A method and system for detecting abnormal state of escalator

Abstract

The present invention discloses a detection method and system for abnormal state of an escalator, and relates to the field of escalator state detection. The method comprises: collecting video information to be judged, cutting the video information into a data set with the running state of the escalator; removing obstacles in the data set by an improved U2‑Net model; calculating the running state of the escalator at the i-th moment and the i+1-th moment respectively through optical flow analysis, and obtaining the i-th running state and the i+1-th running state; comparing the running state of the escalator at the i-th running state and the i+1-th running state, and sending an alarm prompt when the comparison result meets the preset abnormal condition, and the abnormal detection method of the present scheme can greatly improve the recognition accuracy compared with the existing scheme.

Description

Technical Field

[0001] The invention relates to the field of escalator state detection, and in particular to a method and system for detecting abnormal state of an escalator. Background Art

[0002] In recent years, there have been many cases of casualties caused by sudden reversal or stagnation of escalators in public places (such as shopping malls and subways). Once this happens, it often has a bad impact and endangers the lives of citizens. The equipment itself is in operation all year round and it is difficult to avoid rare failures. Therefore, it is very important to detect the escalator operation failure as soon as possible and notify the staff to come to the site for maintenance.

[0003] In the existing technology, simple optical flow or deep learning methods are often used to determine the running direction of the escalator or the running direction of pedestrians on it, and then an alarm is issued if it is inconsistent with the direction sent by the device signal. These methods often result in a large number of false detections and missed detections due to the large number of objects on the escalator and the random shaking of people. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a method and system for detecting abnormal state of an escalator in view of the deficiencies of the prior art.

[0005] The technical solution of the present invention to solve the above technical problems is as follows:

[0006] A method for detecting an abnormal state of an escalator, comprising:

[0007] S1, collecting video information to be judged, and cutting the video information into a data set with an escalator operation status; the data set includes: a plurality of escalator operation states;

[0008] S2, removing obstacles from the data set through the improved U2-Net model;

[0009] S3, calculating the running status of the escalator at the i-th moment and the i+1-th moment respectively through optical flow analysis, and obtaining the i-th running status and the i+1-th running status;

[0010] S4, comparing the escalator operation state of the i-th operation state and the i+1-th operation state;

[0011] S5: When the comparison result meets the preset abnormal condition, an alarm prompt is sent.

[0012] The beneficial effect of the present invention is that the present solution removes obstacles from the data set through the improved U2-Net model, thereby preventing the shaking of people or objects on the escalator from affecting the subsequent judgment of the direction of the optical flow. The U2-Net model is used to filter out parts such as people or objects, leaving only the escalator conveyor belt part, and then the running direction of the escalator is judged based on the sparse optical flow, which greatly improves the accuracy.

[0013] Further, the escalator operation status includes: unknown, stationary, slow inward, fast inward, slow outward and fast outward;

[0014] The i-th running state represents any one of unknown, stationary, slow inward, fast inward, slow outward or fast outward;

[0015] The (i+1)th running state represents any one of unknown, stationary, slow inward, fast inward, slow outward or fast outward.

[0016] The beneficial effect of adopting the above further scheme is: this scheme divides the escalator into 6 states and only changes 4 states with huge changes, such as changing from fast inward to fast outward or stationary, with an early warning prompt when switching, and judges it as an unknown state when uncertain. This can greatly reduce false alarms compared with the existing technology.

[0017] Furthermore, the preset abnormal conditions specifically include:

[0018] The comparison results are from fast inward to fast outward, from fast outward to fast inward, from fast inward to stillness, and from fast outward to stillness.

[0019] The beneficial effect of adopting the above further scheme is that this scheme can greatly reduce misjudgment by only giving early warning prompts when switching between the four states with huge changes.

