoods are the pixels in the 11x11 window with Pi as the window center. In C2, the feature fi of each pixel Pi is the combination of the gradient features [START_REF] Liu | Online and offline handwritten Chinese character recognition: Benchmarking on new databases[END_REF] around Pi and the subtractions between the gray value of Pi and the neighborhoods Pj,j=1,...,121. In the experiment, they used a 45x45 image block around Pi to extract the gradient feature. The image block is divided into 5x5 sub-blocks and 4 direction gradient features are extracted in each sub-block.

Group 2: They employ a Fully Convolutional Network (FCN). It takes a color sub image as input and outputs the probability that each pixel in the sub image is part of the foreground. The FCN is pre-trained on normal handwritten document images with automatically generated "ground truth" binarizations (using the method of Wolf et al [START_REF] Wolf | Text localization, enhancement and binarization in multimedia documents[END_REF]). The FCN is then fine-tuned using DIBCO and HDIBCO competition images and their corresponding ground truth binarizations. Finally, the FCN is fine-tuned again on the provided Balinese Palm Leaf images. For inference, the pixel probabilities of foreground are efficiently predicted for the whole image at once and thresholded at 0.5 to create a binarized output image.

Group 3: The submitted method adopts Lu et al.'s method [START_REF] Lu | Document image binarization using background estimation and stroke edges[END_REF] to estimate the document background based on the polynomial smoothing. The background is estimated by fitting a polynomial function vertically and horizontally. The estimated background is then used to compensate the contrast of the input document image as described in [START_REF] Lu | Document image binarization using background estimation and stroke edges[END_REF]. After that, they apply the local contrast evaluated by the local maximum and minimum [START_REF] Su | Robust Document Image Binarization Technique for Degraded Document Images[END_REF] to further suppress the background variation on the normalized image. The text stroke edge pixels in the processed image can then be segmented by a global threshold. Finally, the text pixels are classified based on the following criteria: 1) There are text stroke edge pixels existing within a local window of the text pixel, 2) The intensity of the text pixel should be similar to the text stroke edge pixel.

Group 4: They proposed a method named: Hue segmented local contrast binarization. Palm Leaf RGB image is converted into HSV image. Hue is used to segment the foreground and the background from the image. The boundary between the foreground and the background is used as boundary image. The RGB image is combined together to form a gray image using the peak position in the individual histogram as the scaling parameter. The gray image is converted to a local contrast image using Weiner filter. The local contrast image is binarized using Sauvola's threshold N=32,k=0.1, and R=128. The binarized image is filtered using the boundary image and the threshold based on the area, the height, and the width of individual connected component in the image.

E. Results and Analysis

The evaluation results for all submitted methods are presented in Table I. We calculated the average score of each evaluation measure from the 50 images of testing subset with two binary ground truth images. The rank scores for each group are presented in Table II. The method proposed by Group 2 outperforms all other methods in all evaluation measures.

A. Description of the Challenge

Word spotting system is one of the most demanding system which has to be developed for the collection of palm leaf manuscript images. This system will facilitate user to find word patch images in all collection of palm leaf manuscript images with a single keyword patch image as a query image. Many image features and descriptors have been proposed to perform the word spotting task. The characteristics of palm leaf manuscripts provide a suitable challenge for testing and evaluation of some image features and descriptors which were already proposed for word spotting methods. Writing in Balinese script, there is no space between words in a text line and some characters are written on upper baseline or under the baseline of text line. The input of this challenge is a set of word-level query patch color images and a set of original color images of palm leaf manuscript. The expected output is a set of spotting area coordinates for each query which are found in the original palm leaf manuscript images.

B. Dataset

To create the word-level annotated ground truth dataset of the manuscript, we asked the Balinese philologists, the students in informatics, and the students in Balinese literature to work together to segment and to annotate the word in manuscript with ALETHEI 1 , an advanced document layout and text ground-truthing system [START_REF] Clausner | Aletheia -An Advanced Document Layout and Text Ground-Truthing System for Production Environments[END_REF]. The dataset is partitioned into training and test subsets. For the training subset, we have provided 130 original images and the corresponding 15,022 word-level annotated patch images (Fig. 2). For the testing subset, 100 original images (different from the training subset) and 36 word-level annotated patch images as query test have been provided. 1 http://www.primaresearch.org/tools/Aletheia

C. Performance Evaluation

We calculated Recall and Precision of spotting area based on ground truth word-level annotated patch images of the testing subset. A spotting area is considered as relevant if it overlaps more than 50% of a ground truth word-level patch area containing the same query word and the size of the spotting area (width and height) is not twice bigger than the size of ground truth area.

Unfortunately, there is no participant who accomplished this challenge. We kindly invite all researchers who work on word spotting method to test their method with our AMADI_LontarSet.

V. CHALLENGE 3: ISOLATED CHARACTER RECOGNITION OF BALINESE SCRIPT IN PALM LEAF MANUSCRIPT IMAGES

A. Description of the Challenge

Isolated handwritten character recognition has been the subject of intensive research during the last decades. Balinese script is considered to be one of the complex scripts from Southeast Asia. The alphabet and numeral of Balinese script is composed of ±100 character classes including consonants, vowels, diacritics, and some other special compound characters. The main objective of this challenge is to be able to efficiently and accurately recognize the isolated characters of Balinese scripts. A set of image patches containing individual Balinese character or compound character from the original manuscript will be used as the input, and a correct class of each character should be identified as the output.

