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In this paper, we introduce some monotonicity rules for the ratio of integrals. Furthermore, we demonstrate that the function $-T_{\nu ,\alpha ,\beta }(s)$ is completely monotonic in $s$ and absolutely monotonic in $\nu $ if and only if $\beta \ge 1$, where $T_{\nu ,\alpha ,\beta }(s)=K_{\nu }^2(s)-\beta K_{\nu -\alpha }(s)K_{\nu +\alpha }(s)$ defined on $s>0$ and $K_{\nu }(s)$ is the modified Bessel function of the second kind of order $\nu $. Finally, we determine the necessary and sufficient conditions for the functions $s \mapsto T_{\mu ,\alpha ,1}(s)/T_{\nu ,\alpha ,1}(s)$, $s \mapsto (T_{\mu ,\alpha ,1}(s) + T_{\nu ,\alpha ,1}(s))/(2T_{(\mu +\nu )/2,\alpha ,1}(s))$, and $s \mapsto \frac{\mathrm{d}^{n_1}}{\mathrm{d} \nu ^{n_1}} T_{\nu ,\alpha ,1}(s)/\frac{\mathrm{d}^{n_2}}{\mathrm{d} \nu ^{n_2}} T_{\nu ,\alpha ,1}(s)$ to be monotonic in $s\in (0,\infty )$ by employing the monotonicity rules.

Target image processing requirements of the TV guided missile is high, and the speed is fast, and the quality of target image segmentation is high.In this paper, an improved genetic algorithm based on genetic algorithm is introduced, which is used in the image segmentation of the TV guided missile, and the processing effect is good and the calculation speed is fast.Simulation results show that the algorithm is effective.