[0020] Further, the calculation of the escalator operation state at the i-th moment includes:

[0021] Randomly extract multiple first coordinates of multiple pixel points of the image at the i-1th moment;

[0022] Calculate multiple second coordinates of multiple pixel points in the image at the i-th moment through optical flow analysis;

[0023] Calculate an offset according to the first coordinate and the second coordinate;

[0024] The running state of the escalator at the i-th moment is calculated according to a plurality of offsets.

[0025] Furthermore, before S2, the method further includes:

[0026] Reduce the number of channels in the U2-Net model to half;

[0027] Replace the maximum pooling in the U2-Net model with a convolution kernel of 3 and a stride of 2;

[0028] The loss function was changed to DiceLoss to obtain the improved U2-Net model.

[0029] The beneficial effects of adopting the above further scheme are: this scheme improves the inference efficiency by reducing the number of channels of the U2-Net model; and reduces feature loss by replacing the maximum pooling with the convolutional layer.

[0030] Another technical solution of the present invention to solve the above technical problems is as follows:

[0031] A detection system for abnormal state of an escalator, comprising: a collection and cutting module, a rejection module, a state analysis and calculation module, a state comparison module and a judgment and prompt module;

[0032] The acquisition and cutting module is used to acquire video information to be judged, and cut the video information into a data set with an escalator operation status; the data set includes: a plurality of escalator operation statuses;

[0033] The elimination module is used to eliminate obstacle objects in the data set through the improved U2-Net model;

[0034] The state analysis and calculation module is used to calculate the escalator operation state at the i-th moment and the i+1-th moment respectively through optical flow analysis to obtain the i-th operation state and the i+1-th operation state;

[0035] The state comparison module is used to compare the escalator operation state of the i-th operation state and the i+1-th operation state;

[0036] The judgment prompt module is used to send an alarm prompt when the comparison result meets the preset abnormal condition.

[0037] The beneficial effect of the present invention is that the present solution removes obstacles from the data set through the improved U2-Net model, thereby preventing the shaking of people or objects on the escalator from affecting the subsequent judgment of the direction of the optical flow. The U2-Net model is used to filter out parts such as people or objects, leaving only the escalator conveyor belt part, and then the running direction of the escalator is judged based on the sparse optical flow, which greatly improves the accuracy.

[0038] Further, the escalator operation status includes: unknown, stationary, slow inward, fast inward, slow outward and fast outward;

[0039] The i-th running state represents any one of unknown, stationary, slow inward, fast inward, slow outward or fast outward;

[0040] The (i+1)th running state represents any one of unknown, stationary, slow inward, fast inward, slow outward or fast outward.

[0041] The beneficial effect of adopting the above further scheme is: this scheme divides the escalator into 6 states and only changes 4 states with huge changes, such as from fast inward to fast outward or stillness, with an early warning prompt when switching, and judges it as an unknown state when uncertain. This can greatly reduce false alarms compared with the existing technology.

[0042] Furthermore, the preset abnormal conditions specifically include:

[0043] The comparison results are from fast inward to fast outward, from fast outward to fast inward, from fast inward to stillness, and from fast outward to stillness.

[0044] The beneficial effect of adopting the above further scheme is that this scheme can greatly reduce misjudgment by only giving early warning prompts when switching between the four states with huge changes.

[0045] Furthermore, the state analysis and calculation module is specifically used to randomly extract a plurality of first coordinates of a plurality of pixel points of the image at the i-1th moment;

[0046] Calculate multiple second coordinates of multiple pixel points in the image at the i-th moment through optical flow analysis;

[0047] Calculate an offset according to the first coordinate and the second coordinate;

[0048] The running state of the escalator at the i-th moment is calculated according to a plurality of offsets.

[0049] Furthermore, it also includes: a model improvement module for reducing the number of channels in the U2-Net model to half;

[0050] Replace the maximum pooling in the U2-Net model with a convolution kernel of 3 and a stride of 2;

[0051] The loss function was changed to DiceLoss to obtain the improved U2-Net model.