B. Dataset

By using our collection of word-level annotated patch images, we applied binarization process to extract automatically all connected component found on the word patch images. The Balinese philologists annotated manually the segment of connected component that represent a correct character in Balinese script. All the data that have been segmented and annotated at character level will serve as our isolated character dataset. The dataset is partitioned into training and test subsets. For the training subset, 11,710 character-level annotated patch images from 130 character classes have been provided (Fig. 3). For the testing subset, 7,673 character-level annotated patch images as query test from 130 character classes have been provided. The number of samples for each classes is different. Some classes are often used in our collection of palm leaf manuscripts, but some others are rarely used.

C. Performance Evaluation

The results are ranked according to the recognition rate, i.e., the percentage of correctly classified samples over the test samples: C/N, where C is the number of correctly recognized samples, and N is the total number of test samples.

D. Participant Methods

Group 1: (VMQDF and VCMF method) The input image is first processed by the following steps: 1) the input image is resized to 64x64 by linear normalization and median blur with window width 3 is applied on the normalized image. The resulted image is denoted as I1, 2) the binary image Ib of I1 is computed by the OTSU method, 3) I1 is then processed by the pre-processing method described in [START_REF] Liu | Online and offline handwritten Chinese character recognition: Benchmarking on new databases[END_REF] to overcome the gray scale variation among different images. The mean and scatter employed in the experiment is set as 100 and 100, respectively. The resulted image is denoted as In. 97 virtual samples are generated based on In by the method proposed in [START_REF] Shao | Fast self-generation voting for handwritten Chinese character recognition[END_REF]. Gradient feature is extracted using NCGF [START_REF] Liu | Online and offline handwritten Chinese character recognition: Benchmarking on new databases[END_REF] for each original or virtual sample. MQDF classifier is trained based on the expanded training set. At the test stage, for each input image, 97 virtual images are generated and features are extracted in the same way. VMQDF classifies the input image by the voting of the MQDF results of the input image and all the virtual images. VCMF classifies the input image by the voting of the MQDF+CMF results of the input image and all the virtual images.

Group 3: The submitted method first segments the text pixels out of the background using the adaptive contrast method [START_REF] Su | Robust Document Image Binarization Technique for Degraded Document Images[END_REF]. To generate more training data, they developed a synthetic data generation method based on the binary images. First, the bounding box of the character can be easily determined in the binary image. They then crop, rotate and warp the origin images without removing the textual information of the origin images. With the synthetic dataset, they build three CNN models to recognize the 133 labels. The CNN model is constructed using the computational network toolkit developed by Microsoft2 . The input images are resized to 28 by 28. The first CNN network takes the origin images as network input, the second one takes the binary images as network input, and the last one combines the origin and binary images together as network input. Each CNN network has 2 convolution layers followed by two max pooling layers. After training, they further design a random forest to ensemble all the outputs of the CNN networks. The random forest is constructed using Scikit Learn package3 with 200 trees. The final recognition result is produced by the random forest classifier.

Group 5: The finite impulse response multilayer perceptron (FIRMLP), a class of temporal processing neural networks, is a multilayer perceptron where the weights have been replaced by finite impulse response filters. The FIRMLP consists of only one type of processing unit -the finite impulse response neuron. They have extended this architecture which consists now of layers with different computational properties and recurrent connections as well. The first layer is composed of temporal quadratic units. Hence, those neurons compute polynomial kernels of order two, transforming the input space into a higher dimensional feature space. The second layer uses temporal radial basis function units and separates the extended input space by spheres. The third and fourth layer incorporate sigmoid and linear neurons, respectively, with usual FIR synapses. By using the finite impulse response filter the neuron possess internal short time memory and represents a model for spatio-temporal processing. By adding recurrent connections, the neuron develops long time memory as well. The neural networks used as input 64x64 grey pixel images obtained as follows: 1) first, the MSRCR-Algorithms (MultiScale Retinex with Color Restoration) is applied 2) image binarization is performed by using the K-Means algorithm (from OpenImaj package) with two centers 3) and finally scaling to 64x64 pixel images is applied.

E. Results and Analysis

The evaluation results and ranks for all submitted methods are presented in Table III. The two methods proposed by Group 1 achieved the top two recognition rates. Group 1 obtained a significant 10% higher recognition rate than two other groups. The method VMQDF from Group 1 outperforms all other methods.

