Hermilo Sánchez-Cruz

Efficiency of chain codes to represent binary objects

We present a study of compression efficiency for binary objects or bi-level images for different chain-code schemes. Chain-code techniques are used for compression of bi-level images because they preserve information and allow a considerable data reduction. Furthermore, chain codes are the standard input format for numerous shape-analysis algorithms. In this work we apply chain codes to represent object with holes and we compare their compression efficiency for seven chain codes. We have also compared all these chain codes with the JBIG standard for bi-level images.

Proposing a new code by considering pieces of discrete straight lines in contour shapes

Pattern substrings analysis to find high redundancy in binary shapes is carried out to improve compression levels in binary objects. Modifications of a recent set of symbols to encode arbitrary contour shapes is proposed. The concept of Pieces of Discrete Straight Lines is introduced and the probability of appearance of symbols in contours is analyzed to propose a code of nine symbols, MDF9. Also, this code is compared with the six well-known contour codes for compression without loss of information: FCCE, FCCF, VCC, 3OT, DFCCE and C_VCC. The proposed MDF9 code in this paper, gives better compression efficiency than existing codes.

Compressing bilevel images by means of a three-bit chain code

We propose a lossless compression method based on a chain code composed of only three symbols. The method is applicable to compress 2-D binary object shapes, and it consists of representing the orthogonal direction changes of the discrete contour, corresponding to each object binary shape, by three bits of a chain code. According to our experimental results, we find that this method is suitable for the representation of bilevel images. The results are about 25% more efficient in compression than the Freeman chain code method, and an average of 29% better than the Joint Bilevel Image Experts Group (JBIG) compressor.

A new relative chain code in 3D

A new chain code to represent 3D discrete curves is proposed. The method is based on a search for relative changes in the 3D Euclidean space, composed of three main vectors: a reference vector, a support vector, and a change direction vector, utilized to obtain a directed simple path in a grid of 26 connected components. A set of rotation transformations is defined in the 3D Euclidean space, and an alphabet of only 25 symbols is required to represent any face, edge or vertex-connected discrete curve. Important properties of this code are found: independence under translation, rotation and mirror transformations, as well as high compression levels. A set of 3D curve-skeletons and digital elevation model data to study the terrain were utilized to prove the proposed code. Compared with the state-of-the-art, our method has more advantages: at first, it represents voxelized paths independently of vicinity, also it gives better representation for the tested objects and detects better the redundant parts. This fact is shown in the entropy calculated for 3D curve-skeletons: our method gives 3.03bits/symbol, whereas the state-of-the-art method gives 4.35bits/symbol. On the other hand, our proposed chain code uses 23% less memory than the well known Freeman code of 26 directions. In case of digital elevation models, our method improves memory for 36.1% regarding Freeman code and 10.7% regarding the well known relative code called orthogonal direction change chain code. Finally, average length of the chain code proposed is 14% shorter than the relative code of the state-of-the-art. HighlightsWe defined new rotations to be used to propose a 3D code.Equivalent simple paths allow to save information to be labeled.We found that a set of 25 symbols codify any face, edge and vertex connected 3D path.We applied the new code to a set of skeletons and digital elevation model data.We found invariance under transformations and high compression level of the new 3D code.

Coding Long Contour Shapes of Binary Objects

This is an extension of the paper appeared in [15]. This time, we compare four methods: Arithmetic coding applied to 3OT chain code (Arith-3OT), Arithmetic coding applied to DFCCE (Arith-DFCCE), Huffman coding applied to DFCCE chain code (Huff-DFCCE), and, to measure the efficiency of the chain codes, we propose to compare the methods with JBIG, which constitutes an international standard. In the aim to look for a suitable and better representation of contour shapes, our probes suggest that a sound method to represent contour shapes is 3OT, because Arithmetic coding applied to it gives the best results regarding JBIG, independently of the perimeter of the contour shapes.