[0052] The beneficial effects of adopting the above further scheme are: this scheme improves the inference efficiency by reducing the number of channels of the U2-Net model; and reduces feature loss by replacing the maximum pooling with the convolutional layer.

[0053] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1A schematic flow chart of a method for detecting abnormal state of an escalator provided by an embodiment of the present invention;

[0055] Figure 2 A structural block diagram of a detection system for abnormal state of an escalator provided by an embodiment of the present invention;

[0056] Figure 3 A network structure diagram of the U2-Net model provided for other embodiments of the present invention. DETAILED DESCRIPTION

[0057] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention but not to limit the scope of the present invention.

[0058] like Figure 1 As shown, a method for detecting an abnormal state of an escalator provided by an embodiment of the present invention includes:

[0059] S1, collecting video information to be judged, and cutting the video information into a data set with escalator operation status; the data set includes: multiple escalator operation status; wherein the multiple escalator operation status includes: unknown, stationary, slow inward, fast inward, slow outward and fast outward;

[0060] S2, removing obstacles from the data set through the improved U2-Net model;

[0061] In one embodiment, the U2-Net model learns which part of the image needs to be set to 0 and which part needs to be set to 1 based on a large amount of labeled data, and then performs a mask operation on the mask and the original image to obtain an image with the background or unnecessary part removed. Our usage process is to find a large number of escalator data images, manually annotate them to make mask images, with the non-escalator conveyor belt part being 0 and the escalator conveyor belt being 1, as labels for deep learning, and then convert the original image into data that the model can process and send it to the model. Based on the above labeled data, the gradient descent strategy in deep learning is used to keep learning so that the output of the model converges and approaches the labeled data.

[0062] After obtaining the learned model, take a frame of image from the camera code stream, convert it into data that can be processed by the model, and then input it into the model to obtain the required mask. Then perform the mask operation with that frame of image, and we will get the image we want without removing any other objects on the escalator.

[0063] S3, calculating the running status of the escalator at the i-th moment and the i+1-th moment respectively through optical flow analysis, and obtaining the i-th running status and the i+1-th running status;

[0064] In one embodiment, determining the running direction of the escalator by optical flow analysis may include: performing image registration for sparse points on an image, that is, given a number of points on an old image (i.e., a previous frame), which may usually be corner points, and finding their corresponding points in a new image (current frame). The specific calculation process may include:

[0065] Take 56 consecutive frames of images (frame rate 25) from the video stream for about 2 seconds, and take 1 frame every 4 frames to obtain 14 frames of images. Roi filters the non-escalator part, then scales the size to 120x240 and sends it to U2-Net to filter out the non-conveyor belt part on the escalator. Then perform sparse optical flow comparison on the 14 frames every 2 consecutive frames. The specific operation is to set two frames A and B, add the coordinates of the points with pixels in the previous frame A to the set {x, y}, randomly select 20 points {old_x, old_y} from {x, y}, calculate the coordinate points {new_x, new_y} corresponding to the sparse optical flow calculation of these 20 points on the next frame B, and then compare them with {old_x, old_y}, use the new coordinates to subtract the old coordinates to get the offset {offset_x, offset_y}, and define six escalator operation states: ① unknown ② stationary ③ slow inward ④ fast inward ⑤ slow outward ⑥ fast outward We need to judge the current running state of the escalator based on the coordinate offset of 20 points. We first define 6 state counters count1, count2, count3, count4, count5, count6 ​​to distinguish the six states respectively. Among them, the offset used to judge the 6 states can be adjusted according to the feedback of the actual detection results. Then judge ① when abs(offset_x)>=20 or abs(offset_y)>=20, count1+=1, because the offset is too large, it is inaccurate and classified as an unknown state; ② when abs(offset_x)<=0.1 or abs(offset_y)<=0.1, count2+=1, indicating static; ③ when offset_y <-0.1 and offset_y>=-4, indicating that the coordinate moves up and the amplitude is not large, which means it is moving slowly inward, count3+=1; ④ When offset_y>-4 and offset_y<-20, it means that the coordinate moves up and the amplitude is large, which means it is moving quickly inward, count4+=1; ⑤ When offset_y>0.1 and offset_y<=4, it means that the coordinate moves down and the amplitude is not large, which means it is moving slowly outward, count5+=1; ⑥ When offset_y>4 and offset_y<20, it means that the coordinate moves down and the amplitude is large, which means it is moving quickly outward, count6+=1; After calculating 20 times, take the state corresponding to the largest count. For example, if count5 is the largest, then the escalator is calculated to be in state ⑤, which means it is moving slowly outward. The above 14 frames are compared once every two consecutive frames, so 13 comparisons can be made, and 13 escalator states are obtained. We assume that the number of occurrences of a certain state is greater than 6, then the final current escalator state is this state, otherwise the escalator state is unknown, which is state ①

