<p>To detect cardiovascular diseases, some efforts have been made, such as computer-assisted automatic diagnosis (CAD) by medical image processing like angiographies. To correct problems derived from this step, some algorithms have been proposed. In this work, an algorithm for automatic blood vessel detection on angiographies is presented. It is based on the Grünwald-Letnikov fractional derivative (GLFD) to compute the Hessian matrix and its eigenvalues, as well as a set of 20 angiographies with their respective ground-truth images. The algorithm’s performance was evaluated using the area under the receiver operating characteristic curve (AUROC) and the full interval of fractional orders of derivatives in the range <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11760_2025_4815_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="74" /> </InlineMediaObject> <EquationSource Format="TEX">$1< \omega < 3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo><</mo> <mi>ω</mi> <mo><</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>. The best results are obtained when the order of derivatives is <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11760_2025_4815_Article_IEq2.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">$\omega > 2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ω</mi> <mo>></mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, especially in the interval <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11760_2025_4815_Article_IEq3.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="107" /> </InlineMediaObject> <EquationSource Format="TEX">$2.0 < \omega \le 2.25$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2.0</mn> <mo><</mo> <mi>ω</mi> <mo>≤</mo> <mn>2.25</mn> </mrow> </math></EquationSource> </InlineEquation>. The results show that better outcomes are obtained when using fractional derivation orders <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11760_2025_4815_Article_IEq2.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">$\omega > 2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ω</mi> <mo>></mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. The algorithm returns to the original method when <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11760_2025_4815_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">$\omega = 2.0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ω</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

Enhancing blood vessel using Hessian matrices and fractional derivatives

期刊论文
发表日期：

2025年9月22日

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Leonardo Martínez–Jiménez,
Adán Flores–Balderas,
Juan Manuel López–Hernández,
Ana Dinora Guzman–Chavez,
Miroslava Cano–Lara,
J. Juan Rosales–García

摘要

To detect cardiovascular diseases, some efforts have been made, such as computer-assisted automatic diagnosis (CAD) by medical image processing like angiographies. To correct problems derived from this step, some algorithms have been proposed. In this work, an algorithm for automatic blood vessel detection on angiographies is presented. It is based on the Grünwald-Letnikov fractional derivative (GLFD) to compute the Hessian matrix and its eigenvalues, as well as a set of 20 angiographies with their respective ground-truth images. The algorithm’s performance was evaluated using the area under the receiver operating characteristic curve (AUROC) and the full interval of fractional orders of derivatives in the range $1< \omega < 3$ $1 < ω < 3$ . The best results are obtained when the order of derivatives is $\omega > 2$ $ω > 2$ , especially in the interval $2.0 < \omega \le 2.25$ $2.0 < ω \leq 2.25$ . The results show that better outcomes are obtained when using fractional derivation orders $\omega > 2$ $ω > 2$ . The algorithm returns to the original method when $\omega = 2.0$ $ω = 2.0$ .