Home Engineering



Table of Contents:
Encoding Rotation Invariant Features of ImagesIn this section, we focus on the innovation of key techniques for our proposed classification framework for identifying staining patterns of HEp2 cells. Pairwise LTPs with Spatial Rotation InvariantHistogrambased features describe an image as an orderless collection of “patterns” occurrence frequency, ignoring spatial layout information. This seriously limits descriptive ability especially for shape of objects in the image. Inspired by the SPM [11], we propose to construct a spatial pyramid structure on the feature space of the HEp2 cell image. Firstly, histogrambased features are extracted from small overlapped patches within an image. Then, the image is partitioned into increasingly finer spatial subregions over the feature space. Let t = 1, 2,...,L denote level of subpartition, such that there are 2^{t1} x 2^{t1} subregions at level t. At level t, the features within each subregion are combined together as
where If is the ith subregion at level t and H_{i} ^{f} is the corresponding image feature vector in If. h = [h_{1}, h_{2}, ??? , h_{N}]^{T} e R^{NxQ} is the patchlevel features and h_{i} e If denotes the features within If. F(?) is a specific statistics method aggregating occurrences of histogrambased features. In this thesis we adopt the maxpooling strategy: where the “max” function is a rowwise manner, Hf is the kth element of and hj_{k} is the kth element of hj. Within the spatial pyramid structure, we extract a new rotation invariant textural feature. As aforementioned, LBP is a simple yet effective textural feature. However, the LBP tends to be sensitive to noise and smooth weak intensity gradients, because it thresholds at the gray value of the central pixel [6]. Therefore, the LBPs are extended to LTP defined as
where I (x_{i}, y_{i}) is the gray value of P equal spaced pixels on a circle of R around (x, y), (x_{i}, yi) = (x + R cos(2ni/P), y + R sin(2ni/P))) is the neighbors location and th is a userspecified threshold value. Usually, each ternary pattern is slipped into a positive pattern and a negative pattern as
The differencebetween theLBP and LTP encoding procedures is shown in Fig. 6.2. The computational complexity for a LBP is mainly based on the number of neighbor pixels P. The complexity for a LTP is almost double that for a LBP. Furthermore, the computational times of the LBP and LTP increase proportionally to the pixel count of the image. In the following procedure, operations are implemented based on positive and negative pattern respectively. LTP partially solve aforementioned problems of LBP by encoding the small pixel difference into a separate state [12] and adding the threshold value. Meanwhile it combines the positive and negative halves making it more discriminative. Following operation is implemented on the positive and negative pattern respectively Fig. 6.2 Difference between LBP and LTP encoding procedures To achieve rotation invariance, we assign a rotation invariant value to each LTP pair which is defined by
where x = (x, y) is the position vector in image I and Ax_{3} = (d cos 3, d sin 3) is a replacement vector between a LTP pair based on the rotation angle 3. It is noted that one LBP has two patterns, i.e., t_{p} and t_{n}. Therefore, the rotation invariant values are assigned to t_{p} and t_{n} respectively. LTP_{3} (x) is the LTP at position x with the rotation angle 3, which can be rewritten as
where I (x + Ar_{i>3}) is the gray value of P neighboring pixels around center pixel with respect to 3 and Ar_{i>3} = (R cos(2ni/P + 3), R sin(2ni/P + 3)) is a replacement vector from the center pixel to neighboring pixels in a LTP. Then, the same value is obtained by P_{3}(x, Ax_{3})(3 = 0, n/4, ж/2, 3п/4, ж) since their LTP pairs are rotational equivalent. We show that the pairwise LTPs can achieve rotation invariance in Fig. 6.3. For the rotation equivalence class ‘A’, all the Fig. 6.3 An example of the rotation equivalence class. Black and white circles correspond to ‘0’ and ‘1’ respectively. s (A) is the start point of the binary sequence, where s(A) = (x + Rcos(A), y + Rsin(A)) Fig. 6.4 Framework of pairwise LTPs with spatial rotation invariant LTP pairs obtain the same value as each of them is equal to the others in terms of rotation; the class ‘B’ is also the same. Particularly, the pairwise LTPs of ‘B’ can be obtained accordingly from that of ‘A’ by rotating 180°. Therefore, we define that the pairwise LTPs in Fig. 6.3 have the same rotation invariant value, that is P$ = P$ _{+ж}. We calculate the histogram h_{R},_{d} of rotation invariant values for every $ and (R, d) from every patch within an image. Based on the experiments, we choose P = 4 for enough accuracy with an affordable costs in computation and memory. The variation of computational cost and memory affected by the choice of parameters R and d is minor. To improve discrimination, the patchlevel rotation invariant textural feature h = {h_{R},_{d}} is obtained by combining h_{R},_{d} with various (R, d). This framework can be illustrated in Fig. 6.4. Firstly, the image is converted to grayscale image. Then, the grayscale image is partitioned into equal sized patches. The pairwise LTPs with rotation invariant are extracted from each patch. Next, the grayscale image is divided into a sequence of increasingly finer grids over the feature space. Within each grid, the extracted features are integrated using the maxpooling strategy. Finally, all the pooled features from the grids are concatenated together for final classification. Our proposed PLTPSRI feature is rotation invariance. Meanwhile, it obtains strong descriptive and discriminative power. 
<<  CONTENTS  >> 

Related topics 