[0066] S4, comparing the escalator operation state of the i-th operation state and the i+1-th operation state;

[0067] S5: When the comparison result meets the preset abnormal condition, an alarm prompt is sent.

[0068] It should be noted that the preset abnormal conditions include: the comparison result is from fast inward to fast outward, from fast outward to fast inward, from fast inward to stillness, and from fast outward to stillness.

[0069] This solution uses the improved U2-Net model to remove obstacles from the dataset, preventing the shaking of people or objects on the escalator from affecting the subsequent judgment of the optical flow direction. The U2-Net model filters out people or objects, leaving only the escalator conveyor belt, and then judges the escalator running direction based on sparse optical flow, which greatly improves the accuracy.

[0070] Preferably, in any of the above embodiments, the escalator operation status includes: unknown, stationary, slow inward, fast inward, slow outward and fast outward;

[0071] The i-th running state represents any one of unknown, stationary, slow inward, fast inward, slow outward or fast outward;

[0072] The (i+1)th running state represents any one of unknown, stationary, slow inward, fast inward, slow outward or fast outward.

[0073] This solution divides the escalator into 6 states and only uses 4 states with huge changes, such as from fast inward to fast outward or stillness, to issue an early warning when switching, and judges it as an unknown state when uncertain. This can greatly reduce false alarms compared to existing technologies.

[0074] Preferably, in any of the above embodiments, the preset abnormal condition specifically includes:

[0075] The comparison results are from fast inward to fast outward, from fast outward to fast inward, from fast inward to stillness, and from fast outward to stillness.

[0076] This solution can greatly reduce misjudgments by only providing early warnings when the four states change dramatically.

[0077] Preferably, in any of the above embodiments, the calculating the running state of the escalator at the i-th moment comprises:

[0078] Randomly extract multiple first coordinates of multiple pixel points of the image at the i-1th moment;

[0079] Calculate multiple second coordinates of multiple pixel points in the image at the i-th moment through optical flow analysis;

[0080] Calculate an offset according to the first coordinate and the second coordinate;

[0081] The running state of the escalator at the i-th moment is calculated according to a plurality of offsets.

[0082] Preferably, in any of the above embodiments, before S2, the step further includes:

[0083] Reduce the number of channels in the U2-Net model to half;

[0084] Replace the maximum pooling in the U2-Net model with a convolution kernel of 3 and a stride of 2;

[0085] The loss function was changed to DiceLoss to obtain the improved U2-Net model.

[0086] In one embodiment, based on the existing U2-Net model, the number of channels is reduced to half of the original number, and the maximum pooling in the original model is replaced by a convolution with a kernel of 3 and a stride of 2, and the loss function is changed to DiceLoss to obtain an improved U2-Net model. The network structure of the U2-Net model can be as follows: Figure 3 shown.

[0087] This solution improves the inference efficiency by reducing the number of channels of the U2-Net model and reduces feature loss by replacing the maximum pooling with the convolutional layer.

