Using graphs for some discrete tomography problems

نویسندگان

  • Marie-Christine Costa
  • Dominique de Werra
  • Christophe Picouleau
چکیده

Given a rectangular array where entries represent the pixels of a digitalized image, we consider the problem of reconstructing an image from the number of occurrences of each color in every column and in every row. The complexity of this problem is still open when there are just three colors in the image. We study some special cases where the number of occurences of each color is limited to small values. Formulations in terms of edge coloring in graphs and as timetabling problems are used; complexity results are derived from the model.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Extremal Theorems for Degree Sequence Packing and the Two-Color Discrete Tomography Problem

A sequence π = (d1, . . . , dn) is graphic if there is a simple graph G with vertex set {v1, . . . , vn} such that the degree of vi is di. We say that graphic sequences π1 = (d (1) 1 , . . . , d (1) n ) and π2 = (d (2) 1 , . . . , d (2) n ) pack if there exist edge-disjoint n-vertex graphs G1 and G2 such that for j ∈ {1, 2}, dGj (vi) = d (j) i for all i ∈ {1, . . . , n}. Here, we prove several ...

متن کامل

Extremal Theorems for Degree Sequence Packing and the 2-Color Discrete Tomography Problem

A sequence π = (d1, . . . , dn) is graphic if there is a simple graph G with vertex set {v1, . . . , vn} such that the degree of vi is di. We say that graphic sequences π1 = (d (1) 1 , . . . , d (1) n ) and π2 = (d (2) 1 , . . . , d (2) n ) pack if there exist edge-disjoint n-vertex graphs G1 and G2 such that for j ∈ {1, 2}, dGj (vi) = d (j) i for all i ∈ {1, . . . , n}. Here, we prove several ...

متن کامل

DISCRETE AND CONTINUOUS SIZING OPTIMIZATION OF LARGE-SCALE TRUSS STRUCTURES USING DE-MEDT ALGORITHM

Design optimization of structures with discrete and continuous search spaces is a complex optimization problem with lots of local optima. Metaheuristic optimization algorithms, due to not requiring gradient information of the objective function, are efficient tools for solving these problems at a reasonable computational time. In this paper, the Doppler Effect-Mean Euclidian Distance Threshold ...

متن کامل

A regularization method for solving a nonlinear backward inverse heat conduction problem using discrete mollification method

The present essay scrutinizes the application of discrete mollification as a filtering procedure to solve a nonlinear backward inverse heat conduction problem in one dimensional space. These problems are seriously ill-posed. So, we combine discrete mollification and space marching method to address the ill-posedness of the proposed problem. Moreover, a proof of stability and<b...

متن کامل

DISCRETE TOMOGRAPHY AND FUZZY INTEGER PROGRAMMING

We study the problem of reconstructing binary images from four projections data in a fuzzy environment. Given the uncertainly projections,w e want to find a binary image that respects as best as possible these projections. We provide an iterative algorithm based on fuzzy integer programming and linear membership functions.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Discrete Applied Mathematics

دوره 154  شماره 

صفحات  -

تاریخ انتشار 2006