The Gradient Product Transform for Symmetry Detection and Blood Vessel Extraction

Dalitz, Christoph; Pohle-Fröhlich, Regina; Schmitt, Fabian; Jeltsch, Manuel

doi:10.5220/0005234101770184

Cited by 3 publications

(10 citation statements)

References 12 publications

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“…In real world images, however, an actually circular object usually appears ellipsoidal due to perspective distortion (see Figure 3) and the C m symmetry only holds approximately. Testing for regions with rectangular bounding boxes thus makes the symmetry score more robust with respect to skew, which was experimentally confirmed in [4]. As the size of the symmetry region is not known in advance, the score (3) must be computed for all radii 1 ≤ r x , r y ≤ r max .…”

Section: Computation Of the Symmetry Scorementioning

confidence: 90%

“…The parameter α has been introduced in [4] in Equations (1) and (2) to compensate for the observation that the raw symmetry score s( x, r) tends to increase with the size of r due to background noise. Without this scale normalization, the radius with the highest score tends to be quite close to r max , even when the actual symmetric object is much smaller.…”

Section: Symmetry Size Normalization Parameter αmentioning

confidence: 99%

“…The present article deals with an algorithm that takes an entire grayscale image as input and assigns each image point a "symmetry score" that measures how suitable the point is as a symmetry center of a C 2m (point reflection) symmetry. As the score value is based on scalar products of gray value gradients at corresponding positions, the method is called Gradient Product Transform (GPT) [4]. The image of symmetry score values thus represents a "symmetry transform", and symmetry points correspond to maxima in the symmetry transform image.…”

Section: Introductionmentioning

confidence: 99%

“…The algorithm was originally defined in [3] for square shaped symmetry regions and a simple criterion for discriminating between rotational and axial symmetries was suggested. In [4], this was extended to rectangular regions, a more robust method for determining the size of the symmetry region was introduced, a quadratic discriminant analysis with more features was suggested to discriminate between axial and rotational symmetries, and an optional modification was proposed to make the GPT applicable to blood vessel extraction. Although the GPT was originally devised for 2D symmetry detection, is has also been applied to 3D symmetry detection in voxel data [15].…”

Section: Introductionmentioning

confidence: 99%

“…For object recognition, we propose a new threshold on a normalized score for identifying actual symmetry points. This problem was circumvented in [3,4] by simply looking for the highest symmetry score in an image, which always yielded exactly one symmetry point, irrespective of the actual number of symmetric objects. We now give a threshold recommendation for detecting more than one (or, which might also happen: none) symmetry.…”

Section: Introductionmentioning

confidence: 99%

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The Gradient Product Transform: An Image Filter for Symmetry Detection

Dalitz¹,

Wilberg²,

Jeltsch³

2019

Image Processing on Line

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The Gradient Product Transform (GPT) is an image filter that converts a grayscale image into a float image, such that points representing a point reflection symmetry center obtain a high score. Beside the symmetry score, it also yields an estimator for the size of the symmetry region around each point. Apart from describing the GPT, the article also explains its application for two use cases: detection of objects with a point reflection or C 2m rotational symmetry, and the extraction of blood vessel skeletons from medical images. For the detection of symmetric objects, a score normalization procedure is suggested that allows to choose a fixed threshold for score values representing actual symmetries. Source Code The reviewed C++ source code for this algorithm is available from the web page of this article 1. Compilation and usage instructions are included in the README.txt file of the archive.

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Section: Computation Of the Symmetry Scorementioning

confidence: 90%

Section: Symmetry Size Normalization Parameter αmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Gradient Product Transform: An Image Filter for Symmetry Detection

Dalitz¹,

Wilberg²,

Jeltsch³

2019

Image Processing on Line

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Detection of Possible Symmetries in Vascular Networks by Computer-Assisted Image Analysis

Guidolin

Tortorella

Ribatti

2022

Methods in Molecular Biology

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Método Automático Para La Medida De La Velocidad De Flujo De Hemosustitutos en Arteriolas Mediante Procesamiento De Imágenes

Forero

Garibello

Polanía

et al. 2021

Encuentro Internacional De Educación en Ingeniería ACOFI 2021

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En algunos casos médicos, como cirugías y tratamiento de enfermedades cardiovasculares, o traumatismos es necesario el uso de la transfusión de sangre debido al riesgo o la presencia de hemorragia. Sin embargo, puede haber inconvenientes como la disponibilidad limitada de sangre, por falta de donantes, así como incompatibilidad de grupo sanguíneo o factor Rh, el riesgo de transmisión de enfermedades a través de la transfusión o el rechazo del procedimiento por parte del paciente. Por ello, se ha hecho necesario desarrollar sustancias denominadas hemosustituto, o hemoglobinas modificadas, que puedan sustituir a la sangre en su función de transporte de oxígeno. Uno de los fenómenos a evaluar para determinar la seguridad de los hemosustitutos, es el esfuerzo cortante sobre el endotelio. Tanto los esfuerzos elevados como muy bajos pueden generar daños en la función del endotelio produciendo arterias rígidas cuando se tiene un esfuerzo cortante elevado o el colapso de la arteria cuando el esfuerzo cortante disminuye o tiende a cero. Este fenómeno puede observarse mediante secuencias de imágenes de microscopía. En esta evaluación se requiere un grado importante de experticia, ya que los vasos capilares son muy pequeños y determinar la velocidad del flujo sanguíneo es difícil manualmente. Por ello, en este trabajo se propone una nueva técnica para la medición del flujo sanguíneo, desarrollada como un plugin para el programa imageJ. Emplea el canal de color con mayor entropía, sobre el que se realiza una detección de simetría y una transformación de producto de gradiente para la extracción del eje central y la estimación de la velocidad del flujo arteriolar hemostático. Los resultados fueron comparados con los obtenidos manualmente, presentando una mayor precisión y una estimación más rápida al permitir una mejor localización del punto por el que transita el hemosustituto en un tiempo determinado.

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The Gradient Product Transform for Symmetry Detection and Blood Vessel Extraction

Cited by 3 publications

References 12 publications

The Gradient Product Transform: An Image Filter for Symmetry Detection

The Gradient Product Transform: An Image Filter for Symmetry Detection

Detection of Possible Symmetries in Vascular Networks by Computer-Assisted Image Analysis

Método Automático Para La Medida De La Velocidad De Flujo De Hemosustitutos en Arteriolas Mediante Procesamiento De Imágenes

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