## MORSE DESCRIPTION AND MORPHOLOGICAL ENCODING OF CONTINUOUS DATA

Citations: | 2 - 1 self |

### BibTeX

@MISC{Caselles_morsedescription,

author = {Vicent Caselles and Guillermo Sapiro and Andrés Solé and Coloma BALLESTER},

title = {MORSE DESCRIPTION AND MORPHOLOGICAL ENCODING OF CONTINUOUS DATA },

year = {}

}

### OpenURL

### Abstract

A geometric representation for images is studied in this work. This is based on two complementary geometric structures for the topographic representation of an image. The first one computes a description of the Morse structure, while the second one computes a simplified version of drainage structures. The topographic significance of the Morse and drainage structures of Digital Elevation Maps (DEM) suggests that they can been used as the basis of an efficient encoding scheme. As an application we then combine this geometric representation with a consistent interpolation algorithm and lossless data compression schemes to develop an efficient compression algorithm for DEM. This coding scheme controls the L ∞ error in the decoded elevation map, a property that is necessary for the majority of applications dealing with DEM. We present the underlying theory and some compression results for standard DEM data.

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Citation Context ...omains, in particular, to visualize structures in 3D medical images. Let us finally mention that a morphological approach to image compression has been proposed by several authors, for instance [34], =-=[41]-=-, [37], [18]. In [41] the authors propose to use binary partition trees to select the level curves which have to be encoded. The trees take into account the cost in bits to encode the selected level b... |

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Citation Context ...ture is too complex, i.e., there are too many criticalities. To simplify the structure of the topographic map while preserving its main features we filter the image with the Vicent-Serra filters [54],=-=[53]-=-, also called extrema filters [19]. Extrema filters eliminate the small connected components of upper and lower level sets of the given image [7], [12]. The resulting image has a simplified topographi... |

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Citation Context ...r topographic significance in DEM data. These mainly correspond to the drainage structures (e.g., rivers and ravines). There exists many different algorithms accurately computing such structures, see =-=[29]-=- and references therein. We will present an approach which is related to the one in [45]. Strictly speaking, we do not compute the drainage structures but a simplified version of them which is adapted... |

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Citation Context ...rent domains, in particular, to visualize structures in 3D medical images. Let us finally mention that a morphological approach to image compression has been proposed by several authors, for instance =-=[34]-=-, [41], [37], [18]. In [41] the authors propose to use binary partition trees to select the level curves which have to be encoded. The trees take into account the cost in bits to encode the selected l... |

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Citation Context ...], which has a near lossless mode where one can impose the maximum allowed error. The use of JPEG-LS for DEM data has been studied in [35]. Let us mention that if you compress an image with JPEG-2000 =-=[1]-=- and then encode the errors greater than a given bound this algorithm can also be used to compress with control of the maximum error (being this not a fully standard approach). To represent and compre... |

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Citation Context ...|Γxy) are encoded separately. To encode the geometry we use a differential chain coding strategy, see [24, 30, 14]. In the future we plan to explore an encoding based on rate-distortion theory, as in =-=[44]-=-. For the gray levels, if we accept losses, we may use an ENO (Essentially Non Oscillatory) based encoding scheme [2] which also controls the sup error, a fundamental requirement of the application as... |

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Citation Context ... We proceed to address this now. The geometry of the sampled curves (Γxy) and their gray levels (u|Γxy) are encoded separately. To encode the geometry we use a differential chain coding strategy, see =-=[24, 30, 14]-=-. In the future we plan to explore an encoding based on rate-distortion theory, as in [44]. For the gray levels, if we accept losses, we may use an ENO (Essentially Non Oscillatory) based encoding sch... |

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Citation Context ...re too many criticalities. To simplify the structure of the topographic map while preserving its main features we filter the image with the Vicent-Serra filters [54],[53], also called extrema filters =-=[19]-=-. Extrema filters eliminate the small connected components of upper and lower level sets of the given image [7], [12]. The resulting image has a simplified topographic map structure. Let us recall the... |

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Citation Context ..., in particular, to visualize structures in 3D medical images. Let us finally mention that a morphological approach to image compression has been proposed by several authors, for instance [34], [41], =-=[37]-=-, [18]. In [41] the authors propose to use binary partition trees to select the level curves which have to be encoded. The trees take into account the cost in bits to encode the selected level boundar... |

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Citation Context ...ead to an efficient representation of the topographic structures of these images. This paper presents the underlying theoretical results and some experimental examples, which are further developed in =-=[48]-=-. DEM data consist of a discrete digital representation of a surface terrain. Each cell in a DEM corresponds to a point (x, y, z) in 3D space. We can think of (x, y) as the coordinates in the image do... |

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Citation Context ...structure is too complex, i.e., there are too many criticalities. To simplify the structure of the topographic map while preserving its main features we filter the image with the Vicent-Serra filters =-=[54]-=-,[53], also called extrema filters [19]. Extrema filters eliminate the small connected components of upper and lower level sets of the given image [7], [12]. The resulting image has a simplified topog... |

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Citation Context ...es (e.g., rivers and ravines). There exists many different algorithms accurately computing such structures, see [29] and references therein. We will present an approach which is related to the one in =-=[45]-=-. Strictly speaking, we do not compute the drainage structures but a simplified version of them which is adapted to our purposes. In a simplistic way we can think of the drainage structures as the set... |

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Citation Context ...articular, to visualize structures in 3D medical images. Let us finally mention that a morphological approach to image compression has been proposed by several authors, for instance [34], [41], [37], =-=[18]-=-. In [41] the authors propose to use binary partition trees to select the level curves which have to be encoded. The trees take into account the cost in bits to encode the selected level boundaries an... |

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