  Eight research groups registered to this competition: seven groups registered to Challenge 1, three groups registered to Challenge 2, and six groups registered for Challenge 3. But only five research groups accomplished the task and submitted their results: four groups accomplished Challenge 1, and three groups accomplished Challenge 3. There is one group who submitted two methods for Challenge 3. Unfortunately, there is no group who accomplished Challenge 2. Brief introduction of the five research groups who submitted their results are as follows: Group 1 (Challenges 1 with two methods and 3): Submitted by Yunxue Shao, Jiantao Zhou and Guanglai Gao, from College of Computer Science, Inner Mongolia University. Group 2 (Challenge 1): Submitted by Chris Tensmeyer, from Computer Science Dept., Brigham Young University. Group 3 (Challenges 1 and 3): Submitted by Su Bolan and Lu Shijian, from Institution of Infocomm Research (I2R), Agency for Science, Technology and Research (A*STAR), Singapore and Zhang Xi, from Advanced Remanufacturing and Technology Centre (ARTC), Agency for Science, Technology and Research (A*STAR), Singapore. Group 4 (Challenge 1): Submitted by Dr. Deepak Kumar, from Department of Electronics & Communication Engineering, Dayananda Sagar Academy of Technology and Management (DSATM), Bengaluru, Karnataka, India. Group 5 (Challenge 3): Submitted by Cristinel Codrescu, from University of Salzburg. Brief description of their methods are given in each section of the challenge.

Figure 1 .

 1 Figure 1. From top to bottom: original image, ground truth binary image version 1, ground truth binary image version 2 C. Performance Evaluation Following our work in [1], three metrics of binarization evaluation which are used in the DIBCO 2009 contest [4], are used in the evaluation for this challenge. Those three metrics are F-Measure (FM), Peak SNR (PSNR), and Negative Rate Metric (NRM). F-Measure (FM): FM is defined from Recall and Precision. Re *100 TP FN TP call

Figure 2 .

 2 Figure 2. Original image and samples of the word-level annotated patch images

Figure 3 .

 3 Figure 3. Samples of character-level annotated patch images

TABLE I .

 I EVALUATION RESULTS OF CHALLENGE 1

	No. Group	FM	1 st GT Binary NRM PSNR FM	2 nd GT Binary NRM PSNR
	1.	Group 1	63.32 0.15	31.37	63.24 0.14	31.34
	2.	Group 2	68.76	0.13	33.39	68.63	0.12	33.32
	3.	Group 3	52.20	0.18	26.92	51.83	0.18	26.83
	4.	Group 4	58.57	0.17	29.98	58.32	0.17	29.92
		TABLE II. RANK SCORE OF CHALLENGE 1
	No. Group	FM	1 st GT Binary NRM PSNR FM	2 nd GT Binary NRM PSNR
	1.	Group 1	2 nd		2 nd	2 nd	2 nd		2 nd	2 nd
	2.	Group 2	1 st		1 st	1 st	1 st		1 st	1 st
	3.	Group 3	4 th		4 th	4 th	4 th		4 th	4 th
	4.	Group 4	3 rd		3 rd	3 rd	3 rd		3 rd	3 rd

IV. CHALLENGE 2: QUERY-BY-EXAMPLE WORD SPOTTING ON PALM LEAF MANUSCRIPT IMAGES

TABLE III

 III

		. EVALUATION RESULTS OF CHALLENGE 3
	No.	Group	Recog. Rate (%)	Rank
	1.	Group 1: Method VCMF	87.44	2 nd
	2.	Group 1: Method VMQDF	88.39	1 st
	3.	Group 3	77.83	3 rd
	4.	Group 5	77.70	4 th

CNTK http://www.cntk.ai/

Scikit-Learn http://scikit-learn.org/

VI. CONCLUSIONS In this Competition on the Analysis of Handwritten Text in Images of Balinese Palm Leaf Manuscripts, the best result for Challenge 1 (Binarization of Palm Leaf Manuscript Images) was obtained by Chris Tensmeyer, from Computer Science Dept., Brigham Young University. This method achieved the best score for all evaluation measures with two different ground truth images. The best result for Challenge 3 (Isolated Character Recognition of Balinese Script in Palm Leaf Manuscript Images) was obtained by Yunxue Shao, Jiantao Zhou and Guanglai Gao, from College of Computer Science, Inner Mongolia University, with their VMQDF method. This method achieved 88.39% of recognition rate. The dataset of each challenge is available on http://amadi.univ-lr.fr/ICFHR2016_Contest/. ACKNOWLEDGMENT The authors would like to thank Museum Gedong Kertya, Museum Bali, and all families in Bali, Indonesia, for providing us the samples of palm leaf manuscripts, and the students from the Department of Informatics Education and the Department of Balinese Literature, Ganesha University of Education for helping us in ground truthing process for this research project. This work is also supported by the DIKTI BPPLN Indonesian Scholarship Program and the STIC Asia Program implemented by the French Ministry of Foreign Affairs and International Development (MAEDI).


Sungpil Yang
email: yang.sungpil@utexas.edu

Maruthi R Akella
email: makella@mail.utexas.edu

Frédéric Mazenc
email: frederic.mazenc@l2s.centralesupelec.fr

Ph D Candidate

Immersion and Invariance Observers for Gyro-Free Attitude Control Systems

I. Introduction

The rigid-body attitude control problem has been extensively studied due to mathematical interest in the study of kinematics, geometric mechanisms, and a wide range of challenging applications such as spacecraft, underwater vehicle and robot manipulator systems [START_REF] Wen | The attitude control problem[END_REF][START_REF] Wie | Space Vehicle Dynamics and Control, AIAA Education Series[END_REF]. Although this problem is now considered to be well understood, it still attracts researchers as control theory develops and applications are diversified. The theoretical difficulties associated with this problem originate not only from the nonlinearity of the dynamics itself, but also from challenging practical constraints additionally imposed to achieve certain objectives -e.g., partial availability of states, system uncertainty, degradation or saturation of actuators [START_REF] Lizarralde | Attitude control without angular velocity measurement: A passivity approach[END_REF][START_REF] Tsiotras | Further passivity results for the attitude control problem[END_REF][START_REF] Akella | Rigid body attitude tracking without angular velocity feedback[END_REF][START_REF] Costic | Quaternion-based adaptive attitude tracking controller without velocity measurements[END_REF][START_REF] Akella | Velocity-free attitude controllers subject to actuator magnitude and rate saturations[END_REF][START_REF] Cai | Indirect robust adaptive fault-tolerant control for attitude tracking of spacecraft[END_REF][START_REF] Seo | High-performance spacecraft adaptive attitude-tracking control through attracting-manifold design[END_REF].

