Question

Consider the histogram of an 8-bit image given below at (1). A piece-wise linear contrast stretch given at (2) is applied on the said image. The minimum and maximum pixel values of the image obtained after applying the given contrast stretch are ................. (minimum value) and ................. (maximum value), respectively. 

• A. 17, 176
• B. 17, 120
• C. 20, 176
• D. 20, 120

Hint:

For piecewise linear contrast stretches: read the breakpoints \((x_i,y_i)\), compute the slope for the segment that contains your input gray level, and apply \(y=y_i+m(x-x_i)\). Use the image’s actual min/max to find the output range.

Answer 1

The Correct Option is A

From the histogram (1), the input gray levels present in the image span approximately \(\mathbf{20}\) to \(\mathbf{120}\).
The piecewise linear stretch (2) shows breakpoints at \(x=15, 50, 150, 250\) with mapping \[ (15,0)⇒(50,120)⇒(150,200)⇒(250,255). \] Hence, - For \(15\le x\le 50\): slope \(m_1=\dfrac{120-0}{50-15}=\dfrac{120}{35}=3.4286\). Input minimum \(x_{\min}=20\) maps to \[ y_{\min}=0+m_1(20-15)\approx3.4286\times5\approx \boxed{17}. \] - For \(50\le x\le 150\): slope \(m_2=\dfrac{200-120}{150-50}=\dfrac{80}{100}=0.8\). Input maximum \(x_{\max}=120\) (falls in this segment) maps to \[ y_{\max}=120+m_2(120-50)=120+0.8\times70= \boxed{176}. \] Therefore the stretched image will have minimum \(\mathbf{17}\) and maximum \(\mathbf{176}\).
\[ \boxed{17,\ 176} \]