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Pixel discontinuity in orthoimages occurs frequently due to altitude variations in the pitch and heading of an airplane, and low performance of real-time analyzing software. This study proposes a scheme to resolve pixel discontinuity. The proposed scheme includes the following steps: 1) capture images by a self-made hyperspectral imager; 2) determine the pixel locations of orthoimages using a top-down approach; 3) repair discontinuities by the Nearest Neighbor (NN) or Bilinear Interpolation (BL) approaches; and, 4) perform a dynamic range adjustment on the orthoimages, according to the maximum pixel value of the raw images and orthoimages. After applying the proposed scheme, this study found that pixel discontinuity was eliminated by both approaches, and that the software dependability and image quality were improved substantially. In addition, the computational efficiency of the NN approach was roughly two minutes faster than that of the BL due to its simpler computation. However, BL produces smoother image edges for landscapes.

Orthorectification of imagery is essential for data to be used with other spatially referenced data sets. Pushbroom imaging systems collect data and analyze images by embedded real-time software as they scan tracks perpendicular to the flight line. The ground location of these pixels can jump dramatically from pixel to pixel because of the pitch, yaw, and roll of the aircraft as it conducts instrument scanning. Thus, pixel discontinuity (blank pixels) occurs quite often in orthoimages. In order to fill in these blank points several pixel repair methods have been proposed. However, before accurate measurements based on aerial photographs are performed, the distortion in photographs must be removed. All landscape metrics are sensitive to geometric distortion.

The pixel-by-pixel approach is one of the proposed approaches for rectifying an orthoimage from raw images [

The first method called the bottom-up method [1,2]. Starting from the object space, each ground object is projected onto the image space. Conversely, the top-down method starts from the image space and projects each image pixel onto the object surface [

This study proposes an algorithm for repairing blank pixels during the orthorectification process to eliminate pixel discontinuity. The algorithm employs bilinear (BL) interpolation and distance-weighted allocation to obtain the gray values of all orthoimage pixels [4-6]. This study evaluates the results of the proposed algorithm by using a near-infrared band of the preliminary hyperspectral images, which were captured by a hyperspectral imager of plants and the environment [7,8]. Simple comparisons of the results using NN and BL were also conducted to provide a reference for future improvements.

Pixel discontinuity primarily results from variations in the pitch of an airplane and the low performance of embedded real-time software within the push-broom imaging system (

After filtering out high-frequency aircraft vibrations using the embedded real-time analyzing software and stabilizer, the exterior orientation can be obtained from the IMU/INS and GPS system for geometric image correction [

The top-down approach, also known as the ray-tracing approach, employs a collinear equation (Formulas 1 and 2) to cross-reference pixels from the image space with the object space (

where f is focal length of the camera and are rotation matrix coefficients calculated by the rotation orientations of each axis from image to object space. and represent the perspective center of the object and image coordinates. (X, Y, Z) is the image point (x, y) in the object coordinate [

For the top-down approach, this study applied the pixel interpolation method to improve the orthoimage quality through pixel allocation by using the Nearest Neighbor (NN) approach. This study also proposed another method for eliminating pixel discontinuity to improve the image quality. This approach is similar to the Bilinear Interpolation (BL) approach for image pixel allocation. The two methods are described below [

To increase the computational efficiency of imagery orthorectification using the top-down approach, referenced gray values are typically allocated to the orthoimage directly using the NN method. A schematic diagram of pixel allocation using the NN method is shown in

To resolve blank pixels, this study also applies the BL method for imagery orthorectification to allocate gray values to the pixels, as shown in _{a }(I, J) is a pixel point in the orthoimage, and I and J are positions in the orthoimage grid system. These results indicate that the four adjacent pixels are highly correlated. Thus, this study applies the BL and area-weighting method to allocate gray values to the adjacent pixels P (i, j), P (i + 1, j), P (i, j + 1), and P (i + 1, j + 1). For a given pixel of an orthoimage, consider the following example using P (i, j). Because P (i, j) is affected by other adjacent points, such as P_{a}, P_{b}, P_{c}, and P_{d}, repeated filling of the pixel value is required. As shown in _{a}, P_{b}, P_{c}, P_{d}, and other points to P (i, j). Therefore, the gray value of point P (i, j) must be adjusted according to each gray valuefilled pixel and its corresponding weight.

The algorithm proposed in this study is detailed below. In the top-down approach, the pixels of the raw image are cross-referenced to the points P_{a} in the orthoimage grid system sequentially. For the BL method, the corresponding area of a pixel is used as the weighting factors for the gray value allocation around the neighboring image points of P (i, j), P (i + 1, j), P (i + 1, j + 1), and P (i, j + 1). The weighting factors of Pa are

, , and,

where dL = (I – i) and dS = (J – j) are the distance components between P_{a}(I, J) and P(i, j) in the line and sample directions.

After completing image orthorectification using the previous two steps, a weighted average calculation of the gray values based on the multiple gray values and weighting factors allocated to each image point must be performed. For example, point P (i, j) can be expressed using the following equation:

where GL represents the gray value of the pixel P (i, j),

and W is the weighting factor of the pixel.

To complete the preceding steps, this study applied a dynamic range adjustment to the gray values of the pixels in the orthoimage to ensure their consistency with the range of gray values in the raw image. By applying the presented scheme, pixel discontinuity was eliminated,

and the quality of the orthoimages was substantially improved.

We used hyperspectral images retrieved by the HOPE imager [