In the case where angular velocity measurements are not readily available for control implementation, numerous output feedback controllers have been proposed only utilizing attitude measurements. Recently, it was shown that a set of unit vector measurements can be directly used in a feedback control law without constructing an attitude vector to regulate the body orientation [START_REF] Tayebi | Inertial vector measurements based velocity-free attitude stabilization[END_REF][START_REF] Thakur | Gyro-free rigid-body attitude stabilization using only vector measurements[END_REF]. Such "gyro-free" controllers are mainly based on construction of auxiliary filters or dynamic observers. Thanks to certain passivity properties of the dynamics, output of an attitude error filter can be used as a replacement for the rate error feedback [START_REF] Lizarralde | Attitude control without angular velocity measurement: A passivity approach[END_REF][START_REF] Tsiotras | Further passivity results for the attitude control problem[END_REF][START_REF] Akella | Rigid body attitude tracking without angular velocity feedback[END_REF]. Alternatively, angular velocity can be estimated regardless of control input through an observer and the estimates are treated in certainty-equivalence fashion as true rate measurements [START_REF] Salcudean | A globally convergent angular velocity observer for rigid body motion[END_REF][START_REF] Nicosia | Nonlinear observer and output feedback attitude control of spacecraft[END_REF]. Compared to passivity-based controllers, the observer-controller combination requires establishment of a separation property which is not automatically guaranteed for nonlinear systems.

Recently in [START_REF] Hu | Bounded output feedback of rigid-body attitude via angular velocity observers[END_REF], an exponentially converging angular velocity observer was proposed based on Immersion and Invariance (I&I) design aided by a new dynamic scaling method suggested in [START_REF] Karagiannis | Dynamic scaling and observer design with application to adaptive control[END_REF].

Readers are referred to [START_REF] Astolfi | Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems[END_REF][START_REF] Astolfi | Nonlinear and adaptive control with applications[END_REF] for further details of the general I&I methodology and to [START_REF] Astolfi | A globally exponentially convergent immersion and invariance speed observer for n degrees of freedom mechanical systems[END_REF][START_REF] Astolfi | A globally exponentially convergent immersion and invariance speed observer for mechanical systems with non-holonomic constraints[END_REF] for nonlinear observer applications. Using switching logic, a C 0 continuous angular velocity observer with an exponential convergence was designed in [START_REF] Chunodkar | Switching angular velocity observer for rigid-body attitude stabilization and tracking control[END_REF] while a C ∞ observer was suggested showing an asymptotic convergence of the estimation errors in [START_REF] Akella | Partial Lyapunov Strictification: Smooth Angular Velocity Observers for Attitude Tracking Control[END_REF]. The aforementioned observers are driven by quaternion measurements and combined with proportional-derivative (PD) type controllers establishing an almost global asymptotic stability for the overall closed-loop system.

In this paper, a new lower dimensional I&I observer is proposed based on a novel definition of the angular velocity estimate. Instead of using a filter for the angular velocity estimate to dominate Coriolis effect suggested in [START_REF] Hu | Bounded output feedback of rigid-body attitude via angular velocity observers[END_REF], the direction cosine matrix associated with the quaternion state is utilized so that cross terms caused by both Coriolis effect and an approximate solution to a partial differential equation (PDE) I&I design inevitably involves are expressed in terms of quaternion filter error in Lyapunov analysis. Consequently, the observer dynamics evolve only in 8-dimensional space instead of the 11-dimensional space in [START_REF] Hu | Bounded output feedback of rigid-body attitude via angular velocity observers[END_REF] and stability analysis becomes simpler due to the fact that the dynamics of the scaling factor are only driven by the quaternion filter error. Moreover, further simplification is made by utilizing a structural property of the quaternion kinematics. Typically, I&I design with dynamic scaling requires additional term in the time-varying gain associated with the quaternion filter in order to bound the scaling factor [START_REF] Karagiannis | Dynamic scaling and observer design with application to adaptive control[END_REF], but the added term is shown to be zero for this particular application. When this observer is equipped with a PD tracking control, a separation property is established through the use of a partially strictified Lyapunov function candidate which is similar to one in [START_REF] Mazenc | Quaternion-based stabilization of attitude dynamics subject to pointwise delay in the input[END_REF]. This note is organized as follows. The rigid-body rotational dynamics and the corresponding quaternion kinematics are described in Section II and some useful lemmas are presented in Section III. Then the I&I observer design is discussed in Section IV. The stability analysis of the PD feedback control is conducted both with true rate measurements in Section V and with its estimates in Section VI, which also establishing the separation property. Section VII provides numerical results showing the performance of the proposed observer and controller. Finally, we ends with some concluding remarks in Section VIII.

