1. A method of generating a high dynamic range (HDR) image, applicable to a digital image pickup device for generating an HDR image according to a single digital image, the method comprising: obtaining an original image; performing a gray-scale processing to convert the original image into an original gray-scale pattern, wherein each pixel in the original gray-scale pattern is assigned with a gray-scale value; performing a conversion procedure according to a gradient and a compensation value of the gray-scale value of each pixel in the original gray-scale pattern, and generating a high dynamic gray-scale pattern by using the gradients and the compensation values, comprising: searching the compensation values for a maximum compensation value and a minimum compensation value; and compensating the original gray-scale pattern with the gradients, the compensation values, the maximum compensation value, and the minimum compensation value, so as to obtain the high dynamic gray-scale pattern, and the gradients, the compensation values, the maximum compensation value, and the minimum compensation value are respectively calculated by the following formulae: H ⁡ ( E i ) = dE i ⁢ x 2 + dE i ⁢ y 2 , ⁢ K ⁡ ( i ) = H ⁡ ( E i ) × ( H ⁡ ( E i ) ∑ i = 1 N ⁢ ⁢ H ⁡ ( E i ) ) α , ⁢ and Y i ′ = β × ( K ⁡ ( i ) - 0.6 ⁢ K min 0.9 ⁢ K max - 0.6 ⁢ K min ) + γ × Y i , where N is a total number of the pixels in the original gray-scale pattern, i is the i th pixel in the original gray-scale pattern, H(E i ) is a gradient of the i th pixel in the original gray-scale pattern, dE i x 2 is a variable of the i th pixel in the original gray-scale pattern in a horizontal direction, dE i y 2 is a variable of the i th pixel in the original gray-scale pattern in a vertical direction, K(i) is a compensation value of the i th pixel in the original gray-scale pattern, Y′ i is a gray-scale value of the i th pixel in the high dynamic gray-scale pattern, Y i is a gray-scale value of the i th pixel in the original gray-scale pattern, K max is the maximum compensation value, K min is the minimum compensation value, i and N are positive integers, and α, β, and γ are positive numbers; and compensating the original image with the high dynamic gray-scale pattern, so as to generate an HDR image.