This paper presents a chronological overview of the developments in interpolation theory, from the earliest times to the present date. It brings out the connections between the results obtained in different ages, thereby putting the techniques currently used in signal and image processing into historical perspective. A summary of the insights and recommendations that follow from relatively recent theoretical as well as experimental studies concludes the presentation.

/pdf/prolog-to-a-chronology-of-interpolation-from-ancient-3h41hasu4i.pdf

Prolog to a chronology of interpolation: from ancient astronomy to modern signal and image processing

A method is presented to interpolate between neighboring slices in a grey-scale tomographic data set. Spatial correspondence between adjacent slices is established using a nonrigid registration algorithm based on B-splines which optimizes the normalized mutual information similarity measure. Linear interpolation of the image intensities is then carried out along the directions calculated by the registration algorithm. The registration-based method is compared to both standard linear interpolation and shape-based interpolation in 20 tomographic data sets. Results show that the proposed method statistically significantly outperforms both linear and shape-based interpolation.

Registration-based interpolation

Three-dimensional (3D) imaging was developed to provide both qualitative and quantitative information about an object or object system from images obtained with multiple modalities including digital radiography, computed tomography, magnetic resonance imaging, positron emission tomography, single photon emission computed tomography, and ultrasonography. Three-dimensional imaging operations may be classified under four basic headings: preprocessing, visualization, manipulation, and analysis. Preprocessing operations (volume of interest, filtering, interpolation, registration, segmentation) are aimed at extracting or improving the extraction of object information in given images. Visualization operations facilitate seeing and comprehending objects in their full dimensionality and may be either scene-based or object-based. Manipulation may be either rigid or deformable and allows alteration of object structures and of relationships between objects. Analysis operations, like visualization operations, may be e...

Three-dimensional visualization and analysis methodologies: a current perspective.

Approaches to three-dimensional (3D) data reconstruction are presented. The 3D data comprises 2D images. In some embodiments, the 2D images are directionally interpolated to generate directionally-interpolated 3D data. The directionally-interpolated 3D data are then segmented to generate segmented directionally-interpolated 3D data. The segmented directionally-interpolated 3D data is then meshed. In other embodiments, a 3D data set, which includes 2D flow images, is accessed. The accessed 2D flow images are then directionally interpolated to generate 2D intermediate flow images.

Data reconstruction using directional interpolation techniques

A new technique is presented for interpolating between grey-scale images in a medical data set. Registration between neighboring slices is achieved with a modified control grid interpolation algorithm that selectively accepts displacement field updates in a manner optimized for performance. A cubic interpolator is then applied to pixel intensities correlated by the displacement fields. Special considerations are made for efficiency, interpolation quality, and compression in the implementation of the algorithm. Experimental results show that the new method achieves good quality, while offering dramatic improvement in efficiency relative to the best competing method.

A New Method for Registration-Based Medical Image Interpolation

Many three-dimensional (3-D) medical images have lower resolution in the z direction than in the x or y directions. Before extracting and displaying objects in such images, an interpolated 3-D gray-scale image is usually generated via a technique such as linear interpolation to fill in the missing slices. Unfortunately, when objects are extracted and displayed from the interpolated image, they often exhibit a blocky and generally unsatisfactory appearance, a problem that is particularly acute for thin treelike structures such as the coronary arteries. Two methods for shape-based interpolation that offer an improvement to linear interpolation are presented. In shape-based interpolation, the object of interest is first segmented (extracted) from the initial 3-D image to produce a low-z-resolution binary-valued image, and the segmented image is interpolated to produce a high-resolution binary-valued 3-D image. The first method incorporates geometrical constraints and takes as input a segmented version of the original 3-D image. The second method builds on the first in that it also uses the original gray-scale image as a second input. Tests with 3-D images of the coronary arterial tree demonstrate the efficacy of the methods. >

Shape-based interpolation of tree-like structures in three-dimensional images

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

C. Morice

Author Tools

Chat about Author

Papers

Shape-based interpolation of tree-like structures in three-dimensional images