II. Model Description

Consider the rigid-body rotational motion. Let ω(t) ∈ R 3 and u(t) ∈ R 3 be the angular rate and the applied control torque respectively both represented in the body-fixed frame. Then the dynamics are governed by Euler's rotational equations of motion given by

J ω(t) = -S (ω(t))Jω(t) + u(t) , (1)
where J ∈ R 3×3 is the positive definite inertia matrix and S : R 3 → R 3×3 is the skew-symmetric matrix operator such that it is equivalent to the vector cross product, i.e., S (x)y = x × y for any

x, y ∈ R 3 .

In this note, the quaternion kinematics are adopted to avoid the singularity:

q(t) = 1 2 E(q(t))ω(t) , (2)
where the quaternion q(t)

∈ Q = {q = (q 0 , q v ) ∈ R × R 3 | q T q = 1}
represents the orientation of the body frame F B with respect to the inertial frame F I . The matrix function

E : R × R 3 → R 4×3 in
Eq. ( 2) is defined by

E(q) =            -q T v S (q v ) + q 0 I 3            , (3)
where I 3 is the 3-dimensional identity matrix. Note that, given a quaternion q ∈ Q, a direction cosine matrix which also represents the body attitude can be obtained by the following identity:

C(q) = I 3 -2q 0 S (q v ) + 2S 2 (q v ) , (4)
whose corresponding kinematics are given by Ċ(q(t)) = -S (ω(t))C(q(t)) .

In our formulation, it is assumed that the inertia matrix J is exactly known and only quaternion measurements are available from attitude sensors. The objective is to design an observer that estimates the states q(t) and ω(t) with an exponential convergence using the I&I design method.

From the subsequent section on, function arguments are often dropped for notational simplicity.

III. Preliminaries

Before presenting our main result, we state some important technical results to make our analysis easier to follow. Detailed proofs are omitted in the interest of brevity.

Lemma 1. Let S O(3) be the 3-dimensional rotation group defined as

S O(3) = {R ∈ R 3×3 | R T R = I 3 , det{R} = 1} . (6)
For any R ∈ S O(3) and

x ∈ R 3 RS (x) = S (Rx)R . (7)
In other words, the vector cross product in three-dimension is invariant under proper rotations.

Lemma 2. For any symmetric matrix M ∈ R 3×3 and any vector x ∈ R 3 , the equality

S (Mx) + MS (x) + S (x)M = Tr(M)S (x) (8)
holds, where Tr(M) is the trace of the matrix M.

Lemma 3. Consider the function E(q) defined in Eq. ( 3). For any q ∈ R 4 , the following equalities are satisfied:

E T (q)q = 0 , (9)
E(q) 2 = q 2 . ( 10
)
Note Eq. ( 9) indicates that the unit-norm constraint is invariant under the quaternion kinematics.

It is induced by Eqs. ( 3) and ( 10) that the function E(q) is globally Lipschitz in q.

IV. I&I Observer Design

A. Observer states Let q(t) and ω(t) be the observer states that track q(t) and ω(t) respectively. Then the errors are defined as

q = q -q , (11)
ω = ω -ω . ( 12
)
The angular velocity estimate is assumed to be

ω = C(q) ω + β( q, q) , (13)
where the mapping β : R 4 × Q → R 3 is to be determined. The objective is to design q(t), ω(t) and

β(t) such that lim t→∞ ( q(t), ω(t)) = (0, 0) . (14)

B. Observer error dynamics

Let us consider the time-derivative of the angular velocity estimate defined in Eq. ( 13). Using

Eq. ( 5), we obtain

ω = Ċ(q) ω + C(q) ω + β( q, q) = -S (ω)C(q) ω + C(q) ω + β . ( 15
)
After arranging terms in the above equation, we have

ω = S ( ω)( ω -β) -S ( ω)C(q) ω + C(q) ω + β , (16)
which leads to

J ω = J ω -J ω = JS ( ω)( ω -β) -JS ( ω)C(q) ω + JC(q) ω + J β + S ( ω -ω)J( ω -ω) -u . (17)
Once Lemma 2 is applied and the following relationships are substituted:

J = Tr(J)I 3 -2J , (18)
µ = C(q) ω -S ( ω)C(q) ω + J -1 (S ( ω)J ω -u) , (19)
the rate error dynamics are obtained as

J ω = S ( ω) J ω + J ω -JS ( ω)β + J(µ + β) . ( 20
)
We will design µ(t) and then recover ω(t) through the following relation:

ω = C T (q) µ + S ( ω)C(q) ω -J -1 (S ( ω)J ω -u) . ( 21
)
Remark 1. The key idea of this work compared to the result in [START_REF] Hu | Bounded output feedback of rigid-body attitude via angular velocity observers[END_REF] is that β is a function of only q and q, so the observer does not require a three-dimensional filter for ω such that the filter state converges to ω as time goes to infinity. This is achieved by use of the direction cosine matrix associated with the quaternion state to define the rate estimate in Eq. ( 13). We prove in the following analysis that the second term JS ( ω)β in the right-hand side of Eq. ( 20) will be managed by designing β such that β → 0 as q → 0 without introducing extra dynamic extension.

