Minimum Error Thresholding Segmentation Algorithm Based on 3D Grayscale Histogram

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="932695.fig.001a" src="https://static.hindawi.com/articles/mpe/volume-2014/932695/figures/932695.fig.001a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Domain of 3D histogram</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="932695.fig.001b" src="https://static.hindawi.com/articles/mpe/volume-2014/932695/figures/932695.fig.001b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Threshold (<svg height="14.5625" id="M32" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 34.0625 14.5625" width="34.0625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>)</td></tr></table></td></tr><tr class="fig-image" id="c"><td><img alt="932695.fig.001c" src="https://static.hindawi.com/articles/mpe/volume-2014/932695/figures/932695.fig.001c.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(c) </b>Eight areas zoning by (<svg height="14.5625" id="M33" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 34.0625 14.5625" width="34.0625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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q-97 56 -97 123q0 50 51 96q19 17 58 32.5t62 15.5q37 0 61 -18t24 -39z" id="x1D460"></path></g><g transform="matrix(.017,-0,0,-.017,6.437,10.125)"><path d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" id="x2C"></path></g><g transform="matrix(.017,-0,0,-.017,13.135,10.125)"><path d="M324 430l-26 -36l-112 -4l-55 -265q-13 -66 7 -66q13 0 44.5 20t50.5 40l17 -24q-38 -40 -85.5 -73.5t-87.5 -33.5q-50 0 -21 138l55 262h-80l-2 8l25 34h66l25 99l78 63l10 -9l-37 -153h128z" id="x1D461"></path></g><g transform="matrix(.017,-0,0,-.017,18.931,10.125)"><path d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" id="x2C"></path></g><g transform="matrix(.017,-0,0,-.017,25.646,10.125)"><path d="M474 429q-19 -69 -47 -222l-65 -347q-8 -49 0 -60t49 -16l26 -3l-4 -26l-246 -12l4 25l17 3q37 6 50 20.5t23 60.5l67 321h-2q-65 -79 -150 -138q-69 -47 -104 -47q-28 0 -48.5 32t-20.5 81q0 78 35 148t90 117q67 57 161 77q23 5 58 5q43 0 90 -15zM387 387
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</svg>)</td></tr></table></td></tr></table>

<table>Three-dimensional histogram.</table>

Mathematical Problems in Engineering

fig1

Figure 1

Figure 1: Minimum Error Thresholding Segmentation Algorithm Based on 3D Grayscale Histogram 