[0088] In one embodiment, if Figure 2 As shown, a detection system for abnormal state of an escalator includes: a collection and cutting module 1101, a rejection module 1102, a state analysis and calculation module 1103, a state comparison module 1104 and a judgment and prompt module 1105;

[0089] The acquisition and cutting module 1101 is used to acquire video information to be judged, and cut the video information into a data set with an escalator operation status; the data set includes: a plurality of escalator operation statuses;

[0090] The elimination module 1102 is used to eliminate obstacle objects in the data set through the improved U2-Net model;

[0091] The state analysis and calculation module 1103 is used to calculate the escalator operation state at the i-th moment and the i+1-th moment respectively through optical flow analysis to obtain the i-th operation state and the i+1-th operation state;

[0092] The state comparison module 1104 is used to compare the escalator operation state of the i-th operation state and the i+1-th operation state;

[0093] The judgment prompt module 1105 is used to send an alarm prompt when the comparison result meets the preset abnormal condition.

[0094] This solution uses the improved U2-Net model to remove obstacles from the dataset, preventing the shaking of people or objects on the escalator from affecting the subsequent judgment of the optical flow direction. The U2-Net model filters out people or objects, leaving only the escalator conveyor belt, and then judges the escalator running direction based on sparse optical flow, which greatly improves the accuracy.

[0095] Preferably, in any of the above embodiments, the escalator operation status includes: unknown, stationary, slow inward, fast inward, slow outward and fast outward;

[0096] The i-th running state represents any one of unknown, stationary, slow inward, fast inward, slow outward or fast outward;

[0097] The (i+1)th running state represents any one of unknown, stationary, slow inward, fast inward, slow outward or fast outward.

[0098] This solution divides the escalator into 6 states and only uses 4 states with huge changes, such as from fast inward to fast outward or stillness, to issue an early warning when switching, and judges it as an unknown state when uncertain. This can greatly reduce false alarms compared to existing technologies.

[0099] Preferably, in any of the above embodiments, the preset abnormal condition specifically includes:

[0100] The comparison results are from fast inward to fast outward, from fast outward to fast inward, from fast inward to stillness, and from fast outward to stillness.

[0101] This solution can greatly reduce misjudgments by only providing early warnings when the four states change dramatically.

[0102] Preferably, in any of the above embodiments, the state analysis and calculation module is specifically used to randomly extract a plurality of first coordinates of a plurality of pixel points of the image at the i-1th moment;

[0103] Calculate multiple second coordinates of multiple pixel points in the image at the i-th moment through optical flow analysis;

[0104] Calculate an offset according to the first coordinate and the second coordinate;

[0105] The running state of the escalator at the i-th moment is calculated according to a plurality of offsets.

[0106] Preferably, in any of the above embodiments, it further comprises: a model improvement module, used to reduce the number of channels in the U2-Net model to half;

[0107] Replace the maximum pooling in the U2-Net model with a convolution kernel of 3 and a stride of 2;

[0108] The loss function was changed to DiceLoss to obtain the improved U2-Net model.

[0109] This solution improves the inference efficiency by reducing the number of channels of the U2-Net model and reduces feature loss by replacing the maximum pooling with the convolutional layer.

[0110] It can be understood that in some embodiments, some or all of the optional implementation modes in the above embodiments may be included.

[0111] It should be noted that the above embodiments are product embodiments corresponding to the previous method embodiments. For the description of the optional implementation methods in the product embodiments, reference can be made to the corresponding description in the above method embodiments, which will not be repeated here.

[0112] The reader should understand that in the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine different embodiments or examples described in this specification and the features of different embodiments or examples without contradiction.

[0113] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are only schematic, for example, the division of units is only a logical function division, and there may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed.

[0114] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the embodiments of the present invention.

[0115] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0116] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the various embodiments of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program codes.