A proposal method for corner detection with an orthogonal three-direction chain code

Only three set of pattern chain elements to detect corners in irregular shapes are introduced. A code based on three orthogonal change directions, when visiting a contour shape, are used. Previous approaches for detecting corners employ eight different symbols and usually compute angles and maximum curvature. The three basic pattern contour chain elements, founded in this paper, represent changes of direction in the contour curves, requiring few computing power to obtain corners. Also, we have found that the method is independent of shape orientation.

Equivalence of chain codes

Abstract. The representation of images is an active and very important area in image processing and pattern recognition. Therefore, in the literature, different contour codes for binary images have been proposed, such as F4,F8,VCC,3OT, and AF8. These codes have been used in many papers since the first chain code, F8, was introduced by Freeman in 1961. All the codes have been tried here as vector representations, including vertex chain code (VCC). To know their properties, this paper provides an analysis of comparisons of each code, and as an important contribution, we investigated the relationship between them and found a series of transformations that allow simple and efficient sets to go from one code to another. We found the equivalences between F4,VCC,3OT,F8, and AF8. As an important consequence of the transition matrix concept, we proposed a new code for eight connectivity by observing a missing code in the state of the art and in the inspiration of the 3OT code.

Study of compression efficiency for three-dimensional discrete curves

A study of compression efficiency of 3-D chain codes to represent discrete curves is described. The 3-D Freeman chain code and the five orthogonal change chain directions (5OT) chain code are compared. The 3-D Freeman chain code consists of 26 directions, in 3-D Euclidean space, with no invariance under rotation. The 5OT chain elements represent the orthogonal direction changes of the contiguous straight-line segments of the discrete curve. This chain code only considers relative direction changes, which allows us to have a curve descriptor invariant under rotation, and mirroring curves may be obtained with ease. In the 2-D domain, Freeman chain codes are widely used to represent contour curves. Until now, the authors have had no information of implementing Freeman chain codes to compress 3-D curves. Our contribution is how to implement the Freeeman chain code in 3-D and how to compare it with the recently proposed 5OT code. Finally, to probe our results, we apply the proposed method to three different cases: arbitrary curves, cube-filling Hilbert curves, and lattice knots.

Refined fixed double pass binary object classification for document image compression

Abstract We propose a method for binary object classification to make lossy compression of document images. The double-pass dictionary formation consists in a Pattern Matching & Substitution (PM&S) algorithm that firstly makes a classification of all objects using Tanimoto distance, whereas the second pass consists of a classification of just the patterns chosen on the first pass in dictionary formation. On each of the two passes is performed the refinement of the generated classes choosing the best representative member as pattern. We tested our dictionary formation method on a compression system that uses 3OT chain code to codify the chosen patterns and the Paq8l archiver to compress the resulting string. The compression ratios applied over the eight CCITT test binary images benchmarks, at 200 and 600 dpi, are better compressed against state of the art and standard methods. Comparing with JBIG2 we obtained 27% better compression level at 200 dpi and 65% at 600 dpi, comparing with DjVus JB2 we obtained 6% better compression level at 200 dpi and 35% at 600 dpi and comparing with 3OT-Paq8l we obtained 38% better compression at 200 dpi and 30% at 600 dpi.

Binary document image compression using a three-symbol grouped code dictionary

A novel method of lossy compression for images of text documents is proposed. The method is based on classifying the objects, characters, and pictures that appear in the images. We used the Tanimoto distance to group the objects into different classes to create an object dictionary; then, we codified the instances of each class by means of a code of three symbols called the three orthogonal symbol chain code (3OT). We applied an entropy coder to the resulting chain, which groups the symbols of 3OT; finally, we compressed the chain obtained by using the Paq8l archiver, which is based on a context-mixing algorithm divided into a predictor and an arithmetic coder. We obtained a high performance in memory storage, with an average of 2.17 times better compression levels with respect to the international standard Joint Bi-level Image Experts Group 2 on its lossy information version.