We also propose the dynamics for the quaternion filter as

q(t) = -k q r 2 (t) q(t) + 1 2 E(q(t)) ω(t) , q(0) = q(0) , (22)
where k q is a positive constant and r(t) is the dynamic scaling factor to be determined in the following section. Then the quaternion error dynamics become

q = -k q r 2 q + 1 2 E(q) ω . (23)

C. Dynamic scaling

The original I&I methodology requires the existence of a function β(q) such that

∂β ∂q = k ω E T (q) , (24)
where k ω is a positive constant. However, no such solution to the above PDE exists. In order to apply I&I methodology, we rather consider an approximate solution β( q, q) such that

∂β ∂q = k ω E T ( q) (25)
and lim t→∞ q(t) = q(t). The effect caused by this approximation will be managed by introducing a dynamic scaling factor to be discussed later.

Let

β = k ω E T ( q)q (26)
and

µ = k ω E T ( q) k q r 2 q - 1 2 E(q) ω . (27)
Since

β = k ω E T ( q) q -k ω E T (q) q = - k ω 2 E T ( q)E(q) ω -k ω E T ( q) k q r 2 q - 1 2 E(q) ω = - k ω 2 ω - k ω 2 E T ( q)E(q) ω -k ω E T ( q) k q r 2 q - 1 2 E(q) ω , (28)
the closed-loop dynamics are obtained as

J ω = S ( ω) J ω + J ω -k ω JS ( ω)E T ( q)q - k ω 2 J ω - k ω 2 JE T ( q)E(q) ω . ( 29
)
Now consider V ω = (1/2) ωJ ω whose time-derivative is given by

V ω = - k ω 2 J 1/2 ω 2 2 -k ω ωT JS ( ω)E T ( q)q - k ω 2 ωT JE T ( q)E(q) ω . ( 30
)
Since V ω is not upper bounded by a non-positive function, it cannot be further analyzed. In oder to handle the sign indefinite terms in Eq. (30) we introduce, using the dynamic scaling factor r(t), the scaled rate error defined as

z(t) = 1 r(t) ω(t) , (31)
and propose

ṙ = -k 1 k ω (r -1) + k 2 k ω q 2 2 r , r(0) = 1 , (32)
where k 1 and k 2 are positive constants. Note that, since the set {r ∈ R | r ≥ 1} is positively invariant, the choice of the initial condition ensures r(t) ≥ 0 for all t ≥ 0. Along the trajectories of Eqs. ( 29) and (32), we have

J ż = S (z) J ω + J ω - k ω 2 Jz - ṙ r Jz -k ω JS (z)E T ( q)q - k ω 2 JE T ( q)E(q)z . ( 33
)
Then the time-derivative of the Lyapunov-like function defined by

V z = 1 2k ω z T Jz (34)
is obtained as

Vz = - 1 2 - k 1 (r -1) r z T Jz -k 2 q 2 2 z T Jz -z T JS (z)E T ( q)q - 1 2 z T JE T ( q)E(q)z . ( 35
)
Let J M and J m denote the largest and the smallest eigenvalues of the inertia matrix J so that the inequalities

J m z 2 2 ≤ z T Jz ≤ J M z 2 2 ( 36
)
and

S (z)Jz 2 2 ≤ J ∆ z 2 2 z T Jz (37)
hold for any z ∈ R 3 , where J ∆ = J M -J m . Using the above inequalities and the fact that E T ( q)q 2 = E T (q)q + E T ( q)q 2 ≤ q 2 (38) from Lemma 3, the upper bound of V z is obtained as

Vz ≤ -            z q z            T (Q 1 ⊗ J)            z q z            , (39)
where

Q 1 =            1 2 -k 1 -J M +2 √ J m J ∆ 4J m -J M +2 √ J m J ∆ 4J m k 2            (40)
and the operator ⊗ denotes the Kronecker product.

Remark 2. As mentioned in Remark 1, the choice of β in Eq. (26) renders the cross term caused by the Coriolis effect to depend on q and z. Similarly, the other cross term coming from the time derivative of the approximate solution β( q, q) is a function of q and z. Together they give r-dynamics driven by q 2 2 only.

If k 1 and k 2 are additionally constrained as

k 1 < 1 2 , (41)
k 2 > J M + 2 √ J m J ∆ 2 8J 2 m (1 -2k 1 ) , (42)
the matrix Q 1 becomes positive definite, and thus there exists a finite constant c 1 > 0 such that

Vz ≤ -c 1 z 2 2 . ( 43
) Moreover, since Vz ≤ - 2k ω c 1 J M V z , (44)
the norm of z(t) is bounded by

z(t) 2 ≤ z(0) 2 J M J m exp - k ω c 1 J M t , (45)
which implies that z(t) converges to zero exponentially fast.

To show the convergence of ω, consider

V o = 1 2 qT q + ζ 1 V z , (46)
where ζ 1 > 1/(8kc 1 ). Along the trajectories of the closed-loop dynamics the time-derivative of

V o yields Vo = -k q r 2 q 2 2 + r 2 qT E(q)z + ζ 1 Vz . ( 47
)
This is upper bounded by

Vo ≤ - k q 2 r 2 q 2 2 -            r q 2 z 2            T Q 2            r q 2 z 2            , (48)
where

Q 2 =            k 2 -1 4 -1 4 ζ 1 c 1            (49)
is positive definite.