[0117] The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present invention, and these modifications or replacements should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for detecting abnormal state of an escalator, characterized in that: include: S1, collecting video information to be judged, and cutting the video information into a data set with an escalator operation status; the data set includes: a plurality of escalator operation states; S2, reduces the number of channels in the U2-Net model to half; Replace the maximum pooling in the U2-Net model with a convolution kernel of 3 and a stride of 2; The loss function was changed to DiceLoss to obtain the improved U2-Net model; The obstacle objects in the data set are removed by using the improved U2-Net model; S3, calculating the running status of the escalator at the i-th moment and the i+1-th moment respectively through optical flow analysis, and obtaining the i-th running status and the i+1-th running status; S4, comparing the escalator operation state of the i-th operation state and the i+1-th operation state; S5: When the comparison result meets the preset abnormal condition, an alarm prompt is sent.

2. The method for detecting abnormal state of an escalator according to claim 1, characterized in that: The escalator operation status includes: unknown, stationary, slow inward, fast inward, slow outward and fast outward; The i-th running state represents any one of unknown, stationary, slow inward, fast inward, slow outward or fast outward; The (i+1)th running state represents any one of unknown, stationary, slow inward, fast inward, slow outward or fast outward.

3. The method for detecting abnormal state of an escalator according to claim 2, characterized in that: The preset abnormal conditions specifically include: The comparison results are from fast inward to fast outward, from fast outward to fast inward, from fast inward to stillness, and from fast outward to stillness.

4. The method for detecting abnormal state of an escalator according to claim 1, characterized in that: The calculation of the escalator operation state at the i-th moment includes: Randomly extract multiple first coordinates of multiple pixel points of the image at the i-1th moment; Calculate multiple second coordinates of multiple pixel points in the image at the i-th moment through optical flow analysis; Calculate an offset according to the first coordinate and the second coordinate; The running state of the escalator at the i-th moment is calculated according to a plurality of offsets.

5. A detection system for abnormal state of escalator, characterized in that: include: Collection and cutting module, rejection module, state analysis and calculation module, state comparison module and judgment and prompt module; The acquisition and cutting module is used to acquire the video information to be judged, and cut the video information into a data set with the running status of the escalator; The data set includes: a plurality of escalator operation states; The system also includes: a model improvement module for reducing the number of channels in the U2-Net model to half; Replace the maximum pooling in the U2-Net model with a convolution kernel of 3 and a stride of 2; The loss function was changed to DiceLoss to obtain the improved U2-Net model; The elimination module is used to eliminate obstacle objects in the data set through the improved U2-Net model; The state analysis and calculation module is used to calculate the escalator operation state at the i-th moment and the i+1-th moment respectively through optical flow analysis to obtain the i-th operation state and the i+1-th operation state; The state comparison module is used to compare the escalator operation state of the i-th operation state and the i+1-th operation state; The judgment prompt module is used to send an alarm prompt when the comparison result meets the preset abnormal condition.

6. The escalator abnormal state detection system according to claim 5, characterized in that: The escalator operation status includes: unknown, stationary, slow inward, fast inward, slow outward and fast outward; The i-th running state represents any one of unknown, stationary, slow inward, fast inward, slow outward or fast outward; The (i+1)th running state represents any one of unknown, stationary, slow inward, fast inward, slow outward or fast outward.

7. The escalator abnormal state detection system according to claim 6, characterized in that: The preset abnormal conditions specifically include: The comparison results are from fast inward to fast outward, from fast outward to fast inward, from fast inward to stillness, and from fast outward to stillness.

8. The escalator abnormal state detection system according to claim 7, characterized in that: The state analysis and calculation module is specifically used to randomly extract a plurality of first coordinates of a plurality of pixel points of the image at the i-1th moment; Calculate multiple second coordinates of multiple pixel points in the image at the i-th moment through optical flow analysis; Calculate an offset according to the first coordinate and the second coordinate; The running state of the escalator at the i-th moment is calculated according to a plurality of offsets.

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