D. Boundedness of scaling factor

It is essential to establish the boundedness of r(t) to show the convergence of q(t) since Eqs. ( 46) and ( 48) are only valid as long as r(t) is finite. To prove r ∈ L ∞ , we construct another Lyapunov function candidate

W = V o + k q 8k 2 k ω r 2 (50)
whose time derivative is given by

Ẇ = Vo - k 1 k q 4k 2 k ω r(r -1) + k q 4 r 2 q 2 2 ≤ - k q 4 r 2 q 2 2 . (51)
Since W(t) is non-increasing, the scaling factor is bounded for all t ∈ [0, ∞).

Remark 3. To ensure r ∈ L ∞ , the quaternion estimate dynamics typically have the form

q(t) = -K(t) q(t) + 1 2 E(q(t)) ω(t) (52) with K(t) = k q r 2 (t) + r 2 (t)ψ(q(t), q(t)) , (53)
where is a positive constant and ψ is a function that cancels the positive term in Ẇ [START_REF] Karagiannis | Dynamic scaling and observer design with application to adaptive control[END_REF]. However, owing to the fact that the function E(q) is globally Lipschitz, the increasing term in the ṙ equation becomes proportional to q 2 2 instead of E( q) 2 2 , and thus the additional term ψ can be set to be zero so that the first term in the dynamic gain K(t) absorbs the other.

E. Convergence properties

As r(t) is finite for all t ≥ 0, standard Lyapunov analysis is now applied. The positive definite matrix Q 2 in Eq. ( 48) allows us to find some c 2 > 0 such that Vo ≤ -

k q 2 q 2 2 -c 2 z 2 2 , (54)
which implies that there exists

c 3 > 0 such that Vo ≤ -c 3 V o . (55)
Therefore, it is concluded that both q(t) and z(t) converge to zero exponentially fast. Finally, since

ω(t) 2 ≤ r(t) ω(0) 2 J M J m exp - k ω c 1 J M t ≤ sup t≥0 {r(t)} ω(0) 2 J M J m exp - k ω c 1 J M t ( 56
)
from Eq. ( 45), we conclude that lim t→∞ ω(t) = 0 (57)

for any ω(0) ∈ R 3 and that the convergence rate is exponential.

Remark 4.

As q converges to zero exponentially fast, so does β by Eq. ( 38). Therefore, we can also conclude that

lim t→∞ C(q(t)) ω(t) = ω(t) (58)
with an exponential convergence rate. Then we can interpret ω as the estimate for the angular velocity expressed in the inertial frame F I .

V. Full State Feedback Tracking Control

It is known that PD controllers stabilize the attitude tracking error when all states are available for the controller implementation. Let q r (t) ∈ Q be the quaternion representing the reference frame F R with respect to the inertial frame F I , and let ω r (t) ∈ R 3 be the reference angular velocity in the reference frame. Define the quaternion tracking error e q = (e 0 , e v ) ∈ Q such that

C(e q ) = C(q)C T (q r ) ( 59
)
and the rate error as

e ω = ω -C(e q )ω r . ( 60
)
If the control torque is given by

u = -k p e v -k v e ω + JC(e q ) ωr + S (ω B r )Jω B r , (61)
where k p , k v > 0 are the control gains and ω B r = C(e q )ω r is the reference angular velocity in the body frame, then the tracking error dynamics are obtained as ėq = 1 2 E(e q )e ω (62)

J ėω = -S (e ω )(Je ω -Jω B r ) -k p e v -k v e ω . (63)
To prove (e v , e ω ) → (0, 0) as t → ∞, consider the partially strictified Lyapunov function candidate taken from [START_REF] Mazenc | Quaternion-based stabilization of attitude dynamics subject to pointwise delay in the input[END_REF]

V c = ζ 2 k p e T v e v + (e 0 -1) 2 + ζ 2 2 e T ω Je ω + e T v Je ω , (64)
where

ζ 2 > k v 4k p + J M 2k v . Since V c ≥ ζ 2 k p (e 0 -1) 2 +            e v e ω            T (Q 3 ⊗ J)            e v e ω            (65)
and Vc ≤ -

           e v e ω            T (Q 4 ⊗ I 3 )            e v e ω            , (66)
where the positive definite matrices Q 3 and Q 4 are defined by

Q 3 =            ζ 2 k p J M 1 2 1 2 ζ 2 2            (67)
and

Q 4 =            k p k v 2 k v 2 ζ 2 k v -J M 2            , (68)
we can conclude, by invoking Barbalat's lemma, that

lim t→∞ (e v (t), e ω (t)) = (0, 0) . (69)

VI. Separation Property

As the angular velocity measurements are not available, the PD control is modified as

u = -k p e v -k v êω + JC(e q ) ωr + S (ω B r )Jω B r , (70)
where

êω = ω -C(e q )ω r . (71)
Consequently, the rate error dynamics are changed to

J ėω = -S (e ω )(Je ω -Jω B r ) -k p e v -k v e ω -k v ω , (72)
which leads to Vc ≤ -

           e v e ω            T (Q 4 ⊗ I 3 )            e v e ω            -k v e T v ω -ζ 2 k v e T ω ω . (73)
To dominate the cross terms in the right hand side of Eq. ( 73), consider the Lyapunov function candidate

V = V c + ζ 3 V z , (74)
where ζ 3 is a positive constant to be determined. From Eqs. ( 43) and ( 73), the upper bound of its time derivative along the closed-loop trajectories is obtained as

V ≤ -                     e v e ω z                     T (Q 5 ⊗ I 3 )                     e v e ω z                     , ( 75
)
where the matrix Q 5 (t) ∈ R 3×3 is given by

Q 5 (t) =            Q 4 R(t) R T (t) ζ 3 c 1            (76)
with

R(t) = k v r(t) 2            1 ζ 2            . ( 77
)
Since Q 4 is positive definite, there exists

c 4 > 0 such that Q 4 ≥ c 4 I 2 , discussed earlier. Let T (t) ∈ R 2×2 be the Schur complement of Q 4 in Q 5 (t) defined by T (t) = Q 4 - 1 ζ 3 c 1 R(t)R T (t) . (78)
Then the choice

ζ 3 > sup t≥0 {r 2 (t)} k 2 v (1 + ζ 2 2 ) 4c 1 c 4 ( 79
)
makes T (t), and thus, Q 5 (t) positive definite for all t ∈ [0, ∞). Applying Barbalat's lemma, we finally have lim t→∞ (e v (t), e ω (t), z(t)) = (0, 0, 0) . (80)

VII. Numerical Simulations

In this section, numerical simulation results are provided to demonstrate the performance of the proposed observer and observer-based PD type tracking controller. The inertia matrix of the rigid spacecraft is taken from [START_REF] Akella | Partial Lyapunov Strictification: Smooth Angular Velocity Observers for Attitude Tracking Control[END_REF].

J =                     10
                    kg m 2 (81)
The initial conditions are set to

q v (0) =                     -0.1 0.1 -0.1                     , ω(0) =                     0.005 0.006 0.004                    
rad/s with q 0 = 1q v (0) 2 2 . The reference quaternion is set to q r (0) = (0.9487, 0.1826, 0.1826, 0.1826) initially and its dynamics are assumed to be driven by the reference angular velocity profile ω r (t) = (ω r (t), ω r (t), ω r (t)) rad/s, where ω r (t) = 0.3 cos(t) 1e -0.01t 2 + (0.08π + 0.006 sin(t)) te -0.01t 2 .

(82)

To show the tracking performance, we set the control gains to k p = 1.5 and k v = 5. For the observer, we use

k 1 = 1 4 , k 2 = J M + 2 √ J m J ∆ 2 4J 2 m (1 -2k 1 )
.

The gains k q and k ω are closely related to the convergence rate of the observer state errors. In the simulation, they are selected such that the convergence rates for the quaternion and angular velocity errors are approximately the same. For comparison, two sets of these gains are chosen:

(k q , k ω ) = (0.3, 0.3) and [START_REF] Karagiannis | Dynamic scaling and observer design with application to adaptive control[END_REF][START_REF] Karagiannis | Dynamic scaling and observer design with application to adaptive control[END_REF]. The initial guess for the angular velocity is selected as ω(0) = (-0.3, 0.1, -0.2) rad/s. The performance of the proposed observer is shown in Fig. 1. The high gains ensure a fast convergence rate as expected. Given fixed gains k q and k ω , the convergence rate of the scaling factor is further restricted by the other observer gains. So the scaling factor converges faster to unity if k 1 and k 2 are close to their constraint boundaries described in Eqs. (41) and (42). The tracking performance of the observer-based PD controller is demonstrated and compared with the full-state feedback control in Fig. 2. When the small gain set is selected for the observer, the tracking error norms are deviated from those of the full-state feedback control, but the convergence rate is not very different because the convergence rate of the observer errors is still faster than that of the tracking errors in the ideal PD control. When the observer gains are increased to the values in the second set, the trajectories are almost identical to the full-state feedback control. Figure 3 also shows the same tendency in the control effort. For the high gain observer, the trajectory of the control torque norm catches up the full-state feedback control within a second.

VIII. Conclusion

In this note, a novel observer-based attitude tracking controller is proposed in the absence of rate measurements. Based on the I&I design method in conjunction with dynamic scaling, an angular velocity observer employing the attitude quaternion measurements is designed. It is shown that the angular velocity estimate globally converges to the true value exponentially fast independent of the choice of control torque. By defining the rate estimate using a direction cosine matrix, the observer structure is far simplified and requires less state variables compared to the existing I&I design. A separation property is then established for the PD tracking controller while asymptotic convergence of the tracking errors is shown. To demonstrate the observer performance, numerical simulations are conducted. Tracking results of two observers with relatively high and low gains are provided and compared with the ideal case where true angular velocity is available for feedback control.

15 Figure 1 .

 151 Figure 1. Time histories of observer errors

15 FullFigure 2 .

 152 Figure 2. Time histories of tracking errors

Figure 3 .

 3 Figure 3. Time histories of control torques

of 20 American Institute of Aeronautics and Astronautics

of 20 American Institute of Aeronautics and Astronautics